Google Patentsopen access

System and method for computing private keys for self certified identity based … — Huawei International Pte. Ltd. (US11563565B2)

ABSTRACT

Abstract

A system and method generate private keys for devices participating in a self-certified identity based encryption scheme. A private key is used by the devices to establish a common session key for encoding digital communications between devices.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No. PCT/SG2018/050050, filed on Feb. 7, 2018, which claims priority to Singaporean Patent Application No. SG10201701044S, filed on Feb. 9, 2017. The disclosures of the aforementioned applications are hereby incorporated by reference in their entireties.

FIELD OF TECHNOLOGY

This application relates to a system and method for generating private keys for devices participating in self-certified identity based signature schemes whereby the private keys are used by the devices to establish a common session key for encoding digital communications between devices. In particular, the private keys generated in accordance with the system and methods of the application are only made known to the devices themselves and not by any other third parties.

BACKGROUND

Due to a convergence of multiple technologies, an ever increasing number of devices are now able to seamlessly communicate wirelessly with the Internet or wirelessly exchange communications between themselves. This convergence has resulted in the vision of the Internet of Things (IoT) gaining more traction through recent years. In the Internet of Things, millions of entities or devices (i.e. Things) will be connected to one another. These devices, which comprise devices or entities such as smart chips, smart plugs, smart watches, smart phones, smart vehicles, smart buildings, and etc., either communicate directly with one another or via the Internet.

As the Internet of Things spreads into more areas, these devices become more prone to cyber-attacks from hackers or unauthorized users as a compromised device would grant a malicious user access to the network to which the device belongs. Hence, it is of utmost importance that a security protocol be set in place to allow one entity to verify the authenticity of a peer entity, with which it communicates with, before data is exchanged between these two entities. In addition to the above, once the authenticity of the entities have been verified, a secret key known to only these two entities, has to be established to facilitate the signing of data messages between these entities. This is to ensure that data communicated between these two entities will not be compromised even if the data were intercepted or redirected.

A common method of establishing a secret key for signing data communications between entities involves the pre-sharing of a common symmetric secret key between the relevant parties. For such a method, data messages that are to be transmitted between the entities will be signed using this pre-shared or pre-agreed-upon secret key. If the receiving entity is able to decrypt the received message using this pre-shared secret key, this implies that the authenticity of the sender has been verified and the receiver may then proceed to process the decrypted message accordingly. Unfortunately, this method is not scalable and is quite inflexible as it requires the common secret to be pre-shared or communicated to all trusted entities or devices before the entities or devices may communicate with one another. In the IoT setting, the high mobility of devices is a norm and devices that are required to exchange data with one another may not have had the opportunity to establish a secret key beforehand.

Another approach that has been proposed utilizes public key infrastructure (PKI) based solutions whereby key-pairs allocated to each authorized entity are bound to its holders by means of a public key certificate. The key pair then utilizes a public key cryptosystem such as public-key encryption or digital signature methodologies to sign data messages or to verify the authenticity of a sender by validating the public key certificate of the sender. The setup and maintenance of such public key infrastructures are notoriously expensive and require entities to constantly maintain contact with a PKI server to validate the respective public key certificates.

Yet another approach that has been proposed utilizes identity based cryptography methodologies to authenticate entities and to sign data messages. Such identity based cryptosystems are special public key cryptosystems, which are based on bilinear pairing and utilize an entity's identity, such as user name, email address, telephone number, IP address, etc. as the public key and a corresponding private key is then derived from the entity's identity by a Key Generation Centre which contains a master secret key, which is utilized in the generation of private keys for entities. The downside of this approach is that bilinear pairing is an expensive and time consuming computation process.

Another inherent weakness of existing identity based cryptographic schemes is that users' private keys are usually generated by a Key Generation Centre. As the users' private keys are escrowed to the key generation centre, this means that the key generation centre will possess all the private keys of the users of the scheme. If the key generation centre were ever to become compromised, this would mean that all the users of the system would be compromised as well.

For the above reasons, those skilled in the art are constantly striving to come up with a system and method to generate private keys for users of an identity based signature scheme whereby the private keys are only made known to each respective user. The private keys are then utilized with the identity based signature scheme to verify the authenticity of users of the scheme and to generate a common session key that is to be used to encode data messages between verified users.

SUMMARY

The above and other problems are solved and an advance in the art is made by systems and methods provided by embodiments in accordance with the application.

A first advantage of embodiments of systems and methods in accordance with the application is that the private keys of devices or entities belonging to the self-certified identity based signature scheme are made known only to the devices themselves and are not escrowed out to any external third parties such as a Key Generating Centre.

A second advantage of embodiments of systems and methods in accordance with the application is that the private keys generated in accordance with embodiments of the application are of the same form as in existing self-certified identity based signature schemes and thus may be used in existing self-certified identity based signature schemes without changing the operation of existing self-certified identity based signature schemes.

A third advantage of embodiments of systems and methods in accordance with the application is that the application allows cross-domain authenticated key exchange to take place whereby users' or entities' respective private keys may be issued by different key generation centres whereby each centre has its own unique system parameters.

A fourth advantage of embodiments of systems and methods in accordance with the application is that the application may be utilized in Transport Layer Security (TLS) or Datagram Transport Layer Security (DTLS) protocols whereby a self-certified identity based signature scheme in accordance with embodiments of the application may be used to sign messages for TLS protocol or DTLS protocol.

The above advantages are provided by embodiments of a method in accordance with the application operating in the following manner. For brevity, in the subsequent description of the embodiments of the application, although multiplicative notations are utilized for finite field arithmetic operations; it should be straightforward for a person skilled in the art to realize that the arithmetic operations should be described using additive notations when implemented over elliptic curves.

According to a first aspect of the application, a system for computing a private key sk for a device participating in a self-certified identity based signature system comprises a secure server configured to: compute parameters for the device based on a second random number r i2 generated by the secure server, a first set of components received from the device, a master secret key x and parameters associated with a master public key mpk, wherein the first set of components comprises a first random number r i1 generated by the device, transmit the computed parameters to the device; and the device configured to compute the private key sk based on the received computed parameters and the random number r i1 .

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the parameters for the device comprises: retrieving an arbitrary first value R i1 and an identity of the device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; computing an arbitrary value of the device R i and a first integer s i1 ; and setting the computed arbitrary value of the device R i1 and the first integer s i1 ; as the parameters for the device, whereby the arbitrary value of the device R i1 is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value of the device R i , the identity of the device id i and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the private key sk comprises: computing an integer s i based on the first integer s i1 as retrieved from the computed parameters transmitted from the secure server, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and forming the private key sk based on the arbitrary value of the device R i and the integer s i .

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =R i1 ·g r

i2 or R i =R i1 /g r

i2 , the arbitrary first value R i1 is defined by R i1 =g r

is and the first integer s i1 is defined by s i1 =r i2 +xH(R i , id i )(mod q) or s i1 =−r i2 +xH(R i , id i )(mod q) where H( ) is a collision-resistant hash function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i =s i1 +r i1 (mod q).

