Attacks on Block Ciphers of Low Algebraic Degree

In this paper an attack on block ciphers is introduced, the interpolation attack. This method is useful for attacking ciphers that use simple algebraic functions (in particular quadratic functions) as S-boxes. Also, attacks based on higher-order differentials are introduced. They are special and important cases of the interpolation attacks. The attacks are applied to several block ciphers, the six-round prototype cipher by Nyberg and Knudsen, which is provably secure against ordinary differential cryptanalysis, a modified version of the block cipher SHARK, and a block cipher suggested by Kiefer. Received April 1999 and revised October 2000 Online publication 9 April 2001