3 ms·
Monoids, groups, rings, fields, etc. are all very relevant to cryptography. In general algebraic constructions come up more often than you might think. The idea
by dkarapetyan 10y ago
Monoids, groups, rings, fields, etc. are all very relevant to cryptography. In general algebraic constructions come up more often than you might think. The idea of a homomorphism though not specific to algebra is prevalent in almost any formal domain. Compilers by and large can be considered homomorphisms that preserve certain semantic properties which if you dig deep enough can be expressed as algebraic structures: http://www.logicmatters.net/resources/pdfs/Galois.pdf http://www.logicmatters.net/resources/pdfs/Galois.pdf.
Developing an intuition for all those things is best accomplished by studying abstract algebra.
- dualogy 10y agoThanks for the link, the whole site (logicmatters.net) seems awesome, aka for me worth bookmarking for future study!
- Smaug123 10y agoSmith is a great expositor. I had the joy of participating in a category theory reading group with him; he really knows his stuff. It's refreshing to be taught by a mathematician/philosopher rather than simply a mathematician.
- jinfiesto 10y agoMonoids aren't just relevant to cryptography. Any structure with an associative "+" operator forms a monoid (technically semi-group, but whatevs.) Lists are a prime example.