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quantum-safe: Bridging the Post-Quantum Production Gap with a Hybrid-by-Default Python Cryptography Library
arXiv:2605.17061v1 [cs.CR] 16 May 2026
Animesh Shaw, Independent Researcher
Abstract—The August 2024 finalisation of FIPS 203 (MLKEM), FIPS 204 (ML-DSA), and FIPS 205 (SLH-DSA) closed the algorithmic gap in post-quantum cryptography (PQC). The production gap — hybrid combiners, versioned key formats, protocol helpers, and migration tooling — remains open. We present quantum-safe, a Python library that closes all three critical gaps we identify, and a systematic evaluation of the nine-library ecosystem that quantifies them. We score nine PQC libraries across eight production-readiness dimensions. Three dimensions have coverage below 35%: hybrid KEM support (11%), migration tooling (22%), and protocol integration (33%). quantum-safe scores Full on all eight. The full API reduces the hybrid KEM task from 45 lines of manual combiner code to three lines, directly lowering the risk of insecure combiner implementations. We report the first statistically rigorous per-operation overhead measurement for a Python hybrid PQC library (3,000 iterations, CPU-pinned, bootstrapped 95% confidence intervals). A full X25519 + ML-KEM-768 handshake completes in 243 µs under Docker/Linux — 0.5–2.5% of a typical TLS 1.3 round-trip budget. At 5,000 concurrent users, throughput holds at 2,848 ops/s with only 4.9% degradation versus the single-user baseline, confirming that liboqs releases the Python GIL during C-level operations. We introduce Coefficient of Variation (CoV) as a practical timing side-channel proxy across all FIPS 203/204 operations. ML-KEM-768 decapsulation achieves CoV = 3.9%, within the AES-256-GCM noise floor (2.1%). ML-DSA-65 signing shows CoV = 51.5%, expected from FIPS 204 rejection sampling, not a side-channel. This CoV methodology has not previously been applied to PQC library evaluation and provides a lightweight complement to formal constant-time verification tools. All results are reproducible via a single Docker command. Index Terms—post-quantum cryptography, hybrid key encapsulation, ML-KEM, ML-DSA, FIPS 203, FIPS 204, Python cryptography library, timing side-channel, Coefficient of Variation, TLS 1.3, production readiness, HKDF
I. I NTRODUCTION N 13 August 2024, the National Institute of Standards and Technology (NIST) published three post-quantum cryptography standards: FIPS 203 [1], FIPS 204 [2], and FIPS 205 [3]. These documents standardise ML-KEM (derived from CRYSTALS-Kyber [4]), ML-DSA (derived from CRYSTALS-Dilithium [5]), and SLH-DSA as the drop-in replacements for RSA and ECDH in key exchange and digital signatures. The algorithmic question is settled. The production question is not.
Consider what a software engineer must do today to add hybrid post-quantum key exchange to a Python service. They must install liboqs-python, write an X25519 key generation step, write a separate ML-KEM key generation step, concatenate the two public keys, run HKDF to combine the two shared secrets, wrap the result in a key derivation function appropriate for their protocol, and handle serialisation for both halves. The result is roughly 45 lines of boilerplate before the first application-specific byte is encrypted. Then they repeat this exercise for signatures, certificates, and protocol configuration. This friction is not accidental. It reflects a genuine gap in the PQC ecosystem: algorithm implementations exist, but the production layer — hybrid combiners, versioned key formats, protocol helpers, migration tooling — does not. Insecure combiner implementations are a known risk [6], and prior work on cryptographic API usability shows that complexity directly predicts misuse [7], [8]. A. The Harvest Now, Decrypt Later Threat The urgency is real. Adversaries with access to encrypted network traffic can store ciphertext today and decrypt it once a cryptographically relevant quantum computer becomes available [9]. This “harvest now, decrypt later” (HNDL) attack is passive, undetectable, and already underway. Data with long confidentiality requirements — government communications, financial records, healthcare data — is already at risk under purely classical encryption. The NSA’s Commercial National Security Algorithm Suite 2.0 (CNSA 2.0) [10] mandates algorithm replacement by 2030 for national security systems. Commercial organisations face comparable regulatory pressure. The gap between the 2024 standard finalisation and the 2030 deadline is not large given the complexity of cryptographic migration in production infrastructure.
O
B. The Production Gap
Manuscript received May 19, 2026. A. Shaw is an independent security researcher. E-mail: [email protected]. The quantum-safe library, 415 tests, and all benchmark data are available at https://github.com/AnimeshShaw/quantum-safe (to be made public upon acceptance). All benchmarks are fully reproducible via Docker; see Section V.
Despite this urgency, deployment stalls at the library layer. To understand why, we evaluated nine actively maintained PQC libraries across eight dimensions measuring production readiness. The results are shown in Fig. 1. Three dimensions have coverage below 35%: • Hybrid KEM support (11%): Only cloudflare/circl provides a built-in hybrid combiner. Every other library exposes raw algorithm primitives, placing the burden of combining X25519 with ML-KEM on the application developer. • Migration path (22%): No library except Bouncy Castle (partially) provides tooling for upgrading classical
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keypairs, re-encrypting stored ciphertext, or scanning codebases for classical cryptography imports. • Protocol integration (33%): Application developers need TLS configuration helpers, X.509 certificate generation, and envelope encryption. Only three libraries provide partial protocol support; none provides full coverage.
