Key Recovery Attack Against 2.5-Round Pi-Cipher

Abstract : In this paper, we propose a guess and determine attack against some variants of the π-Cipher family of authenticated ciphers. This family of ciphers is a second-round candidate of the CAESAR competition. More precisely, we show a key recovery attack with time complexity little higher than 2^4ω , and low data complexity, against variants of the cipher with ω-bit words, when the internal permutation is reduced to 2.5 rounds. In particular, this gives an attack with time complexity 2^72 against the variant π16-Cipher096 (using 16-bit words) reduced to 2.5 rounds, while the authors claim 96 bits of security with 3 rounds in their second-round submission. Therefore, the security margin for this variant of π-Cipher is very limited. The attack can also be applied to lightweight variants that are not included in the CAESAR proposal, and use only two rounds. The lightweight variants π16-Cipher096 and π16-Cipher128 claim 96 bits and 128 bits of security respectively, but our attack can break the full 2 rounds with complexity 2^72. Finally, the attack can be applied to reduced versions of two more variants of π-Cipher that were proposed in the first-round submission with 4 rounds: π16-Cipher128 (using 16-bit words) and π32-Cipher256 (using 32-bit words). The attack on 2.5 rounds has complexity 2^72 and 2^137 respectively, while the security claim for 4 rounds are 128 bits and 256 bits of security.
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Thomas Peyrin FSE 2016 - 23rd International Conference Fast Software Encryption, Mar 2016, Bochum, Germany. Springer, 9783, pp.535 - 553, 2016, LNCS - Lecture Notes in Computer Science. 〈https://fse.rub.de/〉. 〈10.1007/978-3-662-52993-5_27〉
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Christina Boura, Avik Chakraborti, Gaëtan Leurent, Goutam Paul, Dhiman Saha, et al.. Key Recovery Attack Against 2.5-Round Pi-Cipher. Thomas Peyrin FSE 2016 - 23rd International Conference Fast Software Encryption, Mar 2016, Bochum, Germany. Springer, 9783, pp.535 - 553, 2016, LNCS - Lecture Notes in Computer Science. 〈https://fse.rub.de/〉. 〈10.1007/978-3-662-52993-5_27〉. 〈hal-01404164〉

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