Cryptanalysis of a Reduced Version of the Block Cipher E2

TLDR: This paper deals with truncated differential cryptanalysis of the 128-bit block cipher E2, which is an AES candidate designed and submitted by NTT and shows a non-trivial seven round byte characteristic, which leads to a possible attack of E2 reduced to eight rounds without IT and FT by a chosen plaintext scenario.

Abstract: This paper deals with truncated differential cryptanalysis of the 128-bit block cipher E2, which is an AES candidate designed and submitted by NTT. Our analysis is based on byte characteristics, where a difference of two bytes is simply encoded into one bit information "0" (the same) or "1" (not the same). Since E2 is a strongly byte-oriented algorithm, this bytewise treatment of characteristics greatly simplifies a description of its probabilistic behavior and noticeably enables us an analysis independent of the structure of its (unique) lookup table. As a result, we show a non-trivial seven round byte characteristic, which leads to a possible attack of E2 reduced to eight rounds without IT and FT by a chosen plaintext scenario. We also show that by a minor modification of the byte order of output of the round function -- which does not reduce the complexity of the algorithm nor violates its design criteria at all --, a non-trivial nine round byte characteristic can be established, which results in a possible attack of the modified E2 reduced to ten rounds without IT and FT, and reduced to nine rounds with IT and FT. Our analysis does not have a serious impact on the full E2, since it has twelve rounds with IT and FT; however, our results show that the security level of the modified version against differential cryptanalysis is lower than the designers' estimation.