# Questions tagged [cryptography]

Questions on the mathematics behind cryptography, cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers.

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### Trouble detecting cyclic group order crossovers in elliptic curve additions

There's a problem in detecting whether the sum of public key addition has crossed the cyclic group order boundary For this example, think of public keys $Pub$ as private keys $Priv$, (private scalars),...
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### Schnorr signature variant with sum c and k instead of multiplication

I am reading about Schnorr signature and I though what if we calculate response as $r = \alpha + c + k$ instead of $r = \alpha + c*k$? Will it make scheme more insecure? Are there any name for this ...
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### Show that $f(x)=x^2+2x-1 \in \mathbb{Z}_3[x]$ is irreducible over $\mathbb{Z}_3$. And find the elements of a finite field with 9 elements.

Show that $f(x)=x^2+2x-1 \in \mathbb{Z}_3[x]$ is irreducible over $\mathbb{Z}_3$. Using this fact construct a finite field $\mathbb{F}_9$ of $9$ elements. If $\alpha$ is a root of $f(x)$, then find ...
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### Show that $3x^2+A\ne 0$ if $y=0$ for a point on elliptic curve.

Let $(x,y)$ be a point on the elliptic curve $E$ given by $y^2=x^3+Ax+B$. Show that if $y=0$ then $3x^2+A\ne0$. I have a graphical intuition for this. Since $$\frac{dy}{dx}=\frac{3x^2+A}{2y}$$ and ...
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### Using Riemann-Roch Theorem to show every elliptic curve can be written as a plane cubic

I've been studying how to show that every elliptic curve can be written as a plane cubic through the book of Joseph H. Silverman "Arithmetic Elliptic Curves", the proof of proposition III.3....
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### Confusion of Generator point in it's Montgomery Form and Weierstrass Form for secp256k1

I am using GEC Module (https://github.com/HareInWeed/gec) to perform point operations on secp256k1. Here, the generator point is defined as below ...