parameter sets are defined: ML-KEM-512 (NIST security level 1, AES-128 equivalent), ML-KEM-768 (level 3, AES-192 equivalent), and ML-KEM-1024 (level 5, AES-256 equivalent). quantum-safe defaults to ML-KEM-768, balancing security margin with performance. The MLWE problem is believed to be hard even for polynomial-time quantum algorithms, unlike the discrete logarithm and integer factorisation problems underpinning RSA and ECDH. C. Companion Work ML-DSA [2] is a digital signature scheme also built on A companion paper [11] presents the Quantum-Safe Auditor MLWE. Its signing algorithm uses randomised hedged signing (QSA), a static analysis tool that detects classical cryptog- with a rejection-sampling loop, which causes variable execution raphy usage in Python codebases and recommends migra- time. This is a deliberate security design: the variable time tion paths. QSA identifies where PQC migration is needed; is independent of the signing key, preventing fault-injection quantum-safe provides the implementation to migrate to. attacks that exploit deterministic signing. We discuss the timing The two tools are designed to work together in a production implications in Section VI-D. migration workflow. SLH-DSA [3] is a stateless hash-based signature scheme offering security from different mathematical assumptions D. Contributions than ML-KEM and ML-DSA. It is not benchmarked here as quantum-safe does not yet implement SLH-DSA; it is This paper makes six contributions: planned for a future release. Hash-based schemes are important 1) Production gap matrix. A systematic, reproducible as a fallback if lattice-based assumptions are weakened. evaluation of nine PQC libraries across eight productionreadiness dimensions using a ternary rubric. 2) Hybrid overhead quantification. The first statistically B. Hybrid Key Exchange rigorous per-operation latency measurement for a Python The rationale for hybrid construction is defence in depth: if hybrid PQC library, including bootstrap 95% confidence a quantum computer breaks ML-KEM but classical ECDH intervals, Welch’s t-test, and Cohen’s d effect sizes. Full remains secure (or vice versa), the hybrid secret remains handshake: 243 µs (Docker/Linux). secure. Formally, given independent shared secrets ssX25519 3) Concurrent throughput analysis. The first published and ss , the combined shared secret: ML-KEM throughput-vs-concurrency curve for a Python hybrid PQC library, from 100 to 5,000 simultaneous users. ss = HKDF-SHA256(ssX25519 ∥ssML-KEM , salt, info) (1) Throughput degrades only 4.9% across a 50× increase in concurrent load. is secure as long as at least one component shared secret is com4) CoV as timing side-channel proxy. A systematic putationally hidden from the adversary [6]. This composability Coefficient of Variation analysis across all FIPS 203/204 property — the hybrid is at least as secure as its strongest operations, using AES-256-GCM as a constant-time noise component — is the formal justification for deploying hybrid floor reference. KEM during the transition period. 5) Zero-config hybrid API. The quantum-safe library CNSA 2.0 [10] requires hybrid operation through 2030. reduces the hybrid KEM task from 45 lines of manual Cloudflare enabled X25519 + ML-KEM hybrid TLS for all combiner code to three lines. its servers in 2022 [12], and Google Chrome deployed 6) Open-source artefact. All code, 415 tests, and the X25519MLKEM768 in 2023 [13]. complete benchmark harness are released under the Apache 2.0 licence. C. Timing Side Channels E. Paper Organisation Section II covers the cryptographic background. Section III presents the gap analysis. Section IV describes library design. Section V presents benchmark methodology. Section VI presents results. Section VII discusses limitations and deployment implications. Section VIII surveys related work. Section IX concludes. II. BACKGROUND A. Post-Quantum Cryptography Standards ML-KEM [1] is a key encapsulation mechanism based on the module learning-with-errors (MLWE) problem. It replaces Diffie-Hellman and ECDH in key exchange. Three
Timing side-channel attacks exploit correlations between secret values and execution time. Kocher’s 1996 attack on RSA implementations [14] demonstrated that timing differences of nanoseconds can be amplified over many observations to recover private keys. Remote timing attacks on TLS implementations remained practical as recently as 2011 [15]. For lattice-based schemes, the primary constant-time requirement is that decapsulation and decryption do not branch on secret data. ML-KEM specifies this explicitly in FIPS 203 Section 6. Formal constant-time verification uses tools like ct-verif [16] or dudect [17], which operate at the binary or hardware level. Our CoV analysis provides a practical firstorder screen applicable at the Python library level, where formal tools are not directly applicable.
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D. The Python GIL and Cryptographic Concurrency CPython’s Global Interpreter Lock (GIL) serialises Python bytecode execution, preventing true thread parallelism for pure-Python code [18]. However, C extension modules can release the GIL during computationally intensive operations. liboqs [19] is a C library; whether its Python binding releases the GIL has not previously been measured empirically. Our concurrent load tests provide the first published evidence. Note that Python 3.13 introduced optional GIL disabling (PEP 703). The measurements in this paper are from Python 3.12 with the GIL enabled, which remains the dominant deployment target. The behaviour under free-threaded Python 3.13+ is left for future work. E. Key Serialisation and Versioning Post-quantum public keys are substantially larger than their classical counterparts: an ML-KEM-768 public key is 1,184 bytes versus 32 bytes for X25519. A hybrid public key must carry both components together with an algorithm identifier, version field, and parameter set. Without a standard format, each application invents its own, preventing interoperability and complicating future migration. The quantum-safe library addresses this with a CBOR-based [20] versioned key format described in Section IV-D. III. T HE PQC P RODUCTION G AP A. Evaluation Methodology We evaluated nine PQC libraries that are either (a) the primary PQC binding in their language ecosystem, (b) the implementation recommended in NIST migration guidance, or (c) actively maintained with post-FIPS-203/204 support. Table I lists the libraries. TABLE I PQC L IBRARIES E VALUATED (S TATE AS OF M ARCH 2026) #
Library
Language
Notes
1 2 3 4 5 6 7 8 9
liboqs-python cryptography (pyca) liboqs-js noble-post-quantum pqcrypto RustCrypto ml-* oqs (Rust) cloudflare/circl Bouncy Castle
Python Python JavaScript JavaScript Rust Rust Rust Go Java
OQS project Python binding De-facto Python crypto library OQS project JS binding Audited pure-JS PQC FFI wrappers Pure Rust, trait-based OQS project Rust crate Production-deployed Enterprise Java crypto
Each library was assessed against eight production-readiness dimensions using a ternary scoring rubric: Full (F), Partial (P), or None (N). Scores were assigned by inspecting library documentation, source code, published API references, and PyPI/npm/crates.io package metadata as of March 2026. The scoring rubric for each dimension is defined in Table II. B. Results Fig. 1 shows the complete matrix. Table III summarises ecosystem coverage per dimension.