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =g r

i2 /R i1 , the arbitrary first value R i1 is defined by R i1 =g r

i1 and the first integer s i1 is defined by s i1 =r i2 +xH(R i , id i )(mod q) where H( ) is a collision-resistant hash function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i =s i1 −r i1 (mod q).

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the parameters for the device comprises: retrieving an arbitrary first value R i1 , an identity of the device id i and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk to an additive homomorphic encryption function HEnc( ); setting an arbitrary value of the device R i and a first integer s i1 as the parameters for the device, whereby the arbitrary value of the device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed by providing the second random number r i2 , the homomorphic encryption value c, the master secret key x, the arbitrary value of the device R i , the identity of the device id i and the prime number q to the additive homomorphic encryption function HEnc( ).

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the private key sk comprises: computing an integer s i by applying a complementary homomorphic decryption function to the first integer s i1 as retrieved from the computed parameters transmitted from the secure server; and forming the private key sk based on the arbitrary value of the device R i and the integer s i .

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =(R i1 ) r

i2 , the arbitrary first value R i1 is defined by R i1 =g r

i1 , the homomorphic encryption value c is defined by c=HEnc(r i1 −1 mod q) and the first integer s i1 is defined by s i1 =HEnc(r i2 )·c xH(R

i,

id

i

) mod q where HEnc( ) is the additive homomorphic encryption function.

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =(R i1 ) r

i1

−1 , the arbitrary first value R i1 is defined by R i1 =g r

i1 the homomorphic encryption value c is defined by c=HEnc(r i1 −1 ) and the first integer s i1 is defined by s i1 =HEnc(r i2 −1 )·c xH(R

i,

id

i

) mod q where HEnc( ) is the additive homomorphic encryption function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i1 =r i1 HDec(s i1 ); where HDec( ) is the complementary homomorphic decryption function.

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =(R i1 )r i2 , the arbitrary first value R i1 is defined by R i1 =g r

i1

−1 , the homomorphic encryption value c is defined by c=HEnc(r i1 ) and the first integer s i1 is defined by s i1 =HEnc(r i2 )·c xH(R

i

,id

i

) mod q where HEnc( ) is the additive homomorphic encryption function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i =r i1 −1 HDec(s i1 ) where HDec( ) is the complementary homomorphic decryption function.

According to a second aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in a self-certified identity based signature scheme is disclosed, the system comprising: a secure server configured to instruct: the first device to compute a private key ski based on a first set of parameters received from the secure server, and a random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components comprising the first random number r i1 , a master secret key x and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, and the second device to compute a private key sk j based on a sec

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No. PCT/SG2018/050050, filed on Feb. 7, 2018, which claims priority to Singaporean Patent Application No. SG10201701044S, filed on Feb. 9, 2017. The disclosures of the aforementioned applications are hereby incorporated by reference in their entireties.

FIELD OF TECHNOLOGY

This application relates to a system and method for generating private keys for devices participating in self-certified identity based signature schemes whereby the private keys are used by the devices to establish a common session key for encoding digital communications between devices. In particular, the private keys generated in accordance with the system and methods of the application are only made known to the devices themselves and not by any other third parties.

BACKGROUND

Due to a convergence of multiple technologies, an ever increasing number of devices are now able to seamlessly communicate wirelessly with the Internet or wirelessly exchange communications between themselves. This convergence has resulted in the vision of the Internet of Things (IoT) gaining more traction through recent years. In the Internet of Things, millions of entities or devices (i.e. Things) will be connected to one another. These devices, which comprise devices or entities such as smart chips, smart plugs, smart watches, smart phones, smart vehicles, smart buildings, and etc., either communicate directly with one another or via the Internet.

As the Internet of Things spreads into more areas, these devices become more prone to cyber-attacks from hackers or unauthorized users as a compromised device would grant a malicious user access to the network to which the device belongs. Hence, it is of utmost importance that a security protocol be set in place to allow one entity to verify the authenticity of a peer entity, with which it communicates with, before data is exchanged between these two entities. In addition to the above, once the authenticity of the entities have been verified, a secret key known to only these two entities, has to be established to facilitate the signing of data messages between these entities. This is to ensure that data communicated between these two entities will not be compromised even if the data were intercepted or redirected.

A common method of establishing a secret key for signing data communications between entities involves the pre-sharing of a common symmetric secret key between the relevant parties. For such a method, data messages that are to be transmitted between the entities will be signed using this pre-shared or pre-agreed-upon secret key. If the receiving entity is able to decrypt the received message using this pre-shared secret key, this implies that the authenticity of the sender has been verified and the receiver may then proceed to process the decrypted message accordingly. Unfortunately, this method is not scalable and is quite inflexible as it requires the common secret to be pre-shared or communicated to all trusted entities or devices before the entities or devices may communicate with one another. In the IoT setting, the high mobility of devices is a norm and devices that are required to exchange data with one another may not have had the opportunity to establish a secret key beforehand.

Another approach that has been proposed utilizes public key infrastructure (PKI) based solutions whereby key-pairs allocated to each authorized entity are bound to its holders by means of a public key certificate. The key pair then utilizes a public key cryptosystem such as public-key encryption or digital signature methodologies to sign data messages or to verify the authenticity of a sender by validating the public key certificate of the sender. The setup and maintenance of such public key infrastructures are notoriously expensive and require entities to constantly maintain contact with a PKI server to validate the respective public key certificates.

Yet another approach that has been proposed utilizes identity based cryptography methodologies to authenticate entities and to sign data messages. Such identity based cryptosystems are special public key cryptosystems, which are based on bilinear pairing and utilize an entity's identity, such as user name, email address, telephone number, IP address, etc. as the public key and a corresponding private key is then derived from the entity's identity by a Key Generation Centre which contains a master secret key, which is utilized in the generation of private keys for entities. The downside of this approach is that bilinear pairing is an expensive and time consuming computation process.

Another inherent weakness of existing identity based cryptographic schemes is that users' private keys are usually generated by a Key Generation Centre. As the users' private keys are escrowed to the key generation centre, this means that the key generation centre will possess all the private keys of the users of the scheme. If the key generation centre were ever to become compromised, this would mean that all the users of the system would be compromised as well.

For the above reasons, those skilled in the art are constantly striving to come up with a system and method to generate private keys for users of an identity based signature scheme whereby the private keys are only made known to each respective user. The private keys are then utilized with the identity based signature scheme to verify the authenticity of users of the scheme and to generate a common session key that is to be used to encode data messages between verified users.

SUMMARY

The above and other problems are solved and an advance in the art is made by systems and methods provided by embodiments in accordance with the application.

A first advantage of embodiments of systems and methods in accordance with the application is that the private keys of devices or entities belonging to the self-certified identity based signature scheme are made known only to the devices themselves and are not escrowed out to any external third parties such as a Key Generating Centre.

