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Groups are an abstract algebraic concept based on a set and a group law (a binary function which closes the set).

9
votes
A self-distributive algebra is an algebra $(X,*)$ that satisfies the identity $x*(y*z)=(x*y)*(x*z)$. There are several cryptosystems that use self-distributive algebras as platforms and these cryptosy …
answered Mar 14 '17 by Joseph Van Name
1
vote
Let me answer this question in the context of braid group cryptography since braid groups form the group based cryptosystems which I am most familiar with. Keep in mind that today, most if not all bra …
answered Oct 13 '18 by Joseph Van Name
1
vote
1answer
Let $K,X$ be sets and let $F:K\times X\rightarrow X$ be a function. For each $k\in K$, let $f_{k}:X\rightarrow X$ be the function where $f_{k}(x)=F(k,x)$ whenever $k\in K,x\in X$. Assume that each $f_ …
asked Jul 5 '21 by Joseph Van Name