Some Applications of Coding Theory in Cryptography
James L. Massey · 1999
The applicability of techniques in coding theory to problems in cryptography is illustrated by examples concerning secret-sharing schemes with tailored access priveleges, the design of perfect local randomizers, the construction of t-resilient functions, and the quantization of the nonlinearity of boolean functions. Some novel coding concepts, in particular the notions of minimal codewords in linear codes and of a partition of the space of n- tuples based on nonlinear systematic codes akin to the coset partition for linear codes, are shown to be necessary to treat the cryptographic problems considered. The concepts of dual codes and dual distance as well as the relation between codes and orthogonal arrays are seen to play a central role in these applications of coding theory to cryptography. 1 Introduction Coding theory, which had its inception in the late 1940's, is now generally regarded as a mature science. Cryptography on the other hand, at least in the public sector, is ...