# 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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### Are different elliptic curves compatible?

Regarding SubtleCrypto and curves P-256, P-384 and P-521. Can I mix two different curves for key derivation? For example performing key derivation between P-256 and P-521. EDIT: Can I mix two ...
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### CSIDH Squaring Fixing the Base Curve

Consider the following variants of the CSIDH squaring problem. P1. Given $sE, E$ where $s$ is a random ideal class and $E$ is a random curve (reachable from initial $E_0$), find $s^2E$ P2. Given $sE_0$...
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### Problem with the signature of message using ECDSA over GF(2^m)

I'm trying to set up an ECDSA with Elliptic Curves over $\operatorname{GF}(2^m)$ with an example of toy with the following values: Using the Weierstrass equation on binary finite fields. E: y^2 + x*...
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### Doubt on elliptic curve over a finite field and binary representation

I'm a programmer, i.e. agnostic to the mathemathics behind most of cryptographic scheme, but I'm trying to remediate. I'm writing this premise for any possible error or imprecision that I probably put ...
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### Research Guidance on Elliptic Curve Cryptography [closed]

I am a freshman who want to research elliptic curve cryptography. There are a few questions I have: Firstly, I am not sure about how I should narrow down the topic. Where should I focus on? Can I ...
35 views

### Which signature is considered more secure and has less communication cost?

This article uses Elliptic Curve Cryptography, but when it comes to signing and verifying messages it is not using the ECDSA signature algorithm. In the article, they mentioned that the communication ...
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### Is this good way of Elliptical curve point mapping

Mapping a bit string $L$ to elliptical curve point in say prime field $\mathbb Z_p$. A simple way would be to use an integer mapping function that maps $L$ to a number $\{1, q\}$ where $q$ is the ...
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### How does one go about implementing a range proof?

I've attempted to find a solution to this problem, but for the life of me I am unable to. I am attempting to solve whether a point an elliptic curve of prime order is between 2 points, given a ...
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### A card game (for mental poker or any other card game)

I thought of a way to produce trustless card game in a flexible way. One feature that I want is it should be flexible (It should work for any type of card game, though I indeed started it as a ...
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### How to construct Hash function in python3? [duplicate]

In many cryptographic protocols design like this one, I have seen the statement 'Choose a Hash function for example: \begin{align} h&: \{0,1\}^*\times\mathbb G\to\mathbb Z_q^*\\ h_2&: \{0,1\}...
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### Known attacks against ECC in case many multiples are known?

Suppose there's a secret value x, an elliptic curve with the (public) generator G, and a sequence of secret values ...
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### CMS encryption application using Windows system certificate store

Hy! I'm looking for an application, which can make cms encryption/decryption, but with the use of the windows certificate store. I already found out, that openssl can't do it out of the box (just by ...
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### What's going on with the complicated implementations for map_to_curve in draft-irtf-cfrg-hash-to-curve?

I've been looking into implementing cPace, and I saw that two cipher suites defined for it refered to draft-irtf-cfrg-hash-to-curve for its protocol definition. Part of cPace requires mapping a string ...
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### Which of these ECC libraries is more secure, fast and commonly used? [closed]

I have a python project and for this project, I need to use Weierstrass-based ECDSA. On the web, I've found two libraries; Library 1 is called fastecdsa: Library 2 is called ECPy: I couldn't see any ...
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### Breaking Elgamal private key

I have been given a task to explain if - given a public key and a portion of a private key (over 300bits) with a remain unknown of 80 bits - the private key can be broken with an algorithm faster than ...
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### ECDSA signature generation and verification latency

I am performing some measurements of P256 ecdsa signature generation and verification latency and I was expecting that the signature verification will be faster than the signature generation, but is ...
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### Constant time arithmetic implementation in DSA

I am trying to understand why it is a hard problem to have formally verified constant time arithmetic for DSA when compared with ECDSA. For instance, in ECDSA implementations of OpenSSL, we have ...
164 views

### Cryptographic limit to total accounts in secp256k1

Factoring in birth day attacks and all that, with 256-bit elliptic curve cryptography, lets take secp256k1 as example that Bitcoin uses, what is the maximum number of accounts that are secure? It isn'...
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### What EC curve is used by Apple iOS platform?

I can't find information about EC curve used by Apple's iOS platform. The algorithm name that I could see in their docs is: ...
202 views

### Curve25519 Endianness

According to the original paper form Bernstein public/private keys and the shared symmetric key are stored in little-endian. However, the WolfSSL of WolfSSL supports both, little-endian and big-endian....