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TABLE II S CORING RUBRIC — E IGHT P RODUCTION -R EADINESS D IMENSIONS
Dimension
Full (F) requires
Unified API
Single import covers KEM + Sign + key management Built-in X25519 + ML-KEM combiner; one API call All three final standards implemented and exposed Algorithm selection without code change (registry or trait) Published browser/edge deployable package
Hybrid KEM FIPS 203/4/5 Algo Agility WASM Ready Dev / CI Migration Path Protocol Layer
Typed API, comprehensive tests, active CI pipeline Versioned key formats, upgrade tooling, classical scanner At least two of: TLS config, X.509, JWT, envelope encryption
TABLE III PQC E COSYSTEM C OVERAGE BY D IMENSION (9 LIBRARIES ) Dimension Algo Agility FIPS 203/4/5 Unified API Dev / CI WASM Ready Protocol Layer Migration Path Hybrid KEM
Full
Partial
4 5 2 5 3 0 0 1
5 3 7 4 1 3 2 1
Coverage (F+P) 100% 89% 100% 100% 44% 33% 22% 22%
C. Critical Gaps and Per-Library Analysis Hybrid KEM (11% Full, 22% with Partial). Only cloudflare/circl (Go) provides a production-ready hybrid combiner. Bouncy Castle offers partial support via its composite key API. All Python, JavaScript, and Rust libraries expose raw algorithm primitives only. This is the most critical gap: IETF [6] specifies precise domain separation and key binding requirements for hybrid KEM combiners, and prior work [7] shows that manual implementations of complex cryptographic protocols are routinely incorrect. Migration Path (22%). Adopting PQC is not only an API question. Existing deployments carry classical keypairs that must be upgraded; stored ciphertext may need re-encryption; and application code that hard-codes algorithm names must be located and changed. Only Bouncy Castle (partially) addresses this. The consequence is that every organisation migrating to PQC must build migration infrastructure from scratch. The companion QSA tool [11] addresses the detection half of this problem (locating classical crypto in Python codebases); quantum-safe addresses the replacement half. Protocol Layer (33%). Application developers think in terms of TLS connections and X.509 certificates. Partial support in cloudflare/circl (Go) and Bouncy Castle (Java) covers Go and Java users, leaving Python, Rust, and JavaScript developers without protocol-level abstractions.
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Algo Agility
WASM Ready
Dev / CI
Migration Path
Protocol Layer
P P P P P P P F F
N N N N N N N F P
F P F P P F F F F
P P P P F F P F F
N N F F P F N N N
F F P P P F P F F
N N N N N N N N P
N P N N N N N P P
Partial (P)
Full (F)
None (N)
Fig. 1. Production readiness matrix for nine PQC libraries across eight dimensions. F = Full, P = Partial, N = None. Red borders highlight the three critical gaps: Hybrid KEM, Migration Path, and Protocol Layer. quantum-safe scores Full on all eight dimensions.
D. Why Python Python runs on approximately 37% of production web services1 and is the dominant language in data science, ML inference, and API gateway segments where PQC migration is most urgent. A gap in the Python PQC ecosystem therefore affects a large fraction of production deployments. This is the primary motivation for quantum-safe. IV. L IBRARY D ESIGN A. Design Principles
The default signature scheme is Ed25519 + ML-DSA-65. An application developer who does not specify an algorithm gets a production-appropriate default. B. Module Architecture
quantum-safe Module Architecture
Application
FIPS 203/4/5
API layer
Hybrid KEM
Application Code
kem.HybridKEM
sig.HybridSign
Protocol layer
Unified API
protocols.tls protocols.x509 protocols.envelope
Backend layer
liboqs-python cryptography (pyca) liboqs-js noble-postquantum pqcrypto (Rust) RustCrypto ml-* oqs (Rust) cloudflare/ circl (Go) Bouncy Castle (Java)
Production Readiness Matrix 9 PQC Libraries x 8 Dimensions (red border = critical gap: Hybrid KEM, Migration Path, Protocol Layer)
4
liboqs-python
RustCrypto
audit
The library is built around five explicit design principles, each traceable to a specific failure mode observed in the gap analysis. P1: Hybrid by default. The default construction is hybrid. Fig. 2. Module architecture of quantum-safe. Application code interacts Opting into classical-only mode requires an explicit flag. This only with HybridKEM and HybridSign. Protocol helpers (tls, x509, inverts the burden of security: the easy path is the secure path. envelope) and the audit module sit above a backend abstraction layer that The alternative design — classical by default, opt-in PQC — currently exposes liboqs-python and RustCrypto. produces code that looks correct and passes existing tests but The five design principles are directly reflected in the module silently loses quantum resistance when PQC is not explicitly structure shown in Fig. 2. Application code touches only enabled. P2: Backend agnostic. Algorithm implementations are HybridKEM and HybridSign. The protocol helpers (tls, separated from the API by an abstract backend layer. The x509, envelope) and the audit module sit above the backend same application code runs against liboqs [19] (the default abstraction layer. Adding a new backend requires implementing production backend) or RustCrypto (via PyO3 bindings) a single abstract base class in backends/base.py; no without modification. This protects against a backend becoming application code changes. unavailable or being superseded. A future WASM target would expose the same API in browser environments. C. API Usability P3: Protocol ready. The library ships TLS configuration Fig. 3 compares the lines of code required to perform helpers, X.509 hybrid certificate generation, a CBOR-serialised the canonical hybrid KEM task (generate hybrid keypair, envelope format, and JWT signing. Raw byte access is available encapsulate shared secret, decapsulate) across four libraries. but not the primary interface. The quantum-safe implementation is shown in Listing 1. P4: Migration first. Key formats are versioned in The equivalent liboqs-python implementation, which requires CBOR [20] from version 1.0. An upgrade module transforms manual X25519 keygen, ML-KEM keygen, key concatenation, classical keypairs to hybrid keypairs, and a scanner module and HKDF combination, is shown in Listing 2. (exposed via the qs-audit CLI) locates classical cryptography imports in Python source trees. This scanner functionality Listing 1. Hybrid KEM in quantum-safe — three lines. from quantum_safe.kem.hybrid import HybridKEM is complementary to the companion QSA tool [11], which kem = HybridKEM() # default: X25519 + ML-KEM performs deeper static analysis including VQE threat scoring. -768 P5: Safe defaults. The default algorithm is ML-KEMkp = kem.generate_keypair() ct, shared_secret = kem.encapsulate(kp.public) 768 (security level 3) rather than ML-KEM-512 (level 1). 1 Stack Overflow Developer Survey 2024.
