Improvements on Making BKW Practical for Solving LWE

Budroni, Alessandro; Guo, Qian; Johansson, Thomas; Mårtensson, Erik; Wagner, Paul Stankovski

doi:10.3390/cryptography5040031

Cited by 5 publications

(1 citation statement)

References 34 publications

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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

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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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Section: Runtime and Key Sizementioning

confidence: 99%

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

Sehrawat¹,

Yeo²,

Vassilyev³

2022

Preprint

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Further improvements of the estimation of key enumeration with applications to solving LWE

Budroni,

Mårtensson

2024

Cryptogr. Commun.

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In post-quantum cryptography, Learning With Errors (LWE) is one of the dominant underlying mathematical problems. The dual attack is one of the main strategies for solving the LWE problem, and it has recently gathered significant attention within the research community. The attack strategy consists of a lattice reduction part and a distinguishing part. The latter includes an enumeration subroutine over a certain number of positions of the secret key. Our contribution consists of giving a precise and efficient approach for calculating the expected complexity of such an enumeration procedure, which was missing in the literature. This allows us to decrease the estimated cost of the whole dual attack, both classically and quantumly, on well-known protocols such as Kyber, Saber, and TFHE. In addition, we explore different enumeration strategies to investigate some potential further improvements. As our method of calculating the expected cost of enumeration is pretty general, it might be of independent interest in other areas of cryptanalysis or even in different research areas.

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