Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also ...

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Understanding elliptic curve encryption

I'm having a hard time understanding the elliptic curve encryption. One thing thing I don't understand is listing all the points on the curve mod p. Suppose I have the following elliptic curve: $y^2 = ...
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Why recently Edward curve formulas being developed that deviates from unification?

Edward curves were considered initially because it provides a unified formula for both doubling and addition, thus having inherent side-channel resistance. But a lot of work has been done recently ...
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Measure ECC key size

I have implemented a ECC key generation scheme successfully. Now I need to find ECC key sizes of each generating key pairs. I assumed that ECC key size is the size of the ECC private Key. So I would ...
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Parameter choice Supersingular Isogeny DH

In “Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies” by DeFeo, Jao and Plut (PDF), the public parameters are defined as: Supersingular curve $E$, and bases $P, Q$ ...
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EC: Why does $h>200$ need to hold?

The class number of the principal order belonging to the endomorphism ring of E SHOULD be at least 200. From TR-03111 (pdf page 15). This value commonly is referred to as $h$. So my ...
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Point addition in NaCl/libsodium (Curve25519)

In NaCl and libsodium, the crypto_scalarmult function implements the operation $Q = kP$ (scalar/point multiplication). There doesn't seem to be a function for point ...
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Polynomial Inversion over Galois Field

Hello guys I am looking to calculate the Inverse of a given polynomial in Galois field I have found the little Fermat's algorithm and the Itoh-Tsujii I am getting a bit confused with both algorithm ...
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Find generator for irreducible polynomial over binary field

I read this tutorial and I have following question. How they assume that generator: g = (0010) is correct for this polynomial and how to choose the best generator from all for the field.
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how can I change representation of point to Jacobian coordinates in Edward's Curve

I want to simulate this algorithm but I want to change it's output to Jacobian coordinates. what should I do ? In the other way how can we change extended homogeneous coordinates to Jacobian ...
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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 ...
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Elliptic Curves Readdition

I found the term re-addition in https://www.hyperelliptic.org/EFD/g1p/auto-shortw-projective.html and I cannot figure out what it is. It has actually same complexity of addition and I dont see the ...
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initiate the elliptic curve

when we consider a curve in a prime field for example Weierstrass form and want to initiate it in Miracl,we should give these inputs for initiate curve: ebrick_init(&binst,x,y,a,b,n,window,nb) ...
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advantages of hashing over elliptic curve signatures for a proof of work protocol

I'm trying to create a proof-of-work protocol for a proof-of-concept software, and it's basically something like this: ...
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Scalar multiplication of elliptic curve point by a fraction

I'm implementing an algorithm that works on a generic finite cyclic group written in the classic multiplicative notation: (G,*) = < g > , n = |g| At a ...
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Size of Messages Exchanged by PRV and VER for Schnorr Protocol

In this file Elliptic Curve Based Zero Knowledge Proofs and Their Applicability on Resource Constrained Devices I don't understand the Table 6 (Table 6: Size of Messages Exchanged by the Prover(PRV) ...
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RSA and ECDSA Certificate Sizes

Is there a table (or a whitepaper from official sources) that compares the size of X509 certificates generated with RSA (starting from 1024 bits) and ECDSA (starting from 160 bits) ? Thanks for the ...