A finite field is a mathematical construct based on a set of axioms which are held to be true. A number of interesting and useful properties arise from finite fields that makes them particularly suitable for use in cryptography, notably in block ciphers. Questions concerning finite fields should use ...

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How to find roots of equation $f(x)=0 \pmod p $, where $p$ is prime number?

$f(x)$is any nth degree equation $n>0$, how to find roots of $f(x)$ over prime modulo.
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Default algorithm for scalar multiplication of elliptic curve points by the MIRACL Library

What is the default algorithm used by the MIRACL-Library [1] for elliptic curve cryptography systems to perform scalar-point multiplication with curves of Weierstrass form satisfying the equation : ...
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Seeking an implementation of the Satoh algorithm for elliptical curve point counting

I would be very grateful if someone has an implementation of the Satoh algorithm (Fast Elliptic Curve Point Counting). Can someone point me to practical algorithm implementations or provide some ...
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Sextic twist of BN pairing parameters vs security

I've previously asked questions on BN pairing parameters. Here's one more. In the BN construction, one is working in a subgroup of a curve over an extension field $\mathbf{F}_{p^{12}}$ for some ...
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111 views

Can you provide an example in relation to Hidden Field Equations Multivariate?

I'm reading about Hidden Field Equations Multivariate scheme. My lecture states that the central map is a univariate polynomial $$P(X)=\sum_{i=0}^{r-1}\sum_{j=0}^{r-1}p_{ij}x^{q^i+q^j} \in K[X]$$ ...
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Multiplication in GF(2^8)

I am trying to multiply 13 (sub 16) and 11 (sub 16) in $GF(2^8)$. I am given the following irreducible polynomial: P(x) = x^8 + x^4 + x^3 + x +1 Could someone explain to me how to express the ...
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78 views

Multiplicative inverse ($17^{-1} \mod 31$)?

So. Sorry for bothering you with such a simple question, but I can't really get this done. It's just an exam question in which I need to use CRT in order to calculate the RSA signature of a msg ...
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47 views

Discrete log in Galois Extension Field

I was reading 'Pinocchio Coin' paper by Danezis et al. where they have said, "If we use the efficient pairing groups of Pinocchio, computing discrete logarithms in the exponent field $\mathbb{F}_p$ ...
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Affine transformation in finite field SubBytes

Can anyone please explain how this computation was done? I picked it up from How are the AES S-Boxes calculated? The affine transformation is as follows. The input bits are multiplied against the ...
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84 views

Elliptic curve trapdoor function without modular arithmetic?

From what I understand, an elliptic contains a set points satisfying the equation $y^2=x^3 + ax + b$ together with the point at infity. It seems clear how multiplication with a scalar and a point ...