shared_secret_b = kem.decapsulate(kp, ct) assert shared_secret == shared_secret_b
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API Usability: LOC for Hybrid Key Exchange Lines of code (hybrid KEM task)
50
45
40
30
30
18
10
hybrid built-in
Keys are serialised in two formats. PEM is provided for compatibility with existing tooling. CBOR [20] is the primary format: it encodes the algorithm identifier, parameter set, and key material in a compact binary encoding with a version field that supports future migrations. The CBOR schema is:
3
hybrid built-in
liboqspython
the correct HKDF salt and domain separation string? What format should the combined ciphertext use for transmission? How should the two secret shares be ordered in the HKDF input? The IETF [6] draft specifies answers to all of these; quantum-safe implements the specification so that application developers do not have to. D. Key Serialisation and Versioning
20
0
5
noble-post- cloudflare/ quantum (JS) circl (Go)
quantumsafe
liboqs/noble: manual combiner; circl: Go only; quantum-safe: 3-line default Fig. 3. Lines of code required for a complete hybrid KEM operation. liboqspython and noble-post-quantum require manual combiner implementation. cloudflare/circl (Go) is concise but has no Python binding. quantum-safe requires three lines; hybrid is the default.
Listing 2. Equivalent task with liboqs-python — manual combiner. from cryptography.hazmat.primitives.asymmetric. x25519 import ( X25519PrivateKey) from cryptography.hazmat.primitives.hashes import SHA256 from cryptography.hazmat.primitives.kdf.hkdf import HKDF import oqs
Listing 3. CBOR hybrid key structure (CDDL notation). hybrid-key = { "v" : uint, ; version (currently 1) "alg" : text, ; e.g. "X25519+ML-KEM-768" "cls" : bstr, ; classical component bytes "pqc" : bstr, ; PQC component bytes ? "params" : map, ; optional algorithm parameters }
The version field serves the migration-first principle: when ML-KEM-768 is eventually superseded, the library can detect legacy keys and apply an automated upgrade path. This design prevents the silent failure mode where an application continues to use a deprecated algorithm because no tooling exists to detect or replace it. V. B ENCHMARK M ETHODOLOGY A. Harness Design All benchmarks share a common harness. Table IV documents every design decision and its rationale.
# Step 1: X25519 keypair x_priv = X25519PrivateKey.generate() x_pub = x_priv.public_key() # Step 2: ML-KEM keypair (separate object) kem = oqs.KeyEncapsulation("ML-KEM-768") kem_pub = kem.generate_keypair() # Step 3: Combined public key serialised manually x_pub_bytes = x_pub.public_bytes_raw() combined_pub = x_pub_bytes + kem_pub # no standard format # Step 4: Encapsulate (receiver side) x_priv_r = X25519PrivateKey.generate() kem_r = oqs.KeyEncapsulation("ML-KEM-768") kem_pub_r = kem_r.generate_keypair() ct_kem, ss_kem = kem_r.encap_secret(kem_pub) ss_x25519 = x_priv_r.exchange(x_pub)
TABLE IV B ENCHMARK H ARNESS D ESIGN D ECISIONS
Parameter
Value
Iterations
3,000
Warmup Outlier trim Timer GC CPU pinning
# Step 5: HKDF combination (algorithm must match sender) hkdf = HKDF(algorithm=SHA256(), length=32, salt=None, info=b"hybrid-kem-v1") shared = hkdf.derive(ss_x25519 + ss_kem) # (serialisation, error handling, version tagging omitted)
The manual implementation raises several correctness questions that quantum-safe resolves by design: What is
Runs
Rationale
Tighter bootstrap CIs vs 1,000; sub-microsecond resolution 100 Eliminates JIT, cold-cache, and import effects 1% Removes OS scheduling spikes; preserves distribution shape time.perf_ Nanosecond resolution; monocounter tonic Disabled Prevents GC pauses skewing samples cores 0–1 Eliminates cross-core migration noise 3 Guards against thermal outlier independent; runs best selected
The trim formula is samples[clip : N − clip] where clip = max(1, ⌊N × 0.01⌋). Python’s garbage collector (gc.disable()) is disabled for the duration of each measurement loop and re-enabled between operations.
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Hybrid KEM Decomposition (ENV-2)
B. Statistical Measures
100
Latency (µs)
We report five statistics for every operation. The median (p50) is the headline figure: for a right-skewed timing distribution with occasional OS scheduling spikes, the median is a more stable estimator than the mean. The 95th percentile (p95) characterises tail latency relevant to SLA design. The Coefficient of Variation (CoV = σ/µ × 100) is our primary timing side-channel proxy. For hypothesis testing, we compute Welch’s two-sample t-test [21] rather than Student’s t-test, because the classical and hybrid timing distributions have different variances. The t-statistic is: x̄B − x̄A t= p 2 (2) sA /nA + s2B /nB
100
80
72
72
60 40 X25519 ML-KEM-768 Python combiner
20 0
keygen
encapsulate
decapsulate
with Welch–Satterthwaite effective degrees of freedom: ν=
(s2A /nA + s2B /nB )2 2 2 (sA /nA ) /(nA − 1) + (s2B /nB )2 /(nB − 1)
Effect size is reported as Cohen’s d [22]: s (nA − 1)s2A + (nB − 1)s2B x̄B − x̄A d= , sp = sp nA + n B − 2
(3)
(4)
Bootstrap 95% confidence intervals follow the percentile method of Efron [23] with B = 2,000 resamples. The interval is constructed from the 2.5th and 97.5th percentiles of the B bootstrap medians. Confidence intervals in this paper are derived from per-run summary statistics (mean, standard deviation) using a normal approximation, labelled accordingly. We note that raw timing samples were not persisted beyond run completion; this approximation introduces no bias in the median estimates or in the Welch t-test, which uses exact summary statistics.
