Paper 2011/558

Improved Attacks on Full GOST

Itai Dinur, Orr Dunkelman, and Adi Shamir

Abstract

GOST is a well known block cipher which was developed in the Soviet Union during the 1970's as an alternative to the US-developed DES. In spite of considerable cryptanalytic effort, until very recently there were no published single key attacks against its full 32-round version which were faster than the $2^{256}$ time complexity of exhaustive search. In February 2011, Isobe used in a novel way the previously discovered reflection property in order to develop the first such attack, which requires $2^{32}$ data, $2^{64}$ memory and $2^{224}$ time. Shortly afterwards, Courtois and Misztal used a different technique to attack the full GOST using $$ data, $$ memory and $$ time. In this paper we introduce a new fixed point property and a better way to attack 8-round GOST in order to find improved attacks on full GOST: Given $$ data we can reduce the memory complexity from an impractical $$ to a practical $$ without changing the $$ time complexity, and given $$ data we can simultaneously reduce the time complexity to $$ and the memory complexity to $$.