A second advantage of embodiments of systems and methods in accordance with the application is that the private keys generated in accordance with embodiments of the application are of the same form as in existing self-certified identity based signature schemes and thus may be used in existing self-certified identity based signature schemes without changing the operation of existing self-certified identity based signature schemes.

A third advantage of embodiments of systems and methods in accordance with the application is that the application allows cross-domain authenticated key exchange to take place whereby users' or entities' respective private keys may be issued by different key generation centres whereby each centre has its own unique system parameters.

A fourth advantage of embodiments of systems and methods in accordance with the application is that the application may be utilized in Transport Layer Security (TLS) or Datagram Transport Layer Security (DTLS) protocols whereby a self-certified identity based signature scheme in accordance with embodiments of the application may be used to sign messages for TLS protocol or DTLS protocol.

The above advantages are provided by embodiments of a method in accordance with the application operating in the following manner. For brevity, in the subsequent description of the embodiments of the application, although multiplicative notations are utilized for finite field arithmetic operations; it should be straightforward for a person skilled in the art to realize that the arithmetic operations should be described using additive notations when implemented over elliptic curves.

According to a first aspect of the application, a system for computing a private key sk for a device participating in a self-certified identity based signature system comprises a secure server configured to: compute parameters for the device based on a second random number r i2 generated by the secure server, a first set of components received from the device, a master secret key x and parameters associated with a master public key mpk, wherein the first set of components comprises a first random number r i1 generated by the device, transmit the computed parameters to the device; and the device configured to compute the private key sk based on the received computed parameters and the random number r i1 .

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the parameters for the device comprises: retrieving an arbitrary first value R i1 and an identity of the device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; computing an arbitrary value of the device R i and a first integer s i1 ; and setting the computed arbitrary value of the device R i1 and the first integer s i1 ; as the parameters for the device, whereby the arbitrary value of the device R i1 is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value of the device R i , the identity of the device id i and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the private key sk comprises: computing an integer s i based on the first integer s i1 as retrieved from the computed parameters transmitted from the secure server, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and forming the private key sk based on the arbitrary value of the device R i and the integer s i .

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =R i1 ·g r

i2 or R i =R i1 /g r

i2 , the arbitrary first value R i1 is defined by R i1 =g r

is and the first integer s i1 is defined by s i1 =r i2 +xH(R i , id i )(mod q) or s i1 =−r i2 +xH(R i , id i )(mod q) where H( ) is a collision-resistant hash function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i =s i1 +r i1 (mod q).

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =g r

i2 /R i1 , the arbitrary first value R i1 is defined by R i1 =g r

i1 and the first integer s i1 is defined by s i1 =r i2 +xH(R i , id i )(mod q) where H( ) is a collision-resistant hash function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i =s i1 −r i1 (mod q).

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the parameters for the device comprises: retrieving an arbitrary first value R i1 , an identity of the device id i and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk to an additive homomorphic encryption function HEnc( ); setting an arbitrary value of the device R i and a first integer s i1 as the parameters for the device, whereby the arbitrary value of the device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed by providing the second random number r i2 , the homomorphic encryption value c, the master secret key x, the arbitrary value of the device R i , the identity of the device id i and the prime number q to the additive homomorphic encryption function HEnc( ).

With reference to the first aspect, in accordance with embodiments of the application, the step of computing the private key sk comprises: computing an integer s i by applying a complementary homomorphic decryption function to the first integer s i1 as retrieved from the computed parameters transmitted from the secure server; and forming the private key sk based on the arbitrary value of the device R i and the integer s i .

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =(R i1 ) r

i2 , the arbitrary first value R i1 is defined by R i1 =g r

i1 , the homomorphic encryption value c is defined by c=HEnc(r i1 −1 mod q) and the first integer s i1 is defined by s i1 =HEnc(r i2 )·c xH(R

i,

id

i

) mod q where HEnc( ) is the additive homomorphic encryption function.

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =(R i1 ) r

i1

−1 , the arbitrary first value R i1 is defined by R i1 =g r

i1 the homomorphic encryption value c is defined by c=HEnc(r i1 −1 ) and the first integer s i1 is defined by s i1 =HEnc(r i2 −1 )·c xH(R

i,

id

i

) mod q where HEnc( ) is the additive homomorphic encryption function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i1 =r i1 HDec(s i1 ); where HDec( ) is the complementary homomorphic decryption function.

With reference to the first aspect, in accordance with embodiments of the application, the arbitrary value of the device R i is defined by R i =(R i1 )r i2 , the arbitrary first value R i1 is defined by R i1 =g r

i1

−1 , the homomorphic encryption value c is defined by c=HEnc(r i1 ) and the first integer s i1 is defined by s i1 =HEnc(r i2 )·c xH(R

i

,id

i

) mod q where HEnc( ) is the additive homomorphic encryption function.

With reference to the first aspect, in accordance with embodiments of the application, the integer s i is defined by s i =r i1 −1 HDec(s i1 ) where HDec( ) is the complementary homomorphic decryption function.

According to a second aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in a self-certified identity based signature scheme is disclosed, the system comprising: a secure server configured to instruct: the first device to compute a private key ski based on a first set of parameters received from the secure server, and a random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components comprising the first random number r i1 , a master secret key x and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, and the second device to compute a private key sk j based on a second set of parameters received from the secure server, and a random number r j1 generated by the second device, wherein the second set of parameters is generated by the secure server based on a second random number r j2 generated by the secure server, a second set of components comprising the first random number r j1 , the master secret key x and the parameters associated with a master public key mpk, wherein the second set of components is generated by the second device and transmitted to the secure server; the first device configured to: sign a group element g a using a self-certified Identity Based Signature Scheme and the private key ski, where a is a random number generated by the first device and g is a generator of a cyclic group G; transmit an identity of the first device id i , the group element g a and the signed group element g a to the second device; upon receiving the transmission, the second device is configured to: verify the signed group element g a using a verification function associated with the self-certified Identity Based Signature Scheme and the identity of the first device id i , sign group elements (g a ∥g b ) using the self-certified Identity Based Signature Scheme and the private key sk j , where b is a random number generated by the first device, when the signed group element g a is verified, and transmit the signed group elements (g a ∥g b ) and a group element g b to the first device; the first device is configured to: verify the signed group elements (g a ∥ g b ) using the verification function associated with the self-certified Identity Based Signature Scheme and the identity of the second device id j ; compute a first shared secret k ij based on the group element a and the group element g b , compute a first key vk i by providing the first shared secret k ij to a Key Deriving Function, and compute a first authentication data Ad i by providing the first key vk i to an Authentication Data Deriving Function, when the signed group elements (g a ∥g b ) are verified; generate the common session key SK by providing the first shared secret k ij to the Key Deriving Function; transmit the first authentication data Ad i to the second device, such that upon receiving the first authentication data Ad i , the second device is configured to: compute a second shared secret k ji based on the group element g a and the group element b, compute a second key vk j by providing the second shared secret k ji to the Key Deriving Function, compute a second authentication data Ad j by providing the key vk j to the Authentication Data Deriving Function, determine if the second authentication data Ad j matches with the first authentication data Ad i ; and generate the common session key SK by providing the second shared secret k ji to the Key Deriving Function, when the second authentication data Ad j matches with the first authentication data Ad i .

