Hawkynt

NTRU

NTRU, the truncated polynomial ring lattice scheme, in the key encapsulation form submitted to round 3 of the NIST post-quantum process. Works over Z[x]/(x^n - 1): the public key is g/f for a short f and a fixed-weight g, and decapsulation recovers the message by multiplying by f and reducing modulo 3. The three NTRU-HPS parameter sets are implemented; NTRU-HRSS is not.

Properties

Property Value
Category Asymmetric Ciphers
Sub-category Post-Quantum Key Encapsulation
Security status 🎓 Educational Only
Complexity Expert
Inventor Jeffrey Hoffstein, Jill Pipher, Joseph Silverman
Year 1996
Origin 🇺🇸 United States
Source algorithms/asymmetric/ntru.js

Parameters

Parameter Supported values
Key sizes 509 bytes (4072 bits); 677 bytes (5416 bits); 821 bytes (6568 bits)

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

References

Test vectors

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

Vector 1 — NTRU PQCkemKAT_935.rsp record 0: expanded seed to public key (ntruhps2048509)

Field Value
keyGeneration Yes
parameterSet ntruhps2048509
keyGenerationOutput publicKey
input 7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d b505d7cfad1b497499323c8686325e47 92f267aafa3f87ca60d01cb54f29202a … (2413 bytes; the full value is in the source)
expected ead4d1aff780d5aeaf590d73b44b01c8 e45bc3b9eec0b90290c7bceed33849f3 fdd6ba3d2c34ef5652fcab9f76930ee4 9b448ac494dfbc182a78f10dd70014ef … (699 bytes; the full value is in the source)

Vector 2 — NTRU PQCkemKAT_935.rsp record 0: expanded seed and rejection key to secret key

Field Value
keyGeneration Yes
parameterSet ntruhps2048509
keyGenerationOutput privateKey
rejectionKey 1dab0317f0ce5a41ce7672953d301cffd710f80beac3f19c0e96e68cf8fdab81
input 7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d b505d7cfad1b497499323c8686325e47 92f267aafa3f87ca60d01cb54f29202a … (2413 bytes; the full value is in the source)
expected d067d98f0055e2c3deef1076bbb755af d065112c85c46e6c350655d9625073e9 4e4528c053e720206cdb780a61ad5120 c498a4cd3e60c334d8702f0f79d81418 … (935 bytes; the full value is in the source)

Vector 3 — NTRU PQCkemKAT_935.rsp record 0: encapsulation ciphertext

Field Value
publicKey ead4d1aff780d5aeaf590d73b44b01c8 e45bc3b9eec0b90290c7bceed33849f3 fdd6ba3d2c34ef5652fcab9f76930ee4 9b448ac494dfbc182a78f10dd70014ef … (699 bytes; the full value is in the source)
encapsulationOutput ciphertext
input 1b70b064d09425d8431417974c8c02f7 8a4f61b3b475837c51a6aa1ec4850ac3 5c4445d03bbe358399bacae1b776ae48 6181755d2675c5e64222e63fa342b1de … (2413 bytes; the full value is in the source)
expected b934872b0469349cc3c88ae57af98d6e 2330e666ce889e3707523224891c0685 933f0314b28e1d6e1c3559c8695ef26a b6ba3af701f63fe2b0642e896d17f71e … (699 bytes; the full value is in the source)

Vector 4 — NTRU PQCkemKAT_935.rsp record 0: encapsulated shared secret

Field Value
publicKey ead4d1aff780d5aeaf590d73b44b01c8 e45bc3b9eec0b90290c7bceed33849f3 fdd6ba3d2c34ef5652fcab9f76930ee4 9b448ac494dfbc182a78f10dd70014ef … (699 bytes; the full value is in the source)
encapsulationOutput sharedSecret
input 1b70b064d09425d8431417974c8c02f7 8a4f61b3b475837c51a6aa1ec4850ac3 5c4445d03bbe358399bacae1b776ae48 6181755d2675c5e64222e63fa342b1de … (2413 bytes; the full value is in the source)
expected 176fdbb009dd3f848b365ab7f18d9c0c91721931c8594c2c6f043c8600791a6c

Vector 5 — NTRU PQCkemKAT_935.rsp record 0: decapsulation recovers the shared secret

Field Value
inverse Yes
privateKey d067d98f0055e2c3deef1076bbb755af d065112c85c46e6c350655d9625073e9 4e4528c053e720206cdb780a61ad5120 c498a4cd3e60c334d8702f0f79d81418 … (935 bytes; the full value is in the source)
input b934872b0469349cc3c88ae57af98d6e 2330e666ce889e3707523224891c0685 933f0314b28e1d6e1c3559c8695ef26a b6ba3af701f63fe2b0642e896d17f71e … (699 bytes; the full value is in the source)
expected 176fdbb009dd3f848b365ab7f18d9c0c91721931c8594c2c6f043c8600791a6c

Vector 6 — NTRU PQCkemKAT_935.rsp record 0: the recovered secret is the published one

