Cryptology ePrint Archive: Report 2021/586

A New Approach for finding Low-Weight Polynomial Multiples

Laila El Aimani

Abstract: We consider the problem of finding low-weight multiples of polynomials over binary fields, which arises in stream cipher cryptanalysis or in finite field arithmetic. We first devise memory-efficient algorithms based on the recent advances in techniques for solving the knapsack problem. Then, we tune our algorithms using the celebrated Parallel Collision Search (PCS) method to decrease the time cost at the expense of a slight increase in space. Both our memory-efficient and time-memory trade-off algorithms improve substantially the state-of-the-art. The gain is for instance remarkable for large weights; a situation which occurs when the available keystream is small, e.g. the Bluetooth keystream.

Category / Keywords: secret-key cryptography / Low-weight polynomial multiple Stream cipher cryptanalysis Knapsack Collision-finding algorithm Time-memory trade-off.

Date: received 4 May 2021, last revised 5 Jun 2021

Contact author: laila elaimani at gmail com

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Version: 20210605:193835 (All versions of this report)

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