With reference to the second aspect, in accordance with embodiments of the application, the step of generating the first set of parameters for the first device comprises: the secure server being configured to: retrieve an arbitrary first value R i1 and an identity of the first device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; compute an arbitrary value of the first device R i and a first integer s i1 ; and set the computed arbitrary value of the first device R i and the first integer s i1 as the parameters for the first device, whereby the arbitrary value of the first device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value of the first device R i , the identity of the first device id i and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the second aspect, in accordance with embodiments of the application, the computing the private key ski comprises: the first device being configured to: compute an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk.; and form the private key ski based on the arbitrary value of the first device R i and the integer s i .

With reference to the second aspect, in accordance with embodiments of the application, the generating the second set of parameters for the second device comprises: the secure server being configured to: retrieve an arbitrary first value R j1 and an identity of the second device id j from the second set of components, wherein the arbitrary first value R j1 is generated based on the first random number r j1 ; compute an arbitrary value of the second device R j and a first integer s j1 ; and set the computed arbitrary value of the second device R j and the first integer s j1 as the parameters for the second device, whereby the arbitrary value of the second device R j is computed based on the arbitrary first value R j1 and the second random number r j2 ; and whereby the first integer s j1 is computed based on the second random number r j2 , the master secret key x, the arbitrary value of the second device R j , the identity of the second device id j and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the second aspect, in accordance with embodiments of the application, the computing the private key sk j comprises: the second device being configured to: compute an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and form the private key sk j based on the arbitrary value of the second device R j and the integer s j .

According to a third aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j participating in a self-certified identity based signature scheme is provided, the system comprising: a secure server configured to instruct: the first device to compute a private key sk i based on a first set of parameters received from the secure server, and a random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components comprising the first random number r i1 , a master secret key x and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, and the second device to compute a private key sk j based on a second set of parameters received from the secure server, and a random number r j1 generated by the second device, wherein the second set of parameters is generated by the secure server based on a second random number r j2 generated by the secure server, a second set of components comprising the first random number r j1 , the master secret key x and the parameters associated with a master public key mpk, wherein the second set of components is generated by the second device and transmitted to the secure server; the first device configured to: sign a cryptographic nonce Ni using a self-certified Identity Based Signature Scheme and the private key sk i ; transmit an identity of the first device id i , the cryptographic nonce N i and the signed cryptographic nonce N i to the second device; upon receiving the transmission, the second device is configured to: verify the signed cryptographic nonce N i using a verification function associated with the self-certified Identity Based Signature Scheme and the identity of the first device id i , sign cryptographic nonces (N i ∥N j ) using the self-certified Identity Based Signature Scheme and the private key sk j , where N j is a cryptographic nonce, when the signed cryptographic nonce N i is verified, and transmit the signed cryptographic nonces (N i N j ) and the cryptographic nonce N j to the first device; the first device is configured to: verify the signed cryptographic nonces (N i ∥N j ) using the verification function associated with the self-certified Identity Based Signature Scheme and the identity of the second device id j , compute a first shared secret k ij =g sj·si , compute a first key vk i by providing the first shared secret k ij to a Key Deriving Function, and compute a first authentication data Ad i by providing the cryptographic nonces N i and N j and the first key vk i to an Authentication Data Deriving Function, when the signed cryptographic nonces (N i ∥N j ) are verified; generate the common session key SK by providing the first shared secret k ij and the cryptographic nonces N i and N j to the Key Deriving Function; transmit the first authentication data Ad i to the second device; upon receiving the first authentication data Ad i , the second device is configured to: compute a second shared secret k ji =g sj·si , compute a second key vk j by providing the second shared secret k ji to the Key Deriving Function, compute a second authentication data Ad j by providing the key vk j and the cryptographic nonces N i and N j to the Authentication Data Deriving Function, determine if the second authentication data Ad j matches with the first authentication data Ad i ; and generate the common session key SK by providing the second shared secret k ji to the Key Deriving Function, when the second authentication data Ad j matches with the first authentication data Ad i .

With reference to the third aspect, in accordance with embodiments of the application, the generating the first set of parameters for the first device comprises: the secure server being configured to: retrieve an arbitrary first value R i1 and an identity of the first device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; compute an arbitrary value of the first device R i and a first integer s i1 ; and set the computed arbitrary value of the first device R i and the first integer s i1 as the parameters for the first device, whereby the arbitrary value of the first device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value of the first device R i , the identity of the first device id i and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the third aspect, in accordance with embodiments of the application, the computing the private key sk i comprises: the first device being configured to: compute an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and form the private key sk i based on the arbitrary value of the first device R i and the integer s i .

With reference to the third aspect, in accordance with embodiments of the application, the generating the second set of parameters for the second device comprises: the secure server being configured to: retrieve an arbitrary first value R j1 and an identity of the second device id j from the second set of components, wherein the arbitrary first value R j1 is generated based on the first random number r j1 ; compute an arbitrary value of the second device R j and a first integer s j1 ; and set the computed arbitrary value of the second device R j and the first integer s j1 as the parameters for the second device, whereby the arbitrary value of the second device R j is computed based on the arbitrary first value R j1 and the second random number r j2 ; and whereby the first integer s j1 is computed based on the second random number r j2 , the master secret key x, the arbitrary value of the second device R j , the identity of the second device id j and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the third aspect, in accordance with embodiments of the application, the computing the private key sk j comprises: the second device being configured to: compute an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and form the private key sk j based on the arbitrary value of the second device R j and the integer s j .

