Cryptology ePrint Archive: Report 2021/1435

Vectorial Decoding Algorithm for Fast Correlation Attack and Its Applications to Stream Cipher Grain-128a

ZhaoCun Zhou and DengGuo Feng and Bin Zhang

Abstract: Fast correlation attacks, pioneered by Meier and Staffelbach, is an important cryptanalysis tool for LFSR-based stream cipher, which exploits the correlation between the LFSR state and key stream and targets at recovering the initial state of LFSR via a decoding algorithm. In this paper, we develop a vectorial decoding algorithm for fast correlation attack, which is a natural generalization of original binary approach. Our approach benefits from the contributions of all correlations in a subspace. We propose two novel criterions to improve the iterative decoding algorithm. We also give some cryptographic properties of the new FCA which allows us to estimate the efficiency and complexity bounds. Furthermore, we apply this technique to well-analyzed stream cipher Grain-128a. Based on a hypothesis, an interesting result for its security bound is deduced from the perspective of iterative decoding. Our analysis reveals the potential vulnerability for LFSRs over generic linear group and also for nonlinear functions with high SEI multidimensional linear approximations such as Grain-128a.

Category / Keywords: secret-key cryptography / Linear Approximation · Fast Correlation Attack· Iterative Decoding · Grain-128a

Date: received 25 Oct 2021, last revised 22 Nov 2021

Contact author: zhaocun at iscas ac cn, martin_zhangbin at hotmail com

Available format(s): PDF | BibTeX Citation

Version: 20211122:145227 (All versions of this report)

Short URL: ia.cr/2021/1435


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