Field Value
inverse Yes
privateKey d067d98f0055e2c3deef1076bbb755af d065112c85c46e6c350655d9625073e9 4e4528c053e720206cdb780a61ad5120 c498a4cd3e60c334d8702f0f79d81418 … (935 bytes; the full value is in the source)
sharedSecret 176fdbb009dd3f848b365ab7f18d9c0c91721931c8594c2c6f043c8600791a6c
input b934872b0469349cc3c88ae57af98d6e 2330e666ce889e3707523224891c0685 933f0314b28e1d6e1c3559c8695ef26a b6ba3af701f63fe2b0642e896d17f71e … (699 bytes; the full value is in the source)
expected 01

Vector 7 — NTRU PQCkemKAT_935.rsp record 0: a modified ciphertext must not decapsulate to the published secret

Field Value
inverse Yes
privateKey d067d98f0055e2c3deef1076bbb755af d065112c85c46e6c350655d9625073e9 4e4528c053e720206cdb780a61ad5120 c498a4cd3e60c334d8702f0f79d81418 … (935 bytes; the full value is in the source)
sharedSecret 176fdbb009dd3f848b365ab7f18d9c0c91721931c8594c2c6f043c8600791a6c
input b934872b0469349cc3c88ae57af98d6e 2331e666ce889e3707523224891c0685 933f0314b28e1d6e1c3559c8695ef26a b6ba3af701f63fe2b0642e896d17f71e … (699 bytes; the full value is in the source)
expected 00

Vector 8 — NTRU PQCkemKAT_935.rsp: record 0’s ciphertext under record 1’s secret key must not recover record 0’s secret

Field Value
inverse Yes
privateKey 22627b1edc147ac45554273783748c64 731652db85d80c6fd5223f06d733d038 b0075b54052c7342624d879b3bd998a7 e2b51682acdd0b81c876e91bd14c9697 … (935 bytes; the full value is in the source)
sharedSecret 176fdbb009dd3f848b365ab7f18d9c0c91721931c8594c2c6f043c8600791a6c
input b934872b0469349cc3c88ae57af98d6e 2330e666ce889e3707523224891c0685 933f0314b28e1d6e1c3559c8695ef26a b6ba3af701f63fe2b0642e896d17f71e … (699 bytes; the full value is in the source)
expected 00

Vector 9 — NTRU PQCkemKAT_1234.rsp record 0: expanded seed to public key (ntruhps2048677)

Field Value
keyGeneration Yes
parameterSet ntruhps2048677
keyGenerationOutput publicKey
input 7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d b505d7cfad1b497499323c8686325e47 92f267aafa3f87ca60d01cb54f29202a … (3211 bytes; the full value is in the source)
expected 57eee113d3506f111ca9f253d1035c2a ccf68212488724fa9eb144f5d3532e69 14dfde79861d843a26f0a8d43371ee27 3d53b90879fd8c2f985f53c59b338784 … (930 bytes; the full value is in the source)

Vector 10 — NTRU PQCkemKAT_1234.rsp record 0: decapsulation recovers the shared secret (ntruhps2048677)

Field Value
inverse Yes
privateKey d067d98f0055e2c3deef1076bbb755af d065112c85c46e6c350655d9625073e9 4e4528c053e720206cdb780a61ad5120 c498a4cd3e60c334d8702f0f79d81418 … (1234 bytes; the full value is in the source)
input a1d9ce5958daca0f9799c9ae5d4395cb 6368371bb9f93f906dae552f529b1ca5 dfef9bfcbced6c74f3f189f1a165ee30 a90b246dc729fa08d14dc82647e2eddc … (930 bytes; the full value is in the source)
expected 49ac4d5d1634c6affa5a08c2b228ec806d7870b1517990728663d2d8bbc184f2

Vector 11 — NTRU PQCkemKAT_1590.rsp record 0: expanded seed to public key (ntruhps4096821)

Field Value
keyGeneration Yes
parameterSet ntruhps4096821
keyGenerationOutput publicKey
input 7c9935a0b07694aa0c6d10e4db6b1add 2fd81a25ccb148032dcd739936737f2d b505d7cfad1b497499323c8686325e47 92f267aafa3f87ca60d01cb54f29202a … (3895 bytes; the full value is in the source)
expected 5c613a66185d153995ed00f800682f17 cb11d38146a07081bceb403b42de8bea 93af382e8402e7b68a9dd46a1a208a05 79f650a589452b78890d0e0be79929e8 … (1230 bytes; the full value is in the source)

Vector 12 — NTRU PQCkemKAT_1590.rsp record 0: decapsulation recovers the shared secret (ntruhps4096821)

Field Value
inverse Yes
privateKey d067d98f0055e2c3deef1076bbb755af d065112c85c46e6c350655d9625073e9 4e4528c053e720206cdb780a61ad5120 c498a4cd3e60c334d8702f0f79d81418 … (1590 bytes; the full value is in the source)
input c31a29034aeef0469718549dff4f8380 23a19aba55bfb249b4059d37f879219b 0a22f17dab3ff16ba05b3dfd44e9fd43 118a41d4317ea35407aae247e31e90cd … (1230 bytes; the full value is in the source)
expected 293992000dc288e8152f9451f06dd835c75ea008662bace0fb97a97b3afb54e4

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