According a fourth aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in a self-certified identity based signature scheme is provided, the system comprising: a first secure server configured to instruct: the first device to compute a private key sk i based on a first set of parameters received from the first secure server, and a random number r i1 generated by the first device, wherein the first set of parameters is generated by the first secure server based on a second random number r i2 generated by the first secure server, a first set of components comprising the first random number r i1 , a master secret key x, and parameters associated with a master public key mpk i , wherein the first set of components is generated by the first device and transmitted to the first secure server; a second secure server configured to instruct: the second device to compute a private key sk j based on a second set of parameters received from the second secure server, and a random number r j1 generated by the second device, wherein the second set of parameters is generated by the second secure server based on a second random number r j2 generated by the second secure server, a second set of components comprising the first random number r j1 , a master secret key x j and the parameters associated with a master public key mpk j , wherein the second set of components is generated by the second device and transmitted to the second secure server, wherein the first secure server is located in a different domain from the second secure server; the first device configured to: sign a group element g a using a self-certified Identity Based Signature Scheme and the private key sk i , where a is a random number generated by the first device and g is a generator of a cyclic group G; transmit an identity of the first device id i , the group element g a and the signed group element g a to the second device; upon receiving the transmission, the second device is configured to: verify the signed group element g a using a verification function associated with the self-certified Identity Based Signature Scheme and the identity of the first device id i , sign group elements (g a ∥g b ) using the self-certified Identity Based Signature Scheme and the private key sk j , where b is a random number generated by the first device, when the signed group element g a is verified, and transmit the signed group elements (g a ∥g b ) and a group element g b to the first device; the first device is configured to: verify the signed group elements (g a ∥g b ) using the verification function associated with the self-certified Identity Based Signature Scheme and the identity of the second device id j ; compute a first shared secret k ij based on the group element a and the group element g b , compute a first key vk i by providing the first shared secret k ij to a Key Deriving Function, and compute a first authentication data Ad i by providing the first key vk i to an Authentication Data Deriving Function, when the signed group elements (g a g b ) are verified; generate the common session key SK by providing the first shared secret k ij to the Key Deriving Function; transmit the first authentication data Ad i to the second device; upon receiving the first authentication data Ad i , the second device is configured to: compute a second shared secret k ji based on the group element g a and the group element b, compute a second key vk j by providing the second shared secret k ji to the Key Deriving Function, compute a second authentication data Ad j by providing the key vk j to the Authentication Data Deriving Function, determine if the second authentication data Ad j matches with the first authentication data Ad i ; and generate the common session key SK by providing the second shared secret k ji to the Key Deriving Function, when the second authentication data Ad j matches with the first authentication data Ad i .

With reference to the fourth aspect, in accordance with embodiments of the application, the generating the first set of parameters for the first device comprises: the first secure server being configured to: retrieve an arbitrary first value R i1 and an identity of the first device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; compute an arbitrary value of the first device R i and a first integer s i1 ; and set the computed arbitrary value of the first device R i and the first integer s i1 as the parameters for the first device, whereby the arbitrary value of the first device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x i , the arbitrary value of the first device R i , the identity of the first device id i and a prime number q obtained from the parameters associated with the master public key mpk i .

With reference to the fourth aspect, in accordance with embodiments of the application, the computing the private key sk i comprises: the first device being configured to: compute an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk i ; and form the private key sk i based on the arbitrary value of the first device R i and the integer s i .

With reference to the fourth aspect, in accordance with embodiments of the application, the generating the second set of parameters for the second device comprises: the second secure server being configured to: retrieve an arbitrary first value R j1 and an identity of the second device id j from the second set of components, wherein the arbitrary first value R j1 is generated based on the first random number r j1 ; compute an arbitrary value of the second device R j and a first integer s j1 ; and set the computed arbitrary value of the second device R j and the first integer s j1 as the parameters for the second device, whereby the arbitrary value of the second device R j is computed based on the arbitrary first value R j1 and the second random number r j2 ; and whereby the first integer s j1 is computed based on the second random number r j2 , the master secret key xi, the arbitrary value of the second device R j , the identity of the second device id j and a prime number q obtained from the parameters associated with the master public key mpk j .

With reference to the fourth aspect, in accordance with embodiments of the application, the computing the private key sk j comprises: the second device being configured to: compute an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk j ; and form the private key sk j based on the arbitrary value of the second device R j and the integer s j .

According to a fifth aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS) is provided, the system comprising: a secure server configured to instruct: the first device to compute a private key sk i based on a first set of parameters received from the secure server, and a random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components comprising the first random number r i1 , a master secret key x and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, and the second device to compute a private key sk j based on a second set of parameters received from the secure server, and a random number r j1 generated by the second device, wherein the second set of parameters is generated by the secure server based on a second random number r j2 generated by the secure server, a second set of components comprising the first random number r j1 , the master secret key x and the parameters associated with a master public key mpk, wherein the second set of components is generated by the second device and transmitted to the secure server; the first and second devices configured to use a self-certified Identity Based Signature Scheme to generate the common session key SK for the TLS protocol or the DTLS protocol between the first device and the second device, wherein an identity of the first device id i is included in the first device's Certificate message and the identity of the second device id i is included in the second device's Certificate message; wherein the self-certified Identity Based Signature Scheme are dictated by the sk i and sk j .

With reference to the fifth aspect, in accordance with embodiments of the application, the generating the first set of parameters for the first device comprises: the secure server being configured to: retrieve an arbitrary first value R i1 and the identity of the first device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; compute an arbitrary value of the first device R i and a first integer s i1 ; and set the computed arbitrary value of the first device R i and the first integer s i1 as the parameters for the first device, whereby the arbitrary value of the first device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value of the first device R i , the identity of the first device id i and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the fifth aspect, in accordance with embodiments of the application, the computing the private key sk i comprises: the first device being configured to: compute an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and form the private key sk i based on the arbitrary value of the first device R i and the integer s i .

With reference to the fifth aspect, in accordance with embodiments of the application, the generating the second set of parameters for the second device comprises: the secure server being configured to: retrieve an arbitrary first value R j1 and the identity of the second device id j from the second set of components, wherein the arbitrary first value R j1 is generated based on the first random number r j1 ; compute an arbitrary value of the second device R j and a first integer s j1 ; and set the computed arbitrary value of the second device R j and the first integer s j1 as the parameters for the second device, whereby the arbitrary value of the second device R j is computed based on the arbitrary first value R j1 and the second random number r j2 ; and whereby the first integer s j1 is computed based on the second random number r j2 , the master secret key x, the arbitrary value of the second device R j , the identity of the second device id j and a prime number q obtained from the parameters associated with the master public key mpk.

With reference to the fifth aspect, in accordance with embodiments of the application, the computing the private key sk j comprises: the second device being configured to: compute an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk.; and form the private key sk j based on the arbitrary value of the second device R j and the integer s j .

According to a sixth aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS) is provided, the system comprising: a first secure server configured to instruct: the first device to compute a private key sk i based on a first set of parameters received from the first secure server, and a random number r i1 generated by the first device, wherein the first set of parameters is generated by the first secure server based on a second random number r i2 generated by the first secure server, a first set of components comprising the first random number r i1 , a master secret key x, and parameters associated with a master public key mpki, wherein the first set of components is generated by the first device and transmitted to the first secure server, a second secure server configured to instruct: the second device to compute a private key sk j based on a second set of parameters received from the second secure server, and a random number r j1 generated by the second device, wherein the second set of parameters is generated by the second secure server based on a second random number r j2 generated by the second secure server, a second set of components comprising the first random number r j1 , the master secret key x j and the parameters associated with a master public key mpk j , wherein the second set of components is generated by the second device and transmitted to the second secure server, wherein the first secure server is located in a different domain from the second secure server; the first and second devices configured to use a self-certified Identity Based Signature Scheme to generate the common session key SK ij for the TLS protocol between the first device and the second device, wherein an identity of the first device id i is included in the first device's Certificate message and the identity of the second device id j is included in the second device's Certificate message; wherein the self-certified Identity Based Signature Scheme are dictated by the sk i and sk j .

