Differential Cryptanalysis of Round-Reduced Sparx-64/128

Sparx is a family of ARX-based block ciphers designed according to the long-trail strategy (LTS) that were both introduced by Dinu et al. at ASIACRYPT'16. Similar to the wide-trail strategy, the LTS allows provable upper bounds on the length of differential characteristics and linear paths. Thus, the cipher is a highly interesting target for third-party cryptanalysis. However, the only third-party cryptanalysis on Sparx-64/128 to date was given by Abdelkhalek et al. at AFRICACRYPT'17 who proposed impossible-differential attacks on 15 and 16 (out of 24) rounds.

In this paper, we present chosen-ciphertext differential attacks on 16 rounds of Sparx-64/128. First, we show a truncated-differential analysis that requires 2^32
chosen ciphertexts and approximately 2^93 encryptions. Second, we illustrate the effectiveness of boomerangs on Sparx by a rectangle attack that requires approximately 2^59.6 chosen ciphertexts and about 2^122.2 encryption equivalents. Finally, we also considered a yoyo attack on 16 rounds that, however, requires the full codebook and approximately 2^126 encryption equivalents.