[Resource Topic] 2022/1750: Faster Dual Lattice Attacks by Using Coding Theory

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Faster Dual Lattice Attacks by Using Coding Theory

Authors: Kevin Carrier, Yixin Shen, Jean-Pierre Tillich


We present a faster dual lattice attack on the Learning with Errors (LWE) problem, based on ideas from coding theory. Basically, it consists of revisiting the most recent dual attack of \cite{Matzov22} and replacing modulus switching by a decoding algorithm. This
replacement achieves a reduction from small LWE to plain LWE with a very significant reduction of the secret dimension. We also replace the enumeration part of this attack by betting that the secret is zero on the part where we want to enumerate it and iterate this bet over other choices of the enumeration part. We estimate the complexity of this attack by making the optimistic, but realistic guess that we can use polar codes for this decoding task. We show that under this assumption
the best attacks on Kyber and Saber can be improved by 1 and 6 bits.

ePrint: https://eprint.iacr.org/2022/1750

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