With reference to the sixth aspect, in accordance with embodiments of the application, the generating the first set of parameters for the first device comprises: the first secure server being configured to: retrieve an arbitrary first value R i1 and the identity of the first device id i from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; compute an arbitrary value of the first device R i and a first integer s i1 ; and set the computed arbitrary value of the first device R i and the first integer s i1 as the parameters for the first device, whereby the arbitrary value of the first device R i is computed based on the arbitrary first value R i1 and the second random number r i2 ; and whereby the first integer s i1 is computed based on the second random number r i2 , the master secret key x i , the arbitrary value of the first device R i , the identity of the first device id i and a prime number q obtained from the parameters associated with the master public key mpk i .

With reference to the sixth aspect, in accordance with embodiments of the application, the computing the private key sk i comprises: the first device being configured to: compute an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk i .; and form the private key sk i based on the arbitrary value of the first device R i and the integer s i .

With reference to the sixth aspect, in accordance with embodiments of the application, the generating the second set of parameters for the second device comprises: the second secure server being configured to: retrieve an arbitrary first value R j1 and the identity of the second device id j from the second set of components, wherein the arbitrary first value R j1 is generated based on the first random number r j1 ; compute an arbitrary value of the second device R j and a first integer s j1 ; and set the computed arbitrary value of the second device R j and the first integer s j1 as the parameters for the second device, whereby the arbitrary value of the second device R j is computed based on the arbitrary first value R j1 and the second random number r j2 ; and whereby the first integer s j1 is computed based on the second random number r j2 , the master secret key x j , the arbitrary value of the second device R j , the identity of the second device id j and a prime number q obtained from the parameters associated with the master public key mpk j .

With reference to the sixth aspect, in accordance with embodiments of the application, the computing the private key sk j comprises: the second device being configured to: compute an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk j ; and form the private key sk j based on the arbitrary value of the second device R j and the integer s j .

With reference to the sixth aspect, in accordance with embodiments of the application, before the secure server is configured to compute parameters for the device based on the second random number r i2 generated by the secure server, the secure server is configured to: receive a zero-knowledge proof result from the device, whereby the zero-knowledge proof result is generated by the device using the first random number r i1 and a system parameter k; determine from the zero-knowledge proof result if the first random number r i1 is equal or less than the system parameter λ; and compute parameters for the device based on the second random number r i2 generated by the secure server, when the first random number r i1 is equal or less than the system parameter λ.

According to a seventh aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS) is provided, the system comprising: a secure server configured to: generate a private key sk i for the first device based on an identity of the first device id i and generate a private key sk j for the second device based on an identity of the second device id j , using a self-certified Identity Based Signature Scheme; and transmit the private key sk i to the first device and transmit the private key sk j to the second device; the first and second devices configured to use the same self-certified Identity Based Signature Scheme to generate the common session key SK for the TLS protocol or the DTLS protocol between the first device and the second device, wherein the identity of the first device id i is included in the Certificate message of the first device and the identity of the second device id j is included in the Certificate message of the second device; wherein the self-certified Identity Based Signature Scheme are dictated by the sk i and sk j .

According to an eighth aspect of the application, a system for generating a common session key SK for encoding digital communications between a first device i and a second device j that are participating in an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS) is provided, the system comprising: a first secure server configured to: generate a private key sk i for the first device based on an identity of the first device id i using a self-certified Identity Based Signature Scheme, and transmit the private key sk i to the first device; a second secure server configured to: generate a private key sk j for the second device based on an identity of the second device id j , using a self-certified Identity Based Signature Scheme, and transmit the private key sk j to the second device; wherein the first secure server is located in a different domain from the second secure server, the first and second devices configured to use the same self-certified Identity Based Signature Scheme with different parameters or different self-certified Identity Based Signature Schemes to generate the common session key SK for the TLS or DTLS protocol between the first device and the second device, wherein the identity of the first device id i is included in the Certificate message of the first device and the identity of the second device id j is included in the Certificate message of the second device; wherein the self-certified Identity Based Signature Scheme are dictated by sk i and sk j .

According to a ninth aspect of the application, a secure server configured to compute a private key sk for a device participating in a self-certified identity based signature system comprising: a processor; and a non-transitory media readable by the processor, the media storing instructions that when executed by the

CLAIMS

Claims ( 23 )

What is claimed is:

1. A system, comprising:

a secure server; and

a device;

wherein the secure server is configured to:

compute parameters for the device based on a second random number r i2 generated by the secure server, a first set of components received from the device, a master secret key x, and parameters associated with a master public key mpk, wherein the first set of components comprises a first random number r i1 generated by the device, an arbitrary first value R i , and an identity id i of the device, and wherein the arbitrary first value R i is generated based on the first random number r i1 ; and

transmit the computed parameters to the device; and

wherein the device is configured to compute a private key sk based on the received computed parameters and the first random number r i1 , wherein the private key sk is for the device to participate in a self-certified identity based signature system,

wherein computing the parameters for the device comprises:

retrieving the arbitrary first value R i1 , the identity id i of the device, and a homomorphic encryption value c from the first set of components, wherein the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk to an additive homomorphic encryption function HEnc( ); and

setting an arbitrary value R i of the device and a first integer s i1 as the parameters for the device, wherein the arbitrary value R i of the device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed by providing the second random number r i2 , the homomorphic encryption value c, the master secret key x, the arbitrary value R i of the device, the identity id i of the device and the prime number q to the additive homomorphic encryption function HEnc( ).

2. The system according to claim 1 , wherein computing the private key sk comprises:

computing an integer s i by applying a complementary homomorphic decryption function to the first integer s i1 as retrieved from the computed parameters transmitted from the secure server; and

forming the private key sk based on the arbitrary value R i of the device and the integer s i .

3. The system according to claim 1 , wherein the arbitrary value R i of the device is defined by R i =(R i1 ) r

i2 , the arbitrary first value R i1 is defined by R i1 =g r

i1 , the homomorphic encryption value c is defined by c=HEnc(r i1 −1 mod q), and the first integer s i1 is defined by s i1 =HEnc(r i2 )·c xH(R

i

,id

i

) mod q , where HEnc( ) is the additive homomorphic encryption function.

4. The system according to claim 1 , wherein the arbitrary value R i of the device is defined by R i =(R i1 ) r

i2

−1 , the arbitrary first value R i1 is defined by R i1 =g r

i1 , the homomorphic encryption value c is defined by c=HEnc(r i1 −1 ), and the first integer s i1 is defined by s i1 =HEnc(r i2 −1 )·c xH(R

i

,id

i

) mod q , where HEnc( ) is the additive homomorphic encryption function.

5. The system according to claim 2 , wherein the integer s i is defined by s i =r i1 HDec(s i1 ), where HDec( ) is the complementary homomorphic decryption function.