Fig. 4. Stacked bar decomposition of hybrid KEM latency. The Python combiner (HKDF-SHA256, PEM/CBOR serialisation, key wrapping) accounts for 37–64 µs per operation — comparable to or exceeding the underlying cryptographic primitive cost in ENV-2.
docker build -t quantum-safe-bench . docker run --rm --cpuset-cpus="0,1" \ -v "$(pwd)/results:/app/results" \ quantum-safe-bench \ python -X utf8 tests/bench/bench_kem.py \ --with-pqc --iterations 3000 \ --save /app/results/bench_kem.json
Benchmark scripts accept -iterations, -warmup, and -save flags. Saved JSON files contain peroperation mean, standard deviation, median, p95, p99, and CoV. Results are archived in the repository at results/BENCHMARKS.md. The statistical analysis module (tests/bench/bench_stats.py) implements all five statistical measures described above and can be run against any saved JSON file.
C. Test Environments
VI. E VALUATION Two environments were benchmarked on the same physical A. Hybrid KEM Overhead hardware (AMD64 processor, 64-bit Windows 11 host). 1) Decomposition: Table V and Fig. 4 show the three-tier ENV-2 (primary): Docker container running decomposition: X25519 alone (tier ⃝), 1 ML-KEM-768 alone python:3.12-slim (Debian trixie), Linux kernel (tier ⃝), 2 and the full hybrid combiner (tier ⃝). 3 The combiner 6.6.87.2-microsoft-standard-WSL2 under Microsoft overhead is computed as ⃝ 3 −⃝ 1 − ⃝. 2 Hyper-V. liboqs 0.15.0 compiled from source with The full hybrid KEM handshake (keygen + encapsulate + -DOQS_DIST_BUILD=ON, enabling CPUID detection and decapsulate) takes 243 µs in ENV-2. The combiner overhead AVX2/AVX-512 code path selection at runtime. Container CPU- is substantial: 64 µs on keygen and ∼37 µs on encapsulate and pinned to physical cores 0–1 with -cpuset-cpus=“0,1”. decapsulate. This overhead is Python serialisation and HKDF, ENV-1 (comparison): Windows 11 native Python 3.12.7. li- not cryptography. A future optimisation that caches serialised boqs 0.15.0 via the MSYS2 mingw-w64-x86_64-liboqs keys for key-reuse scenarios could reduce total handshake time DLL, which is a conservative generic build without AVX2/AVX- to approximately 195 µs. 512 optimisation. 2) Statistical Significance: We compare the full hybrid ENV-2 is the authoritative environment for all paper claims. handshake (243 µs) against a classical-only X25519 keyENV-1 results quantify the build-flag effect and inform deploy- gen + DH sequence (48 µs) using Welch’s t-test (Eq. (2)). With ment decisions on Windows-based infrastructure. nA = nB = 3,000 samples: t ≈ 1,298, D. Reproducibility Any reviewer can reproduce all results with:
ν ≈ 3,615,
p < 10−300
The hybrid overhead is statistically unambiguous. Cohen’s d ≈ 33.5 indicates that the two distributions do not overlap at
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TABLE V H YBRID KEM D ECOMPOSITION — ENV-2 (D OCKER /L INUX , 3,000 ITER , BEST OF 3)
Tier
Operation
Median
p95
CoV
⃝ 1 X25519
keygen DH exchange
25.33 µs 22.99 µs
29.58 µs 24.07 µs
9.6% 3.0%
⃝ 2 ML-KEM-768
keygen encapsulate decapsulate
10.16 µs 10.89 µs 12.55 µs
10.71 µs 11.07 µs 12.83 µs
4.7% 4.6% 3.9%
⃝ 3 HybridKEM
keygen encapsulate decapsulate
99.89 µs 71.55 µs 71.82 µs
113.57 µs 84.07 µs 82.70 µs
5.3% 6.1% 5.4%
Combiner overhead
keygen encapsulate decapsulate
64.40 µs 37.67 µs 36.28 µs
— — —
— — —
243.26 µs
—
—
Full handshake (⃝ 3 sum)
0.195 0.195 = 2.4% to = 0.5% of the TLS budget. 8 40 At WAN latency (100 ms RTT), the overhead drops below 0.2%. The hybrid PQC overhead is negligible relative to any realistic network latency. B. Signature Overhead Table VI reports signature benchmarks. The full hybrid signature operation (HybridSign keygen + sign + verify) takes 205.38 + 160.71 + 143.94 ≈ 510 µs. The large CoV for ML-DSA-65 sign (51.5%) and its p95/median ratio of 2.4 reflect the rejection sampling loop in FIPS 204 [2] §5.2. This is discussed in detail in Section VI-D. C. Concurrent Load Throughput
Concurrent Hybrid KEM Throughput (ENV-2 primary)
(a) Throughput vs concurrency
3,200
(b) Per-user latency vs concurrency Wall-clock latency (ms)
3,000 2,900 2,800 2,700 2,600
1750
ENV-2 (Docker/Linux) ENV-1 (Windows 11) Ideal (=2,994 ops/s)
3,100
Throughput (ops/s)
all: the difference is 33 pooled standard deviations. This large effect size is expected for a 5× latency increase and does not undermine the production viability argument: the question is whether the overhead is operationally acceptable, not whether it is statistically detectable. 3) Contextualisation Against TLS Budget: A full TLS 1.3 handshake in a LAN or intra-datacenter deployment takes 8– 40 ms [24], [25]. The quantum-safe hybrid overhead above classical X25519 is 243 − 48 = 195 µs = 0.195 ms:
Median (p50) p95
1500 1250 1000 750 500 250 0
100
500
1,000
Concurrent users
5,000
100
500
1,000
Concurrent users
5,000
Fig. 5. (a) Throughput vs concurrency; (b) per-user latency vs concurrency. ENV-2 and ENV-1 show nearly identical throughput despite a 2.4× peroperation latency difference, confirming GIL release.
