Improved Attacks on Full GOST

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 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 data, 2 memory and 2 time. Shortly afterwards, Courtois and Misztal used a different technique to attack the full GOST using 2 data, 2 memory and 2 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 2 data we can reduce the memory complexity from an impractical 2 to a practical 2 without changing the 2 time complexity, and given 2 data we can simultaneously reduce the time complexity to 2 and the memory complexity to 2.