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simple algebra

# simple algebra - Simple modern algebra Groups rings and...

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Conventional crypto - Noack Simple modern algebra Groups, rings, and fields Modular arithmetic Euclid’s algorithm Polynomials and Galois multiplication

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Conventional crypto - Noack Elementary terms and notation Set – a collection of objects – not otherwise defined in naïve set theory Correspondence – can be one-to-one or many-to-one or one-to-many Common symbols ε Belongs to – is a member of 2200 For all 5 There exists (at least one) Not equal
Common relationships and definitions Equality – relationship is an equality relationship if: Reflexive a = a Transitive a = b and b = c imply a = c Symmetric a = b implies b = a Objects do not need to be equal numerically to satisfy an equivalence relationship – example, similar triangles Closure a,b ε S implies a b ε S Associativity a (b c) = (a b) c – can be written a b c Identity 5 e ε S such that 2200 a ε S e a = a, a e = a Inverse 2200 a ε S 5 a’ ε S such that a’ a = e, a a’ = e Commutativity 2200 a,b ε S a b = b a Distributivity a(b + c) = ab + ac This is notational, the two operations are + and implied * even though they are

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simple algebra - Simple modern algebra Groups rings and...

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