Lattice Reduction for Modules, or How to Reduce ModuleSVP to ModuleSVP

Mukherjee, Tamalika; Stephens-Davidowitz, Noah

doi:10.1007/978-3-030-56880-1_8

“…In particular, a 2012 work by Langlois and Stehle ´ [182] provides a relatively tight reduction from worst-case Module-SIVP to average-case Module-LWE. Additional results have given evidence that, roughly speaking, transitioning from rank one (i.e., Ring-LWE) to constant rank (i.e., Module-LWE) is likely to increase performance and unlikely to sacrifice security [183][184][185].…”

Section: Crystals-kybermentioning

confidence: 99%

Status report on the third round of the NIST Post-Quantum Cryptography Standardization process

Moody¹

2022

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The National Institute of Standards and Technology is in the process of selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signature, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers. The first round of the NIST Post-Quantum Cryptography Standardization Process began in December 2017 with 69 candidate algorithms that met both the minimum acceptance criteria and submission requirements. The first round lasted until January 2019, during which candidate algorithms were evaluated based on their security, performance, and other characteristics. NIST selected 26 algorithms to advance to the second round for more analysis. The second round continued until July 2020, after which seven 'finalist' and eight 'alternate' candidate algorithms were selected to move into the third round. This report describes the evaluation and selection process, based on public feedback and internal review, of the third-round candidates. The report summarizes each of the 15 third-round candidate algorithms and identifies those selected for standardization, as well as those that will continue to be evaluated in a fourth round of analysis. The public-key encryption and key-establishment algorithm that will be standardized is CRYSTALS-Kyber. The digital signatures that will be standardized are CRYSTALS-Dilithium, Falcon, and SPHINCS+. While there are multiple signature algorithms selected, NIST recommends CRYSTALS-Dilithium as the primary algorithm to be implemented. In addition, four of the alternate key-establishment candidate algorithms will advance to a fourth round of evaluation: BIKE, Classic McEliece, HQC, and SIKE. These candidates are still being considered for future standardization. NIST will also issue a new Call for Proposals for public-key digital signature algorithms to augment and diversify its signature portfolio.

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“…In particular, a 2012 work by Langlois and Stehlé [180] provides a relatively tight reduction from worst-case Module-SIVP to average-case Module-LWE. Additional results have given evidence that, roughly speaking, transitioning from rank one (i.e., Ring-LWE) to constant rank (i.e., Module-LWE) is likely to increase performance and unlikely to sacrifice security [181][182][183].…”

Section: Crystals-kybermentioning

confidence: 99%

Status report on the third round of the NIST Post-Quantum Cryptography Standardization process

Moody¹

2022

View full text Add to dashboard Cite

The National Institute of Standards and Technology is in the process of selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signature, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers. The first round of the NIST Post-Quantum Cryptography Standardization Process began in December 2017 with 69 candidate algorithms that met both the minimum acceptance criteria and submission requirements. The first round lasted until January 2019, during which candidate algorithms were evaluated based on their security, performance, and other characteristics. NIST selected 26 algorithms to advance to the second round for more analysis. The second round continued until July 2020, after which seven 'finalist' and eight 'alternate' candidate algorithms were selected to move into the third round. This report describes the evaluation and selection process, based on public feedback and internal review, of the third-round candidates. The report summarizes each of the 15 third-round candidate algorithms and identifies those selected for standardization, as well as those that will continue to be evaluated in a fourth round of analysis. The public-key encryption and key-establishment algorithm that will be standardized is CRYSTALS-Kyber. The digital signatures that will be standardized are CRYSTALS-Dilithium, Falcon, and SPHINCS+. While there are multiple signature algorithms selected, NIST recommends CRYSTALS-Dilithium as the primary algorithm to be implemented. In addition, four of the alternate key-establishment candidate algorithms will advance to a fourth round of evaluation: BIKE, Classic McEliece, HQC, and SIKE. These candidates are still being considered for future standardization. NIST will also issue a new Call for Proposals for public-key digital signature algorithms to augment and diversify its signature portfolio.

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“…Similarly, the key size for our star-specific key-homomorphic PRF family is the same as that of the key-homomorphic PRF family from [35]. Specifically, for security parameter L and 2 L security against known lattice reduction algorithms [11,121,126,128,129,190,231,229,217,216,254,271,272,273,230,257,195,16,46,153,225,224,79], the key size for our star-specific key-homomorphic PRF family is L.…”

Section: Runtime and Key Sizementioning

confidence: 99%

Star-specific Key-homomorphic PRFs from Linear Regression and Extremal Set Theory

Sehrawat¹,

Yeo²,

Vassilyev³

2022

Preprint

0

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We introduce a novel method to derandomize the learning with errors (LWE) problem by generating deterministic yet sufficiently independent LWE instances, that are constructed via special linear regression models. We also introduce star-specific key-homomorphic (SSKH) pseudorandom functions (PRFs), which are defined by the respective sets of parties that construct them. We use our derandomized variant of LWE to construct a SSKH PRF family. The sets of parties constructing SSKH PRFs are arranged as star graphs with possibly shared vertices, i.e., some pair of sets have non-empty intersections. We reduce the security of our SSKH PRF family to the hardness of LWE. To establish the maximum number of SSKH PRFs that can be constructed -by a set of parties -in the presence of passive/active and external/internal adversaries, we prove several bounds on the size of maximally cover-free at most t-intersecting k-uniform family of sets H, where the three properties are defined as:For the same purpose, we define and compute the mutual information between different linear regression hypotheses that are generated via overlapping training datasets.

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Lattice Reduction for Modules, or How to Reduce ModuleSVP to ModuleSVP

Cited by 8 publications

References 32 publications

Status report on the third round of the NIST Post-Quantum Cryptography Standardization process

Status report on the third round of the NIST Post-Quantum Cryptography Standardization process

Status report on the third round of the NIST Post-Quantum Cryptography Standardization process

Star-specific Key-homomorphic PRFs from Linear Regression and Extremal Set Theory

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