A New Class of Invertible Mappings

摘要: Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is small (e.g., = 8) we can compactly represent any such transformation as a lookup table, but when large 64) usually have to it composition of simpler operations linear mappings, S-P networks, Feistel structures, etc. Since these constructions often implemented software on standard microprocessors, particularly interested invertible univariate or multivariate which be compositions basic machine instructions 32 64 bit words. In this paper introduce new class provably mappings mix arithmetic (negation, addition, subtraction, multiplication) and boolean (not, xor, and, or), highly efficient, desirable properties. particular, show that for the mapping x ? + (x2 C) (mod 2n) permutation with single cycle length 2n iff both least significant third constant C 1.