Abstract
The DES is described in purely mathematical terms by means of confusion, diffusion and arithmetic involving a group of messages and a group of keys. It turns out to be a diffusion/arithmetic cryptosystem in which confusion plays no role, although the S-boxes effect an arithmetic operation of replacement (which is sometimes mistaken for confusion) as an important part of the encryption process.
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Key Words
- alphabet
- arithmetic
- associativity
- Caesar cipher
- code
- codomain
- commutativity
- composite
- confusion
- continuous
- cryptosystem
- cyclic group
- DES
- diffusion
- discrete
- distributivity
- domain
- field
- function
- galois field
- group
- matrix
- message
- polyalphabet
- position
- product
- ramp scheme
- relation
- replacement
- ring
- substitution
- sum
- symbol
- symmetric group
- threshold scheme
- toroidal matrix
- transposition
- universal algebra
- vector space
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Blakley, G.R. (1986). Information theory without the finiteness assumption, II. Unfolding the DES. In: Williams, H.C. (eds) Advances in Cryptology — CRYPTO ’85 Proceedings. CRYPTO 1985. Lecture Notes in Computer Science, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39799-X_23
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