Youssef El Housni
  • Member for 3 years, 2 months
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  • Tetouan, Morocco
How does the process of creating a new secure Elliptic Curve look like?
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8 votes

As you said, you need to define the goals. You can take a look at SafeCurves, which is a joint work by Bernstein and Lange to help choose/construct elliptic curves w.r.t. ECDLP difficulty and ECC ...

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Understanding BLS12-381 Curve
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8 votes

The 12 in BLS12-381 means that the embedding degree is 12 and the 381 means that the prime in the finite field $\mathbb{F}_p$ is of 381 bits. Now talking about your bulletpoints: The order is not $\...

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Geometric interpretation of an Edwards curve
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6 votes

The normal form (later Edwards form) of an elliptic curve was first introduced by Harlod Edwards in his AMS bulletin by its addition law but gave no geometric interpretation. To give an interpretation ...

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Elliptic curves on finite fields
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3 votes

You are correct about the graphical representation. A line in the finite field $\mathbb{F}_p$ is not $y=ax+b$ but "informally" $y \equiv ax+b \pmod p$, so the line "repeats" itself. For the tangent, ...

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Can specific Weierstrass curves be some benefit from Montgomery/Edward form?
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2 votes

Curves P-256 and Secp256k1 cannot be converted to Montgomery or Edwards forms because they are of prime order. Let's take the example of Secp256k1 and try to convert it to a Montgomery curve: A ...

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Please explain parameters of RFC5639 Elliptic Curves including brainpoolP160r1
2 votes

The order of the curve $\#E(\mathbb{F}_p)$ is different from $p$. In fact, according to Hasse's theorem, $\#E(\mathbb{F}_p)=p+1-t$ where $t$ the Frobenius trace satisfies $|t|<2\sqrt{p}$. So the ...

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Algorithm for computing modular inverse in MPC
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2 votes

In general: $a^{-1} \equiv a^{\phi (q)-1} \pmod q$ where $\phi$ is euler totient function. If $q$ is a prime, then $\phi (q)=q-1$ and thus $a^{-1} \equiv a^{q-2} \pmod q$.

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Curve 25519 (X25519, Ed25519) Convert coordinates between Montgomery curve and twisted Edwards curve
2 votes

You operations have to be modulo $p$ where $p=2^{255}-19$ because you are working in $\mathbb{F}_p$.

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Choosing asymmetric pairing for Elliptic Curves
1 votes

Let's start from the beginning. We have symmetric encryption, an AES128 for example is said to have a security level $128$ because we need $2^{128}$ operations to recover the key (brute force). ...

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Homomorphic properties of Paillier
1 votes

Given two plaintexts $\alpha$ and $\beta$, Pailler cryptosystem $\mathcal{E}$ homomotphic property is: $\mathcal{E}(\alpha)\times \mathcal{E}(\beta)=\mathcal{E}(\alpha+\beta)$. So, $\mathcal{E}(\alpha)...

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Diffie-Hellman key exchange: Why is $(g^{k_1} \bmod n )^{k_2} \bmod n \equiv (g^{k_2} \mod n)^{k_1} \bmod n$
1 votes

let $a=g^{k_1} \pmod n$ and $b=g^{k_2} \pmod n$. We want to prove that $a^{k_2} \equiv b^{k_1} \pmod n$. By congruence definition, $\exists t_1 \in \mathbb{Z}/\,a=nt_1+g^{k_1}$ and $\exists t_2 \in \...

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Decoding a message on elliptic curve
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1 votes

if your $e$ is coprime to $p-1$ where $p=2^{255}-19$ you can calculate the $e$-th of an integer modulo $p$ which means you can recover $E(m)$ given $E(m)^e$. In fact, if the condition holds, there ...

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Need help understanding public key format of Barreto-Naehrig signature
1 votes

It is common to define pairing-friendly curve such as Barreto-Naehrig on sextic twists to implement efficient pairings (https://eprint.iacr.org/2012/232.pdf). for example, $E(\mathbb{F}_p): y^2 = x^3 ...

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Need a test suite for my RSA implementation
0 votes

For the modulus $n=pq$ you need to verify that $p$ and $q$ are prime numbers. You can do this with a probabilistic primality test like Rabin-Miller. For the public key $e$ you need to verify that it ...

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