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.

1,152 questions
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Why would Diffie-Hellman Group 21 be 521 bits rather than 512?

Diffie-Hellman groups tend to increment in key sizes as you'd expect up until group 21. Any idea why the key size is 521 rather than 512? I haven't been able to find an answer at all.
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The use of Elliptic Curves as part of a blockchain transaction

As I understand it, Elliptic-Curve Cryptography is used in the verification step of a transaction (i.e. when creating a digital signature), but not in the creation and security of a 'block' (when ...
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Issues with Elliptic Curve Point Addition

I'm trying to implement elliptic curve point addition in hardware. I've managed to create a working module using Affine coordinates however I've been reading about how points can be added by using ...
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X25519 - why openssl shows 253 bits?

When using ECDHE with Curve25519 with openssl: Server Temp Key: X25519, 253 bits I thought when we use X25519, it use 256 bit key. Why openssl shows the server temp key as 253 bits?
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How implement doubling point using VHDL language [closed]

I have a problem with my implementation. I want to make a multiplication in finite field. I don't know If my scheme is correct, but I made code on this base. I want to calculate: D= XY D=DX Some ...
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Schnorr Pubkey Recovery

As per How does recovering the public key from an ECDSA signature work? , it's possible to recover public keys from ECDSA signatures. Is this possible for EC-Schnorr signatures as well? I'm looking ...
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ECC Curve25519: How to generate this kind of private key? / Strange key exchange mechanism

I'm currently reverse engineering a program that uses Curve25519 key exchange in network communication. I have only a basic understanding of ECC, so maybe this thing just seems strange to me. The ...
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The compression of the eliptic curve point coordinates

Some time ago I faced the problem of the unexpected format compression of the points on elliptic curve. I used ECDH procedure with a third party service on the base of the $\mathbb({F}_{2^m})$ curve ...
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Signal double ratchet vs. future breaks in ECC?

I made a feature request on the Signal forum: https://community.signalusers.org/t/3469 And now I have a cryptographic question about Signal's "double ratchet". Assume the symmetric algorithm (...
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Using two elliptic curves to do a range proof

Suppose Alice holds a secret value $a$ to which she has publicly committed to using two elliptic curves of distinct order. The curves are $g$ and $g'$ of orders $q$ and $q'$ (with $q < q'$) and ...