Introduction to Cryptography with Coding Theory, 3rd Edition

A.2 Some Commands

The following are some Mathematica commands that are used in the Computer Examples. The commands that start with capital letters, such as EulerPhi, are built into Mathematica. The ones that start with small letters, such as addell, have been written specially for this text and are in the Mathematica notebook available at

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addell[{x,y}, {u,v}, b, c, n] finds the sum of the points $\{x\text{,}y\}$ and $\{u\text{,}v\}$ on the elliptic curve $y^2\equiv x^3+bx+c(\text{mod}n)$, where $n$ is odd.

affinecrypt[txt,m,n] affine encryption of txt using $mx+n$.

allshifts[txt] gives all 26 shifts of txt.

ChineseRemainder[{a,b,...},{m,n,...}] gives a solution to the simultaneous congruences $x\equiv a(\text{mod}m)\text{,}x\equiv b(\text{mod}n)\text{,}\dots$.

choose[txt,m,n] lists the characters in txt in ...