Cryptanalysis of Helix and Phelix Revisited

Abstract

Helix, designed by Ferguson et al., is a high-speed asynchronous stream cipher with a built-in MAC functionality. At FSE 2004, Muller presented two attacks on Helix. Motivated by these attacks, Phelix was proposed and selected as a Phase 2 focus cipher for both Profile 1 and Profile 2 by the eSTREAM project, but was not advanced to Phase 3 mainly due to a key recovery attack by Wu and Preneel when the prohibition against reusing a nonce is violated.

In this paper, we study the security of Helix and Phelix in the more realistic chosen nonce model. We first point out a flaw in Muller’s second attack, which results in the failure of his attack. Then we propose our distinguishing attack on Helix with a data complexity of 2¹³², faster than exhaustive search when the key length is larger than 132 bits. Furthermore, when the maximal length of output keystream is extended, the data complexity can be reduced to 2¹²⁷ and we also can construct a key recovery attack with a data complexity of 2¹⁶³. Since this flaw is overlooked by the designers of Phelix, we can extend the distinguishing attack to Phelix with the same complexity, which shows that Phelix fails to strengthen Helix against internal state collision attacks. Our results provide new insights on the design of such dedicated ciphers with built-in authentication.

This work was supported by the National Grand Fundamental Research 973 Program of China(Grant No. 2013CB338002), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA06010701), IIE’s Research Project on Cryptography (Grant No. Y3Z0016102) and the programs of the National Natural Science Foundation of China (Grant No. 60833008, 60603018, 61173134, 91118006, 61272476).