2.30 pm, Seminar Hall
Symmetric Key Encryption from Affine Spaces
Given a secret key, accepted standard block ciphers such as AES give a permutation of a set of cardinality 2^128, or 2^256. (called a block) As the number of blocks is huge even for computers, one cannot store these permutation values; they need to be computed on the fly. So we need an efficient way of spelling out a permutation.
And for security reasons we want a massive collection of permutations one for each secret key. Practical issue with hardware meant most existing block ciphers can work only with block sizes in powers of 2.
We give a scheme for explicitly constructing a massive collection of permutations for sets of general cardinality. They arise from known automorphisms of affine spaces.
Mathematical pre-requisites are minimal. We make use of Chinese Remainder Theorem and elementary facts on polynomial rings.