6. The system according to claim 1 , wherein the arbitrary value R i of the device is defined by R i =(R i1 ) r

i2 , the arbitrary first value R i1 is defined by R i =g r

i1

−1 , the homomorphic encryption value c is defined by c=HEnc(r i1 ), and the first integer s i1 is defined by s i1 =HEnc(r i2 )·c xH(R

i

,id

i

) mod q , where HEnc( ) is the additive homomorphic encryption function.

7. The system according to claim 2 , wherein the integer s i is defined by s i =r i1 −1 HDec(s i1 ), where HDec( ) is the complementary homomorphic decryption function.

8. A system, comprising:

a secure server;

a first device; and

a second device;

wherein the secure server is configured to:

instruct the first device to compute a private key sk i based on a first set of parameters received from the secure server and based on a first random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components, a master secret key x, and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, wherein the first set of components comprises the first random number r i1 , an arbitrary first value R i1 , and an identity id i of the first device, and wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; and

instruct the second device to compute a private key sk j based on a second set of parameters received from the secure server and based on a first random number r j1 generated by the second device, wherein the second set of parameters is generated by the secure server based on a second random number r j2 generated by the secure server, a second set of components, the master secret key x, and the parameters associated with a master public key mpk, wherein the second set of components is generated by the second device and transmitted to the secure server, wherein the second set of components comprises the first random number r j1 , an arbitrary first value R j1 , and an identity id j of the second device, and wherein the arbitrary first value R j1 is generated based on the first random number r j1 ; and

wherein the first and second devices are configured to use a self-certified identity based signature scheme to generate a common session key SK for encoding digital communications between the first and second devices with respect to an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS), wherein the identity id i of the first device is included in a certificate message of the first device and the identity id j of the second device is included in a certificate message of the second device, and wherein the self-certified identity based signature scheme is dictated by the private keys sk i and sk j ,

wherein the secure server is configured to generate the second set of parameters for the second device, wherein generating the second set of parameters for the second device comprises:

retrieving the arbitrary first value R i and the identity id i of the second device from the second set of components;

computing an arbitrary value R j of the second device and a first integer s j1 ; and

setting the computed arbitrary value R j of the second device and the first integer s j1 as the second set of parameters for the second device, wherein the arbitrary value R j of the second device is computed based on the arbitrary first value R j and the second random number r j2 , and wherein the first integer s j1 is computed based on the second random number r j2 , the master secret key x, the arbitrary value R j of the second device, the identity id j of the second device, and a prime number q obtained from the parameters associated with the master public key mpk.

9. The system according to claim 8 , wherein the secure server is configured to generate the first set of parameters for the first device, wherein generating the first set of parameters for the first device comprises:

retrieving the arbitrary first value R i1 and the identity id i of the first device from the first set of components;

computing an arbitrary value R i of the first device and a first integer s i1 ; and

setting the computed arbitrary value R of the first device and the first integer s i1 as the first set of parameters for the first device, wherein the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value R i of the first device, the identity id i of the first device, and a prime number q obtained from the parameters associated with the master public key mpk.

10. The system according to claim 9 , wherein the first device is configured to compute the private key sk i , wherein computing the private key sk i comprises:

computing an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and

forming the private key sk i based on the arbitrary value R i of the first device and the integer s i .

11. The system according to claim 8 , wherein the second device is configured to compute the private key sk i , wherein computing the private key sk j comprises:

computing an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk; and

forming the private key sk j based on the arbitrary value R j of the second device and the integer s j .

12. A system, comprising:

a first secure server;

a second secure server;

a first device; and

a second device;

wherein the first secure server is configured to instruct the first device to compute a private key sk i based on a first set of parameters received from the first secure server and based on a first random number r i1 generated by the first device, wherein the first set of parameters is generated by the first secure server based on a second random number r i2 generated by the first secure server, a first set of components, a master secret key x i , and parameters associated with a master public key mpk i , and wherein the first set of components is generated by the first device and transmitted to the first secure server, wherein the first set of components comprises the first random number r i1 , an arbitrary first value R i1 , and an identity id i of the first device, and wherein the arbitrary first value R i1 is generated based on the first random number r i1 ;

wherein the second secure server is configured to instruct the second device to compute a private key sk j based on a second set of parameters received from the second secure server and based on a first random number r j1 generated by the second device, wherein the second set of parameters is generated by the second secure server based on a second random number r j2 generated by the second secure server, a second set of components, the master secret key x j and the parameters associated with a master public key mpk j , wherein the second set of components is generated by the second device and transmitted to the second secure server, wherein the second set of components comprises the first random number r j1 , an arbitrary first value R j1 , and an identity id j of the second device, and wherein the arbitrary first value R j1 is generated based on the first random number r j1 ;

wherein the first secure server is located in a different domain from the second secure server;

wherein the first and second devices are configured to use a self-certified identity based signature scheme to generate a common session key SK ij for encoding digital communications between the first and second devices with respect to an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS), wherein the identity id i of the first device is included in a certificate message of the first device and the identity id j of the second device is included in a certificate message of the second device, and wherein the self-certified identity based signature scheme is dictated by the private keys sk i and sk j ;

wherein the first secure server is configured to generate the first set of parameters for the first device, wherein generating the first set of parameters for the first device comprises:

retrieving the arbitrary first value R i1 and the identity id i of the first device from the first set of components;

computing an arbitrary value R i of the first device and a first integer s i1 ; and

setting the computed arbitrary value R i of the first device and the first integer s i1 as the first set of parameters for the first device, wherein the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed based on the second random number r i2 , the master secret key x i , the arbitrary value R i of the first device, the identity id i of the first device and a prime number q obtained from the parameters associated with the master public key mpk i .

13. The system according to claim 12 , wherein the first device is configured to compute the private key sk i , wherein computing the private key sk i comprises:

computing an integer s i based on the first integer s i1 as retrieved from the first set of parameters, the first random number r i1 , and a prime number q as obtained from the parameters associated with the master public key mpk i ; and

forming the private key sk i based on the arbitrary value R i of the first device and the integer s i .

14. The system according to claim 12 , wherein the second secure server is configured to generate the second set of parameters for the second device, wherein generating the second set of parameters for the second device comprises:

retrieving the arbitrary first value R j1 and the identity id j of the second device from the second set of components;

computing an arbitrary value R j of the second device and a first integer s i1 ; and

setting the computed arbitrary value R j of the second device and the first integer s j1 as the second set of parameters for the second device, wherein the arbitrary value R j of the second device is computed based on the arbitrary first value R j1 and the second random number r j2 , and wherein the first integer s j1 is computed based on the second random number r j2 , the master secret key x j , the arbitrary value R j of the second device, the identity id j of the second device and a prime number q obtained from the parameters associated with the master public key mpk j .

15. The system according to claim 14 , wherein the second device is configured to compute the private key sk i , wherein computing the private key sk j comprises:

computing an integer s j based on the first integer s j1 as retrieved from the second set of parameters, the first random number r j1 , and a prime number q as obtained from the parameters associated with the master public key mpk j ; and

forming the private key sk j based on the arbitrary value R j of the second device and the integer s j .

