Hawkynt

HQC

Hamming Quasi-Cyclic, the code-based key encapsulation mechanism NIST selected in March 2025 as its backup to ML-KEM. The public key is a random quasi-cyclic h with the syndrome x + h y of a low weight secret; a message is carried by a concatenated Reed-Solomon and duplicated Reed-Muller codeword masked by that syndrome, so decryption is a decoding problem only the secret makes tractable. All three round 4 parameter sets are implemented and verified against the submission’s own Known Answer Tests.

Properties

Property Value
Category Asymmetric Ciphers
Sub-category Post-Quantum Key Encapsulation
Security status 🎓 Educational Only
Complexity Expert
Inventor Carlos Aguilar Melchor, Nicolas Aragon, Slim Bettaieb, Loic Bidoux, Olivier Blazy, Jean-Christophe Deneuville, Philippe Gaborit, Edoardo Persichetti, Gilles Zemor
Year 2017
Origin 🇫🇷 France
Source algorithms/asymmetric/hqc.js

Parameters

Parameter Supported values
Key sizes 128 bytes (1024 bits); 192 bytes (1536 bits); 256 bytes (2048 bits)

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

References

Test vectors

15 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — HQC-128 hqc-128_kat.rsp record 0: seed to public key

Field Value
keyGeneration Yes
parameterSet hqc-128
keyGenerationOutput publicKey
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 5009c2e5c95aa03dcbf09f69c9529da9 7f496712e083181f51f06aa7e7f73314 9cce4bd1a190a9b5cd376f2400ea478b 9416b4969034f791bb2aa09eaa62b828 … (2249 bytes; the full value is in the source)

Vector 2 — HQC-128 hqc-128_kat.rsp record 0: seed to secret key

Field Value
keyGeneration Yes
parameterSet hqc-128
keyGenerationOutput privateKey
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 9ede2a61c7f15adc29dda6cb30e086e2 d67b86fec8172369f3953548d3bd1474 94c86c53da5ab23a5009c2e5c95aa03d cbf09f69c9529da97f496712e083181f … (2289 bytes; the full value is in the source)

Vector 3 — HQC-128 hqc-128_kat.rsp record 0: seed to ciphertext

Field Value
keyGeneration Yes
parameterSet hqc-128
keyGenerationOutput ciphertext
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected d02633bd49ce27afe750e0582f8152ee 484e1a2787c0277ed436244616c9a0d5 71e94b107db13da59528960e2b2c469b 735a6c20f60bb2e7c1b2046ebddf82ba … (4497 bytes; the full value is in the source)

Vector 4 — HQC-128 hqc-128_kat.rsp record 0: seed to encapsulated shared secret

Field Value
keyGeneration Yes
parameterSet hqc-128
keyGenerationOutput sharedSecret
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected dab185fe3faf252eff8f563ee157c709 43fadbf11dd493fb561e70f22d4dc0e7 0a207e084109d96f1a7da36ea4e661ce 2ae9907632d74a8f45dfb6971c4124f6

Vector 5 — HQC-128 hqc-128_kat.rsp record 0: decapsulating its own ciphertext returns the published secret

Field Value
keyGeneration Yes
parameterSet hqc-128
keyGenerationOutput decapsulatedSecret
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected dab185fe3faf252eff8f563ee157c709 43fadbf11dd493fb561e70f22d4dc0e7 0a207e084109d96f1a7da36ea4e661ce 2ae9907632d74a8f45dfb6971c4124f6

Vector 6 — HQC-128 hqc-128_kat.rsp record 0: decapsulation of the published ciphertext under the published secret key

Field Value
inverse Yes
privateKey 9ede2a61c7f15adc29dda6cb30e086e2 d67b86fec8172369f3953548d3bd1474 94c86c53da5ab23a5009c2e5c95aa03d cbf09f69c9529da97f496712e083181f … (2289 bytes; the full value is in the source)
input d02633bd49ce27afe750e0582f8152ee 484e1a2787c0277ed436244616c9a0d5 71e94b107db13da59528960e2b2c469b 735a6c20f60bb2e7c1b2046ebddf82ba … (4497 bytes; the full value is in the source)
expected dab185fe3faf252eff8f563ee157c709 43fadbf11dd493fb561e70f22d4dc0e7 0a207e084109d96f1a7da36ea4e661ce 2ae9907632d74a8f45dfb6971c4124f6

Vector 7 — HQC-128 hqc-128_kat.rsp record 0: the recovered secret is the published one

Field Value
inverse Yes
privateKey 9ede2a61c7f15adc29dda6cb30e086e2 d67b86fec8172369f3953548d3bd1474 94c86c53da5ab23a5009c2e5c95aa03d cbf09f69c9529da97f496712e083181f … (2289 bytes; the full value is in the source)
sharedSecret dab185fe3faf252eff8f563ee157c709 43fadbf11dd493fb561e70f22d4dc0e7 0a207e084109d96f1a7da36ea4e661ce 2ae9907632d74a8f45dfb6971c4124f6
input d02633bd49ce27afe750e0582f8152ee 484e1a2787c0277ed436244616c9a0d5 71e94b107db13da59528960e2b2c469b 735a6c20f60bb2e7c1b2046ebddf82ba … (4497 bytes; the full value is in the source)
expected 01

