# Questions tagged [elliptic-curves]

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 consider more specific tags such as discrete-logarithm and ecdsa.

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### Expected data is incorrect when scalar_mul_size is different from the modulus size in ECC MUL [closed]

Does that when the scalar_mul_size was different from the modulus_mul_size this impact on the output data?
32 views

### How to calculate Cardinality of an Elliptic curve over $\mathbb Z_{23}$

How to calculate Cardinality of an Elliptic curve over $\mathbb Z_{23}$. $E: y^2 = x^3 + x + 1$ defined over $\mathbb Z_{23}$.
183 views

### Can we use several times the same RSA and ECC keys?

For RSA or elliptic cryptography, can we use the same public/private keys for several exchanges, or is that unsafe? Does it lower the security of the protocol? To me it doesn't matter, as receiving ...
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### Is it fine to use ECDSA with edwards25519?

The elliptic.js library allows instantiating ECDSA with the edwards25519 curve. I've rarely seen this combination in the wild. ...
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1 vote
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### Why do we need additional secret value (k) in ECDSA?

Formula for calculating an ECDSA signature (r, s) is: s = k-1(z + qr) k - private key for a random point R z - hash of a message q - original private key r - x(R) I am interested in why do we need ...
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### Is there an algebra group (or ring) in which computing the inverse element is hard without some trapdoor information?

Specifically, I want an algebra group $G$ (or ring $R$) features: Given elements $g,h\in G$ (or $R$ ), computing $g\cdot h \in G$ (or $R$ ) is easy. Given an element $g \in G$ (or $R$ ), finding the ...
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### Understanding Point Negation in secp256k1 Elliptic Curve

I'm exploring the secp256k1 elliptic curve in the context of cryptography and encountered the concept of Point negation. I would appreciate clarification on what point negation means in this context. ...
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1 vote