Cryptanalysis of 249-, 250-, ..., 256-Bit Key HyRAL via Equivalent Keys

Abstract

HyRAL is a blockcipher whose block size is 128bits, and it supports the key lengths of 128, 129, ..., 256bits. The cipher was proposed for the CRYPTREC project, and previous analyses did not identify any security weaknesses. In this paper, we first consider the longest key version, 256-bit key HyRAL, and present the analysis in terms of equivalent keys. We first show that there are 2^51.0 equivalent keys (or 2^50.0 pairs of equivalent keys). Next, we propose an algorithm that derives an instance of equivalent keys with the expected time complexity of 2^48.8 encryptions and a limited amount of memory. Finally, we implement the proposed algorithm and fully verify its correctness by showing several instances of equivalent keys. We then consider shorter key lengths, and show that there are equivalent keys in 249-, 250-, ..., 255-bit key HyRAL. For each of these key lengths, we present the expected time complexity to derive an instance of equivalent keys.