16. The system according to claim 12 , wherein the secure server is configured to:

receive a zero-knowledge proof result from a respective device, wherein the zero-knowledge proof result is generated by the respective device using the first random number r i1 and a system parameter λ;

determine from the zero-knowledge proof result whether or not the first random number r i1 is less than or equal to the system parameter λ; and

based on the first random number r i1 being less than or equal to the system parameter λ, compute parameters for the respective device based on the second random number r i2 generated by the secure server.

17. A secure server, comprising:

a processor; and

a non-transitory medium readable by the processor having processor-executable instructions stored thereon, wherein the processor-executable instructions, when executed by the processor, facilitate:

computing parameters for a device based on a second random number r i2 generated by the secure server, a first set of components received from the device, a master secret key x, and parameters associated with a master public key mpk, wherein the first set of components comprises a first random number r i1 generated by the device, an arbitrary first value R i1 , and an identity id i of the device, and wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; and

transmitting the computed parameters to the device to facilitate the device computing a private key sk based on the received computed parameters and the first random number r i1 , wherein the private key sk is for the device to participate in a self-certified identity based signature system,

wherein computing the parameters for the device comprises:

retrieving the arbitrary first value R i and the identity id i of the device from the first set of components;

computing an arbitrary value R i of the device and a first integer s i1 ; and

setting the computed arbitrary value R i of the device and the first integer s i1 as the parameters for the device, wherein the arbitrary value R i of the device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value R i of the device, the identity id i of the device, and a prime number q obtained from the parameters associated with the master public key mpk.

18. The secure server according to claim 17 , wherein computing the parameters for the device comprises:

retrieving the arbitrary first value R i , the identity id i of the device, and a homomorphic encryption value c from the first set of components, and wherein the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk to an additive homomorphic encryption function HEnc( ); and

setting an arbitrary value R i of the device and a first integer s i1 as the parameters for the device, wherein the arbitrary value R i of the device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed by providing the second random number r i2 , the homomorphic encryption value c, the master secret key x, the arbitrary value R i of the device, the identity id i of the device and the prime number q to the additive homomorphic encryption function HEnc( ).

19. The secure server according to claim 17 , wherein the processor-executable instructions, when executed by the processor, further facilitate:

receiving a zero-knowledge proof result from a respective device, wherein the zero-knowledge proof result is generated by the respective device using the first random number r i1 and a system parameter λ;

determining from the zero-knowledge proof result whether or not the first random number r i1 is less than or equal to the system parameter λ; and

based on the first random number r i1 being less than or equal to the system parameter λ, computing parameters for the respective device based on the second random number r i2 generated by the secure server.

20. A method, comprising:

computing, by a secure server, parameters for a device based on a second random number r i2 generated by the secure server, a first set of components received from the device, a master secret key x, and parameters associated with a master public key mpk, wherein the first set of components comprises a first random number r i1 generated by the device, an arbitrary first value R i1 , and an identity id i of the device, and wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; and

transmitting, by the secure server, the computed parameters to the device to facilitate the device computing a private key sk based on the received computed parameters and the first random number r i1 , wherein the private key sk is for the device to participate in a self-certified identity based signature system,

wherein computing the parameters for the device comprises:

retrieving the arbitrary first value R i1 , the identity id i of the device, and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk to an additive homomorphic encryption function HEnc( ); and

setting an arbitrary value R i of the device and a first integer s i1 as the parameters for the device, wherein the arbitrary value R i of the device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed by providing the second random number r i2 , the homomorphic encryption value c, the master secret key x, the arbitrary value R i of the device, the identity id i of the device, and the prime number q to the additive homomorphic encryption function HEnc( ).

21. The method according to claim 20 , wherein computing the parameters for the device comprises:

retrieving the arbitrary first value R i1 and the identity id i of the device from the first set of components;

computing an arbitrary value R i of the device and a first integer s i1 ; and

setting the computed arbitrary value R i of the device and the first integer s i1 as the parameters for the device, wherein the arbitrary value R i of the device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value R i of the device, the identity id i of the device and a prime number q obtained from the parameters associated with the master public key mpk.

22. A method, comprising:

receiving, by a first device, instructions from a secure server to compute a private key sk i based on a first set of parameters received from the secure server and based on a first random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components, a master secret key x, and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, wherein the first set of components comprises the first random number r i1 , an arbitrary first value R i1 , and an identity id i of the first device, and wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; and

communicating, by the first device, with a second device to generate a common session key SK by using a self-certified identity based signature scheme, wherein the common session key SK is for encoding digital communications between the first and second devices with respect to an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS), wherein the identity id i of the first device is included in a certificate message of the first device and an identity id j of the second device is included in a certificate message of the second device, wherein the self-certified identity based signature scheme is dictated by the private key sk i and a private key sk j computed by the second device,

wherein the first set of parameters is generated based on:

retrieving the arbitrary first value R i1 and the identity id i of the first device from the first set of components;

computing an arbitrary value R i of the first device and a first integer s i1 ; and

setting the computed arbitrary value R i of the first device and the first integer s i1 as the first set of parameters for the first device, wherein the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed based on the second random number r i2 , the master secret key x, the arbitrary value R i of the first device, the identity id i of the first device, and a prime number q obtained from the parameters associated with the master public key mpk.

23. A first device, comprising:

a processor; and

a non-transitory medium readable having processor-executable instructions stored thereon, wherein the processor-executable instructions, when executed by the processor, facilitate:

receiving instructions from a secure server to compute a private key sk i based on a first set of parameters received from the secure server and based on a first random number r i1 generated by the first device, wherein the first set of parameters is generated by the secure server based on a second random number r i2 generated by the secure server, a first set of components, a master secret key x, and parameters associated with a master public key mpk, wherein the first set of components is generated by the first device and transmitted to the secure server, wherein the first set of components comprises the first random number r i1 , an arbitrary first value R i1 , and an identity id i of the first device, and wherein the arbitrary first value R i1 is generated based on the first random number r i1 ; and

communicating with a second device to generate a common session key SK by using a self-certified identity based signature scheme, wherein the common session key SK is for encoding digital communications between the first and second devices with respect to an extended Transport Layer Security (TLS) protocol or an extended Datagram Transport Layer Security protocol (DTLS), wherein the identity id i of the first device is included in a certificate message of the first device and an identity id j of the second device is included in a certificate message of the second device, wherein the self-certified identity based signature scheme is dictated by the private key sk i and a private key sk j computed by the second device,

wherein the first set of parameters is generated based on:

retrieving the arbitrary first value R i1 , the identity id i of the first device, and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk to an additive homomorphic encryption function HEnc( ); and

setting an arbitrary value R i of the first device and a first integer s i1 as the parameters for the first device, wherein the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2 , and wherein the first integer s i1 is computed by providing the second random number r i2 , the homomorphic encryption value c, the master secret key x, the arbitrary value R i of the first device, the identity id i of the first device, and the prime number q to the additive homomorphic encryption function HEnc( ).

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