Cryptology ePrint Archive: Report 2017/780

New Algorithms for Solving LPN

Bin Zhang and Xinxin Gong

Abstract: The intractability of solving the LPN problem serves as the security source of many lightweight/post-quantum cryptographic schemes proposed over the past decade. There are several algorithms available so far to fulfill the solving task. In this paper, we present further algorithmic improvements to the existing work. We describe the first efficient algorithm for the single-list $k$-sum problem which naturally arises from the various BKW reduction settings, propose the hybrid mode of BKW reduction and show how to compute the matrix multiplication in the Gaussian elimination step with flexible and reduced time/memory complexities. The new algorithms yield the best known tradeoffs on the %time/memory/data complexity curve and clearly compromise the $80$-bit security of the LPN instances suggested in cryptographic schemes. Practical experiments on reduced LPN instances verified our results.

Category / Keywords: LPN, Single-list $k$-sum problem, Gaussian elimination, Tradeoff, BKW.

Date: received 16 Aug 2017

Contact author: {zhangbin, gongxinxin} at tca iscas ac cn

Available format(s): PDF | BibTeX Citation

Note: Parts of the work have been done when Bin Zhang has taken a visit in NTU, Singapore in 2016.

Version: 20170816:123025 (All versions of this report)

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