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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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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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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Is this ECC encryption key sharing method okay?

Is this encryption key sharing okay to use? Or is much better to use ECIES? $G$ = base point $a$ = Alice’s private key $b$ = Bob’s private key $A = aG$ = Alice’s public key $B = bG$ = Bob’s public ...
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Key exchange using ECDH vs ECIES

I'm a beginner to ECC crypto programming. Does any one explain to me the difference with using ECDH for shared key exchange and use of ECIES by encrypting shared key with the public key of the ...
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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 ...