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# Kyber
- **Algorithm type**: Key encapsulation mechanism.
- **Main cryptographic assumption**: Module LWE+R with base ring Z[x]/(3329, x^256+1).
- **Principal submitters**: Peter Schwabe.
- **Auxiliary submitters**: Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Gregor Seiler, Damien Stehlé.
- **Authors' website**: https://pq-crystals.org/
- **Specification version**: NIST Round 3 submission.
- **Primary Source**<a name="primary-source"></a>:
- **Source**: https://github.com/pq-crystals/kyber/commit/441c0519a07e8b86c8d079954a6b10bd31d29efc with copy_from_upstream patches
- **Implementation license (SPDX-Identifier)**: CC0-1.0 or Apache-2.0
- **Optimized Implementation sources**: https://github.com/pq-crystals/kyber/commit/441c0519a07e8b86c8d079954a6b10bd31d29efc with copy_from_upstream patches
- **oldpqclean-aarch64**:<a name="oldpqclean-aarch64"></a>
- **Source**: https://github.com/PQClean/PQClean/commit/8e220a87308154d48fdfac40abbb191ac7fce06a with copy_from_upstream patches
- **Implementation license (SPDX-Identifier)**: CC0-1.0 and (CC0-1.0 or Apache-2.0) and (CC0-1.0 or MIT) and MIT
- **Formally-verified Implementation sources**:
- **libjade**:<a name="libjade"></a>
- **Source**: https://github.com/formosa-crypto/libjade/tree/release/2023.05-2 with copy_from_upstream patches
- **Implementation license (SPDX-Identifier)**: CC0-1.0 OR Apache-2.0
## Parameter set summary
| Parameter set | Parameter set alias | Security model | Claimed NIST Level | Public key size (bytes) | Secret key size (bytes) | Ciphertext size (bytes) | Shared secret size (bytes) |
|:---------------:|:----------------------|:-----------------|---------------------:|--------------------------:|--------------------------:|--------------------------:|-----------------------------:|
| Kyber512 | NA | IND-CCA2 | 1 | 800 | 1632 | 768 | 32 |
| Kyber768 | NA | IND-CCA2 | 3 | 1184 | 2400 | 1088 | 32 |
| Kyber1024 | NA | IND-CCA2 | 5 | 1568 | 3168 | 1568 | 32 |
## Kyber512 implementation characteristics
| Implementation source | Identifier in upstream | Supported architecture(s) | Supported operating system(s) | CPU extension(s) used | No branching-on-secrets claimed? | No branching-on-secrets checked by valgrind? | Large stack usage?‡ |
|:-----------------------------------------:|:-------------------------|:----------------------------|:--------------------------------|:------------------------|:-----------------------------------|:-----------------------------------------------|:----------------------|
| [Primary Source](#primary-source) | ref | All | All | None | True | True | False |
| [Primary Source](#primary-source) | avx2 | x86\_64 | Linux,Darwin | AVX2,BMI2,POPCNT | True | True | False |
| [oldpqclean-aarch64](#oldpqclean-aarch64) | aarch64 | ARM64\_V8 | Linux,Darwin | None | True | False | False |
| [libjade](#libjade) | ref | x86\_64 | Linux,Darwin | None | True | False | False |
| [libjade](#libjade) | avx2 | x86\_64 | Linux,Darwin | AVX2,BMI2,POPCNT | True | False | False |
Are implementations chosen based on runtime CPU feature detection? **Yes**.
‡For an explanation of what this denotes, consult the [Explanation of Terms](#explanation-of-terms) section at the end of this file.
## Kyber768 implementation characteristics
| Implementation source | Identifier in upstream | Supported architecture(s) | Supported operating system(s) | CPU extension(s) used | No branching-on-secrets claimed? | No branching-on-secrets checked by valgrind? | Large stack usage? |
|:-----------------------------------------:|:-------------------------|:----------------------------|:--------------------------------|:------------------------|:-----------------------------------|:-----------------------------------------------|:---------------------|
| [Primary Source](#primary-source) | ref | All | All | None | True | True | False |
| [Primary Source](#primary-source) | avx2 | x86\_64 | Linux,Darwin | AVX2,BMI2,POPCNT | True | True | False |
| [oldpqclean-aarch64](#oldpqclean-aarch64) | aarch64 | ARM64\_V8 | Linux,Darwin | None | True | False | False |
| [libjade](#libjade) | ref | x86\_64 | Linux,Darwin | None | True | False | False |
| [libjade](#libjade) | avx2 | x86\_64 | Linux,Darwin | AVX2,BMI2,POPCNT | True | False | False |
Are implementations chosen based on runtime CPU feature detection? **Yes**.
## Kyber1024 implementation characteristics
| Implementation source | Identifier in upstream | Supported architecture(s) | Supported operating system(s) | CPU extension(s) used | No branching-on-secrets claimed? | No branching-on-secrets checked by valgrind? | Large stack usage? |
|:-----------------------------------------:|:-------------------------|:----------------------------|:--------------------------------|:------------------------|:-----------------------------------|:-----------------------------------------------|:---------------------|
| [Primary Source](#primary-source) | ref | All | All | None | True | True | False |
| [Primary Source](#primary-source) | avx2 | x86\_64 | Linux,Darwin | AVX2,BMI2,POPCNT | True | True | False |
| [oldpqclean-aarch64](#oldpqclean-aarch64) | aarch64 | ARM64\_V8 | Linux,Darwin | None | True | False | False |
Are implementations chosen based on runtime CPU feature detection? **Yes**.
## Explanation of Terms
- **Large Stack Usage**: Implementations identified as having such may cause failures when running in threads or in constrained environments.