Efficient reconfigurable hardware architecture for accurately computing success probability and data complexity of linear attacks

Abstract

An accurate estimation of the success probability and data complexity of linear cryptanalysis is a fundamental question in symmetric cryptography. In this paper, we propose an efficient reconfigurable hardware architecture to compute the success probability and data complexity of Matsui's Algorithm 2 which is the central technique in linear cryptanalysis for block ciphers. Using this dedicated architecture, we are able to investigate the complexity of the algorithm for up to 40-bit block ciphers for low-correlation lineaer approximations and high advantages. Performing experiments on larger block lengths ensures that any empirical observations are not due to differences in statistical behavior for artificially small block lengths. Rather surprisingly, we observed in previous experiments a significant deviation between the theory and practice for Matsui's Algorithm 2 for larger block sizes in a vast range of parameters. The new hardware architecture allows us to verify the existing theoretical models for the complexity estimation in linear cryptanalysis. The designed hardware architecture is realized on two Xilinx Virtex-6 XC6VLX240T FPGAs for smaller block lengths, and on RIVYERA platform with 128 Xilinx Spartan-3 XC3S5000 FPGAs for larger block lengths.