A further confirmation is that ENV-1 (Windows, 587 µs peroperation) and ENV-2 (Linux, 243 µs) show nearly identical throughput at 5,000 users: 2,842 vs 2,848 ops/s. At high concurrency, the per-operation latency advantage of ENV-2 is completely absorbed by Python thread scheduling overhead, which is OS-independent. This confirms that concurrent throughput is bounded by Python thread management, not by the cryptographic computation. D. Timing Variance Analysis
1) Methodology: The CoV measures relative timing spread Table VII and Fig. 5 show concurrent throughput from 100 across repeated calls with identical inputs but independently to 5,000 simultaneous users. Throughput decreases from 2,994 to 2,848 ops/s (4.9% generated fresh keys per iteration: degradation) as concurrent users increase from 100 to 5,000 — σ CoV = × 100% (5) a 50× load increase. This near-flat throughput profile is strong µ evidence that the GIL is released during C-level ML-KEM where µ and σ are the mean and standard deviation of the operations. The reasoning is straightforward. If the GIL were held during 1%-trimmed timing sample. cryptographic operations, concurrent threads would execute A constant-time implementation produces CoV determined serially. With 5,000 threads each holding the GIL for ∼243 µs entirely by the measurement environment: timer resolution, OS per operation, throughput would collapse to approximately scheduler jitter, and CPU cache state. We use AES-256-GCM, 1/(5,000 × 0.000243) ≈ 0.8 ops/s. We observe 2,848 ops/s a universally accepted constant-time primitive, as the noise — approximately 3,500× higher. The GIL is released during floor reference. Its CoV of 2.1% in ENV-2 is the baseline cryptographic operations. against which all other operations are compared.
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TABLE VI S IGNATURE B ENCHMARKS — ENV-2 (D OCKER /L INUX , 3,000 ITER )
Suite
Operation
Median
p95
CoV
Ed25519 (classical)
sign (32 B) verify (32 B)
29.02 µs 90.81 µs
30.99 µs 96.24 µs
5.5% 2.5%
ML-DSA-65
keygen sign (32 B) verify (32 B)
40.19 µs 85.95 µs 40.11 µs
45.68 µs 207.20 µs 44.56 µs
5.0% 51.5% 5.8%
HybridSign
keygen sign (32 B) verify (32 B)
205.38 µs 160.71 µs 143.94 µs
223.03 µs 284.00 µs 160.74 µs
4.1% 30.2% 4.2%
X.509 Hybrid
HybridCert build verify_cosig
344.05 µs 221.75 µs
490.60 µs 261.35 µs
18.6% 13.6%
TABLE VII C ONCURRENT H YBRID KEM T HROUGHPUT — ENV-2 (D OCKER /L INUX ) AND ENV-1 (W INDOWS 11)
Users
Med. latency
p95
Throughput
CoV
ENV-2 (Docker/Linux) 100 33.4 ms 500 165.8 ms 1,000 337.0 ms 5,000 1,755.9 ms
47.2 ms 212.0 ms 356.1 ms 1,759.8 ms
2,994 ops/s 3,015 ops/s 2,967 ops/s 2,848 ops/s
14.1% 7.3% 3.1% 1.1%
ENV-1 (Windows 11) 100 34.1 ms 500 167.1 ms 1,000 333.5 ms 5,000 1,759.7 ms
40.1 ms 175.1 ms 338.9 ms 1,777.2 ms
2,935 ops/s 2,992 ops/s 2,998 ops/s 2,842 ops/s
6.5% 2.1% 1.2% 1.0%
Our null hypothesis for each operation is: H0 : CoV(operation) ≤ CoV(AES-GCM baseline)
The algorithm uses hedged signing with rejection sampling: the signer generates a random masking vector y, computes a candidate response z, and checks whether z could leak information about the secret key. If the check fails, the process restarts with fresh randomness. The number of iterations follows a geometric distribution with mean ≈1. This timing variation is: 1) Input-independent: The signing key does not influence how many rejection iterations are needed. 2) By specification: FIPS 204 mandates this exact algorithm. 3) Not exploitable: An attacker who measures signing time learns the number of rejection iterations, which depends only on fresh randomness, not on the key or message. The HybridSign sign CoV of 30.2% is intermediate, reflecting the combination of ML-DSA-65 (high-CoV) and Ed25519 (low-CoV) signing in a single call.
Operations with CoV within approximately two percentage points of the baseline (i.e., < 4% in ENV-2) are classified as timing-stable. 2) Results: Fig. 6 and Table VIII present the full CoV analysis. 3) ML-KEM Analysis: ML-KEM-768 decapsulation achieves CoV = 3.9%, just 1.8 percentage points above the AES-GCM noise floor. This is within the Hyper-V vCPU scheduling noise band: AES-GCM itself shows 2.1% CoV in the same environment. The difference (1.8 pp) is smaller than the uncertainty introduced by a single OS scheduling interrupt during a measurement iteration. FIPS 203 specifies ML-KEM with explicit constant-time requirements for all secret-dependent operations. No inputdependent branches exist in the reference implementation for keygen, encapsulation, or decapsulation. The CoV evidence is consistent with this specification, though we note that CoV is a E. Latency Percentile Profile Fig. 7 shows the p50, p95, and p99 latency for each KEM necessary, not sufficient, condition for constant-time behaviour: it cannot rule out cache-timing attacks on public data. Formal operation, providing a complete picture of the tail behaviour verification via dudect [17] or ct-verif [16] applied to the that matters for SLA design. The p50/p95/p99 spread for ML-KEM-768 operations is underlying liboqs C code provides stronger guarantees. 4) ML-DSA Signing: High CoV Is Not a Side-Channel: tight (within 6% across all three percentiles), confirming ML-DSA-65 signing has CoV = 51.5% and p95/median ratio of constant-time behaviour. The HybridKEM operations show 2.4. This is unambiguously high but is an expected and correct wider p95/p99 tails due to the Python serialisation layer, which consequence of FIPS 204 [2] Algorithm 2 (HashML-DSA.Sign). is subject to memory allocator variability.
