# 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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### Ed25519 and sealed boxes libsodium

Accidentally used ed25519 public key to create libsoidum_sealed_box. Is there any way to decrypt the data if the private key ed25519 is known?
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### EC public key with leading zeros

Let us take example of secp256k1 curve. The current known public key with most leading zero (in x cordinate) is: ...
1 vote
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### How to convert (Rx1 and Ry1) to (Rx2 and Ry2)

I'm working with the secp256k1 elliptic curve and have point doubling and point addition formulas for this curve. If a point is given $Q_x$ and $Q_y$ ...
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### Same message different nonce but similarities in r value of the signatures(r,s)

I'm studying a case where when i sign a same message with the same private key and a different nonce, i sometimes get signatures (r,s) where r values share some similarities (same numbers at the same ...
1 vote
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### PAGE 2: Can I move elements from cyclic subgroup to its cyclic parent group?

We will continue our previous topic here⬇️ for clarity... The following context is based on elliptic curves in short-weierstrass form y^2 = x^3 + b. pls read carefully- I am looking for a function/...
1 vote
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### Can I move elements from cyclic subgroup to its cyclic parent group?

The following context is based on elliptic curves in short-weierstrass form y^2 = x^3 + b. I know that elements of a non-prime order cyclic group G can be moved to its subgroup H by a process called &...
1 vote
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### Zero Knowledge Argument for Elliptic Curve Multiplication/Inverse Multiplication Correctness?

I was reading this post and the accepted answer wrote about a way to “prove that some list of points $[A,B,C,...]$ when multiplied by $x$ produces $[A′,B′,C′,...]$”. However, in their explanation ...
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### Who originally generated the elliptic curve now known as P256/secp256r1

Background: there is a theory going around that claims that P256 was backdoored by the NSA. The theory goes is that the NSA found a weakness that applies to a nontrivial fraction of elliptic curves (...
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### Does BearSSL Library Support ECC Encryption/Decryption Functionality?

I'm researching cryptographic libraries for a project I'm working on, and I'm particularly interested in the BearSSL Library due to its lightweight nature. But I'm not sure if it supports ECC (...
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### Formula for deriving the x-coordinate using the y-coordinate (decompressing a compress public key)

According to my understanding a public key is made up of x and y coordinate and a compress public key is made up of the y-coordinate since it's possible to directly calculate the uncompress public key ...
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### Why do Ed25519 use Twisted Edwards curve but not regular Edwards curve

I'm trying to understand benefits of using Twisted Edwards curve over regular Edwards curve. I'm aware of some properties of Twisted Edwards curve that regular Edwards curve missing like isomorphism ...
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### Use secp384r1 PEM key to sign a Verifiable Credential with Linked Data proofs

Ok, let me preface this by clarifying that I am not a cryptographer by trade, but I've been using cryptographic suites in the context of signing w3c Verifiable Credentials, and I am not sure if this ...
1 vote
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### Statistics-heavy crypto papers

I'm currently taking a course in which we choose a stats-heavy paper and analyse it, summarising our work in the form of a written report and presentation. I have tried to find such a paper in crypto, ...
1 vote
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### Does exist an Elliptic analogue of Benaloh encryption scheme?

The definition of Benaloh encryption scheme can be found here. Does exist an elliptic analogue of this scheme? I want to use this scheme but the length of the key ...
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### Reflecting a point on the Edwards curve

Let's say we have a point $nP = (x,y)$ on a curve $E$ over a prime $p$. The corresponding Edwards curve coordinates are $(u,v)$. I want to construct the point corresponding to $(u,-v)$ on the Edwards ...
1 vote
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### Deriving $y$-coordinate

Is there any formula for deriving the $y$-coordinate using the $x$-coordinate and the slope in the secp256k1 elliptic curve? For example: Calculate the slope: ...
1 vote
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### Why are my Curve25519 points so different than standard? [closed]

I'm trying to implement X25519 for a little game I'm working on. I knew nothing about this stuff a week ago so it's been a bit of a learning curve (that was really funny). Most of the resources I ...
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### Determining the order of operations in elliptic curve cryptography: Point doubling vs point addition for obtaining x and y values of a public key

I have a question regarding the operations performed on an elliptic curve, specifically related to point doubling and point addition. I am trying to understand whether it is possible to determine the ...
1 vote
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### In TLS 1.2 and TLS 1.3, does the EC curve used to generate the ephemeral keys be the same on both client and server sides?

In TLS 1.2 and TLS 1.3, does the EC curve used to generate the ephemeral keys at the client side, does it need to be the same as that on the and server sides? For example can I use secp521r1 at the ...
1 vote
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### is it possible to calculate the difference between 2 public keys of secp256k1

I am inquiring about the feasibility of calculating the point difference between two distinct secp256k1 elliptic curve points. Given the nature of secp256k1, which is widely used in cryptographic ...
1 vote
I want to construct a non-interactive ZK proof that in a set of pairs of group (where the DDH-assumption holds true) elements: $(g_1, Y_1), (g_2, Y_2), ..., (g_n, Y_n)$ , the prover knows at least one ...
Let's imagine two entities: Bob and Alice. Bob's public key is $B = bG$. Alice's public key is $A = aG$. Alice encrypts her number $n$ with Bob's public key so Bob could decrypt it ($n$ is small ...