Vector 8 — HQC-128 hqc-128_kat.rsp record 0: a modified ciphertext must not decapsulate to the published secret

Field Value
inverse Yes
privateKey 9ede2a61c7f15adc29dda6cb30e086e2 d67b86fec8172369f3953548d3bd1474 94c86c53da5ab23a5009c2e5c95aa03d cbf09f69c9529da97f496712e083181f … (2289 bytes; the full value is in the source)
sharedSecret dab185fe3faf252eff8f563ee157c709 43fadbf11dd493fb561e70f22d4dc0e7 0a207e084109d96f1a7da36ea4e661ce 2ae9907632d74a8f45dfb6971c4124f6
input d12633bd49ce27afe750e0582f8152ee 484e1a2787c0277ed436244616c9a0d5 71e94b107db13da59528960e2b2c469b 735a6c20f60bb2e7c1b2046ebddf82ba … (4497 bytes; the full value is in the source)
expected 00

Vector 9 — HQC-128 hqc-128_kat.rsp: record 0’s ciphertext under record 1’s secret key must not recover record 0’s secret

Field Value
inverse Yes
privateKey 35e7ff98c3905928348699356538d3da 488ad91c0c81bfd72bb3de8e91b1b478 e39c57579d11f20b2237fa9ed7968133 4bcd1d0faf36cf1d8b00ed17cccd8fd1 … (2289 bytes; the full value is in the source)
sharedSecret dab185fe3faf252eff8f563ee157c709 43fadbf11dd493fb561e70f22d4dc0e7 0a207e084109d96f1a7da36ea4e661ce 2ae9907632d74a8f45dfb6971c4124f6
input d02633bd49ce27afe750e0582f8152ee 484e1a2787c0277ed436244616c9a0d5 71e94b107db13da59528960e2b2c469b 735a6c20f60bb2e7c1b2046ebddf82ba … (4497 bytes; the full value is in the source)
expected 00

Vector 10 — HQC-192 hqc-192_kat.rsp record 0: seed to public key

Field Value
keyGeneration Yes
parameterSet hqc-192
keyGenerationOutput publicKey
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 5009c2e5c95aa03dcbf09f69c9529da9 7f496712e083181f51f06aa7e7f73314 9cce4bd1a190a9b5b42558a7328aa100 87044e5c9017402c8af07ffaaace70a7 … (4522 bytes; the full value is in the source)

Vector 11 — HQC-192 hqc-192_kat.rsp record 0: seed to encapsulated shared secret

Field Value
keyGeneration Yes
parameterSet hqc-192
keyGenerationOutput sharedSecret
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 857169e8d11add62b7072ee33c4a4a6a 229e2477598cc6c534bf61523d7a5b5e 04ea03760c3527de11baa9e31da2bf38 2ddc9d3ec5c5e6ba938f7f8ea0d6af7f

Vector 12 — HQC-192 hqc-192_kat.rsp record 0: decapsulating its own ciphertext returns the published secret

Field Value
keyGeneration Yes
parameterSet hqc-192
keyGenerationOutput decapsulatedSecret
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 857169e8d11add62b7072ee33c4a4a6a 229e2477598cc6c534bf61523d7a5b5e 04ea03760c3527de11baa9e31da2bf38 2ddc9d3ec5c5e6ba938f7f8ea0d6af7f

Vector 13 — HQC-256 hqc-256_kat.rsp record 0: seed to public key

Field Value
keyGeneration Yes
parameterSet hqc-256
keyGenerationOutput publicKey
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 5009c2e5c95aa03dcbf09f69c9529da9 7f496712e083181f51f06aa7e7f73314 9cce4bd1a190a9b53ff761db49c50bb1 a8231631e4946eec090707fd6cb8a5ad … (7245 bytes; the full value is in the source)

Vector 14 — HQC-256 hqc-256_kat.rsp record 0: seed to encapsulated shared secret

Field Value
keyGeneration Yes
parameterSet hqc-256
keyGenerationOutput sharedSecret
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 8bdd2446f939f77a5e6075b0244a804a 33d3ed5978f8055f29f4431629cb3311 25fb1cf05b45f0d6723a915ecd9bee2e f7b0f362093a20464f8bdd56282ac9be

Vector 15 — HQC-256 hqc-256_kat.rsp record 0: decapsulating its own ciphertext returns the published secret

Field Value
keyGeneration Yes
parameterSet hqc-256
keyGenerationOutput decapsulatedSecret
input 42c667a186390f26c8f024d31d5fe3d2 0145bc2fccf26c865e20df7626cef09e 4d9eadd263d95ede934a74b3721eaab0
expected 8bdd2446f939f77a5e6075b0244a804a 33d3ed5978f8055f29f4431629cb3311 25fb1cf05b45f0d6723a915ecd9bee2e f7b0f362093a20464f8bdd56282ac9be

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