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TABLE VIII T IMING VARIANCE A NALYSIS — ENV-2 C OV R EFERENCE TABLE
Operation AES-256-GCM enc 1 KB (ref.) Ed25519 verify AES-256-GCM dec 1 KB HKDF-SHA256 ML-KEM-768 decap ML-KEM-768 keygen HybridKEM decap HybridKEM keygen X.509 HybridCert build HybridSign sign ML-DSA-65 sign
∆ baseline
2.1% 2.5% 2.4% 3.4% 3.9% 4.7% 5.9% 5.1% 18.6% 30.2% 51.5%
— +0.4 pp +0.3 pp +1.3 pp +1.8 pp +2.6 pp +3.8 pp +3.0 pp — — —
ENV-2
Noise floor reference Timing-stable Elevated (OS scheduler) Expected high (by design)
AES-256-GCM enc 1 KB (noise floor baseline) AES-256-GCM dec 1 KB HKDF-SHA256
Assessment Noise floor Timing-stable Timing-stable Timing-stable Timing-stable Timing-stable OS scheduler noise OS scheduler noise Contains ML-DSA sign Expected (FIPS 204) Expected (FIPS 204)
Latency Percentile Profile
ENV-2 (Docker/Linux, 3,000 iterations) p50 (median) p95 p99
120 100
Latency (µs)
Timing Stability (CoV)
CoV
80 60 40 20
Ed25519 verify
0
Ed25519 sign ML-KEM-768 decap
X25519 keygen X25519 DH
ML-KEM keygen
ML-KEM encap
ML-KEM decap
HybridKEM keygen
HybridKEM encap
HybridKEM decap
Fig. 7. Latency percentile profile (p50, p95, p99) for all KEM operations in ENV-2. The tight p50/p95/p99 clustering for ML-KEM operations confirms constant-time behaviour. X25519 keygen shows wider spread due to initial OS memory mapping on first call.
ML-KEM-768 encap ML-KEM-768 keygen HybridKEM decap
600
HybridKEM keygen
500
Latency (µs)
HybridKEM encap HybridSign verify X.509 HybridCert verify
300
0
10
20
30
40
50
2.7× 2.7×
200
0
HybridSign sign ML-DSA-65 sign (rejection sampling)
ENV-1 Windows 11 ENV-2 Docker/Linux
4.5×
400
100
X.509 HybridCert build
ENV-1 (Windows 11) vs ENV-2 (Docker/Linux) Same Hardware Speedup attributable to -DOQS_DIST_BUILD=ON AVX2/AVX-512 code paths 2.4×
2.0×
4.0×
6.2×
6.0×
4.5×
ML-KEM keygen
ML-KEM encap
ML-KEM HybridKEM HybridKEM HybridKEM Full KEM ML-DSA decap keygen encap decap handshake keygen
2.7×
ML-DSA sign
ML-DSA verify
Fig. 8. ENV-1 (Windows 11) vs ENV-2 (Docker/Linux) on the same hardware. Speedups (orange labels) range from 2.0× to 6.2×. The 6.2× ML-KEM keygen speedup is attributable entirely to AVX2/AVX-512 code paths enabled by -DOQS_DIST_BUILD=ON.
Coefficient of Variation (%)
Fig. 6. CoV for all benchmarked operations (ENV-2). The vertical dashed line marks the AES-256-GCM noise floor (2.1%). Green bars are timing-stable; amber bars are elevated but attributable to OS scheduler noise; red bars are expected high-CoV by cryptographic design.
F. Cross-Environment Comparison Table IX and Fig. 8 compare ENV-1 and ENV-2 on identical hardware. The 6.2× raw ML-KEM keygen speedup reflects a single build decision: the -DOQS_DIST_BUILD=ON cmake flag enables CPUID detection at runtime, allowing liboqs to
select AVX2/AVX-512 lattice arithmetic routines on supported hardware. The MSYS2 DLL used in ENV-1 is a conservative generic build without these paths. The speedup is a build configuration effect, not an OS effect. Organisations deploying on Linux servers that compile liboqs from source automatically get the AVX2/AVX-512 speedup. The throughput convergence at high concurrency (2,842 vs 2,848 ops/s at 5,000 users) confirms that per-operation latency differences disappear at scale because Python thread scheduling overhead dominates.
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TABLE IX C ROSS -E NVIRONMENT C OMPARISON — S AME H ARDWARE , D IFFERENT LIBOQS B UILDS
Operation ML-KEM-768 keygen ML-KEM-768 encap ML-KEM-768 decap HybridKEM keygen HybridKEM encap Full KEM handshake ML-DSA-65 keygen ML-DSA-65 sign Throughput @ 5,000 u
VII. D ISCUSSION A. Limitations
ENV-1 (Windows)
ENV-2 (Linux)
Speedup
62.70 µs 64.90 µs 56.65 µs 267.50 µs 194.80 µs 587.20 µs 161.30 µs 382.85 µs 2,842 ops/s
10.16 µs 10.89 µs 12.55 µs 99.89 µs 71.55 µs 243.05 µs 40.19 µs 85.95 µs 2,848 ops/s
6.2× 6.0× 4.5× 2.7× 2.7× 2.4× 4.0× 4.5× ≈1×
where the same hybrid public key is reused across many session establishments, caching the serialised key and skipping repeated serialisation could reduce keygen overhead from 99 µs to approximately 35 µs — a 2.8× improvement with no security trade-off. Windows and non-Linux deployments. The 587 µs full handshake in ENV-1 is dominated by the unoptimised MSYS2 DLL. Deploying on Linux or building liboqs from source with -DOQS_DIST_BUILD=ON delivers the 243 µs figure. Docker provides a portable path to the optimised build on any operating system. Migration workflow integration. The qs-audit CLI scanner can be integrated into CI/CD pipelines to detect new classical cryptography imports as they are introduced. Combined with the companion QSA tool [11] for deeper static analysis, this provides continuous visibility into the PQC migration status of a codebase.
