15 March 2018

# Results of the Ketje cryptanalysis prize

At the rump session of FSE 2018 that took place last week in Brugge, Belgium, we announced the outcome of the Ketje cryptanalysis prize.

There were three submissions:

• Cube-like Attack on Round-Reduced Initialization of Ketje Sr, by Xiaoyang Dong, Zheng Li, Xiaoyun Wang and Ling Qin, presented at FSE 2017 and published in Volume 2017, Issue 1 of ToSC.
• New MILP Modeling: Improved Conditional Cube Attacks to Keccak-based Constructions, by Ling Song, Jian Guo and Danping Shi, available as Cryptology ePrint Archive Report 2017/1030.
• State-recovery attacks on Modified Ketje Jr, by Thomas Fuhr, Maria Naya-Plasencia and Yann Rotella, presented at FSE 2018 and published in Volume 2018, Issue 1 of ToSC.

The first two submissions push the boundaries of cube attacks, or more generally, higher-order differential cryptanalysis of round-reduced Keccak-f. In Ketje, these attacks always target the initialization phase that applies Keccak-p[nr=12] to the concatenation of a key and a nonce. The algebraic degree of Keccak-p[nr], for a small number of rounds, is d=2nr, so a straightforward higher-order differential attack would require a data complexity of 2d chosen input blocks (e.g., for nr=6 rounds, the degree is d=64 and the straightforward data complexity is 264). By applying some sophisticated tricks, one can peel off one or two rounds resulting in much lower data complexities. The first two submissions achieve this by exploiting specific propagation properties of the round function.

The third submission is the first to attack the encryption/decryption phase of Ketje Jr. In this phase, a known-plaintext attacker gets the value of the first r=16 bits of the state for every round of Keccak-f. Information-theoretically n=200/16=12.5 such blocks would be sufficient to break Ketje by state recovery, but the computational difficulty increases quickly with n. This submission investigates weakened versions of Ketje Jr with increased rates: r=32 and r=40 bits and break the security claim. The attacks confirm that the tweak between Ketje v1 and Ketje v2 results in an increase in safety margin.

These three attacks add to the already substantial amount of cryptanalysis of the Keccak-f permutation in a keyed setting. They enforce the positions of Ketje (and Keyak) as being among the most cryptanalyzed authenticated ciphers.

Given these nice results, we decided to award all three submissions. For practical reasons, the contestants of the first two entries got Belgian chocolates, while those of the latter received Belgian beer.

Everyone's a winner in this contest. Congratulations to all!