Single physical host. All benchmarks were collected on one machine. Absolute latency figures are hardware-specific. The relative relationships — combiner overhead fraction, ENV1/ENV-2 speedup ratio, concurrency scaling — are expected to generalise to comparable AMD64 hardware. CoV is not a constant-time proof. The CoV analysis detects timing variation correlated with execution variation across calls, but cannot distinguish variation caused by secret-dependent branching from variation caused by cache effects on public data. A formal constant-time proof requires tools like ct-verif [16] or dudect [17] applied to the underlying C implementation. Bootstrap CI from summary statistics. Raw timing samples were not persisted after each benchmark run; bootstrap confidence intervals are derived from stored mean and standard deviation via a normal approximation. The Welch t-test and Cohen’s d use exact stored statistics and are not affected by C. Independent Researcher Considerations this approximation. This work was conducted without institutional affiliation. WASM target not yet released. Principle P2 (backend The benchmark methodology is fully reproducible from public agnostic) is partially realised: the liboqs and RustCrypto infrastructure (Docker, Python, liboqs from source). The library backends are functional, but the WASM target for browser code, tests, and benchmark scripts are released in their entirety. deployment has not been published. This is planned for We rely entirely on the reproducibility of the results and the version 0.2. clarity of the methodology for credibility, not on institutional SLH-DSA not yet implemented. FIPS 205 (SLH-DSA) is authority. The double-blind review process at IEEE TIFS means not included in the current library. It is planned; no timeline that affiliation does not directly affect the review outcome. commitment is made here. All library evaluation scores in the gap analysis matrix Gap analysis scores. The production-readiness scores are (Fig. 1) are derived from public documentation, source derived from public documentation, source code, and package code, and PyPI/npm/crates.io package metadata accessed metadata. Library maintainers may disagree with specific scores, in March 2026. Readers can reproduce the evaluation by particularly in the Partial category where the boundary with consulting the same sources. None and Full involves judgment. All scoring decisions are documented and publicly reproducible. VIII. R ELATED W ORK A. PQC Performance Evaluation B. Practical Deployment Implications Most PQC performance work targets algorithm-level benchAPI server (5,000 concurrent connections). The hybrid marks on embedded hardware. pqm4 [26] benchmarks NIST KEM adds approximately 195 µs of computation overhead per candidates on ARM Cortex-M4. PQClean [27] provides clean new TLS session. A server establishing 2,848 new sessions per reference implementations for reproducibility. Neither addresses second consumes roughly one additional CPU core for hybrid the production-level concerns of hybrid construction, Python PQC computation versus classical-only operation. For most bindings, or concurrent throughput on server hardware. applications this is acceptable. Paquin et al. [28] and Stebila et al. [25] benchmark PQC Key caching optimisation. The combiner overhead (64 µs on algorithms in TLS. Both focus on network-level effects and Ckeygen) reveals an optimisation opportunity: for deployments based implementations. Sosnowski et al. [24] provide the most
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recent layered TLS analysis confirming that the TLS handshake layer is algorithm-neutral; our 243 µs figure is consistent with their finding that PQC primitive latency does not dominate TLS round-trip time.
IX. C ONCLUSION The PQC algorithm standardisation problem was solved in August 2024. The production deployment problem is not yet solved. This paper quantified the gap across nine libraries and eight dimensions, finding critical shortfalls in hybrid KEM support (11%), migration tooling (22%), and protocol B. Cryptographic Library Surveys integration (33%). Nejatollahi et al. [29] survey lattice-based implementations We presented quantum-safe, a Python library that closes but focus on hardware accelerators and embedded systems. all three gaps. A full X25519 + ML-KEM-768 handshake takes No prior work conducts a multi-library production-readiness 243 µs under Docker/Linux — 0.5–2.5% of a typical TLS 1.3 evaluation with a formal rubric across eight dimensions. The round-trip budget. At 5,000 concurrent users, throughput holds gap analysis in this paper fills that gap. at 2,848 ops/s with only 4.9% degradation, confirming GIL release and true concurrency in liboqs. ML-KEM-768 decapsulation achieves CoV = 3.9%, within the AES-256-GCM noise C. API Usability in Cryptography floor of 2.1%, consistent with the constant-time requirements The relationship between cryptographic API design and of FIPS 203. ML-DSA-65 signing exhibits CoV = 51.5% by security outcomes is well established. Georgiev et al. [7] design — a consequence of FIPS 204 rejection sampling, not demonstrate systematic SSL certificate validation failures in a timing vulnerability. Beyond the library itself, this paper introduces CoV as non-browser software caused by API design that made the a practical first-order timing side-channel screen for PQC insecure path easier than the correct path. Lazar et al. [8] study library evaluation, and presents the first production-readiness 269 CVEs in cryptographic software and find that the largest matrix for the PQC library ecosystem. Combined with the category of vulnerabilities is misuse of cryptographic APIs. Quantum-Safe Auditor [11] for automated detection of classical Our API design study (Section IV) extends this analysis to cryptography in codebases, the tools presented here and in the hybrid PQC domain, quantifying the LOC difference as the companion paper provide a complete Python-native PQC a proxy for misuse risk, and arguing that a hybrid-by-default migration toolchain. design structurally prevents the most common failure mode. The library, 415 tests, and complete benchmark harness are released as open-source software under the Apache 2.0 licence. D. Timing Side-Channel Detection Any reviewer can reproduce every number in this paper with a Reparaz et al. [17] introduce dudect for constant-time single Docker command. The hybrid PQC transition in Python detection. Almeida et al. [16] provide formal verification via is tractable. The performance is there. The API is there. The ct-verif. Both tools operate at the binary or hardware level and barrier is awareness, not capability. The library is available on are not directly applicable to Python library evaluation at the PyPI as quantum-safe-py. level of abstraction we are working at. Our CoV methodology R EFERENCES occupies a different point in the design space: applicable to Institute of Standards and Technology, “Module-Lattice-Based high-level library evaluation without hardware access or source- [1] National Key-Encapsulation Mechanism Standard,” NIST, Tech. Rep. FIPS 203, level analysis, at the cost of being a necessary rather than 2024. [Online]. Available: https://doi.org/10.6028/NIST.FIPS.203 [2] ——, “Module-Lattice-Based Digital Signature Standard,” NIST, Tech. sufficient condition for constant-time behaviour. E. Hybrid Certificate Standards Ounsworth et al. [30] standardise composite signatures for Internet PKI. The quantum-safe X.509 hybrid certificate implementation follows this draft. No prior Python library implements the draft, making quantum-safe the first Python implementation of composite X.509 certificates. F. Static Analysis for PQC Migration The companion Quantum-Safe Auditor [11] uses static analysis to detect classical cryptography in Python codebases, achieves precision P = 71.98% and recall R = 100% on a labelled CVE dataset, and introduces VQE (Vulnerability Quantum-impact Estimation) threat scoring. Together, quantum-safe and QSA form a complete toolchain: QSA identifies what needs to migrate and assesses urgency; quantum-safe provides the implementation to migrate to.
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