# 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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### Schnorr Protocol Implementation - Sometimes Fails on Curve25519

I am implementing the Schnorr Protocol in python and am having reliability issues when using some curves. I am wondering if this is an issue with my logic, or some implementation issue. I am using ...
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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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### Elliptic curve discrete logarithm problem

I'd like to know what is the maximum bits of the finite field that we can solve the ECDLP in a "regular" computer in trivial time. Is there any recent data about this?
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### EC threshold private key's multiplicative inverse and derived-key sharing

I have two devices, and each has a private key xPriv-i. Each device computes the corresponding EC public key xPub-i, shares it, and the linear combination of the keys is the "real" public key xPub. ...
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### How to know if a point on a discrete elliptic curve be represented uniquely using its y-coordinate?

Let's say we have a point on an elliptic curve $p=(x, y)$ which is not the point-at-infinity. Can there be some other point $\hat{p} = (\hat{x}, y)$ that is also on the curve and that has the same y-...
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### Ensure Data Integrity In An ECDH Key Excange

Been playing around with the inner workings of onion routing and I have a problem. If I wanted to send the 2nd node of a relay network an ephemeral ECC public key, it has to go through node 1, so that ...
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### GPG implementation of ECC “Encryption” (ECDH) vs RSA

My understanding of GPG with traditional RSA keys, is that RSA is by definition can be used to both sign and encrypt. This is because RSA can be directly applied to plaintext in the following form: <...
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### ECC with 512bit compatible curves

I understand that given solutions for solving a discrete logarithm problem are on the order of 𝑂(2𝑛/2), ergo, 256bit private keys based on 25519 or secp256k1 have an effective bit strength of ...
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### short signature for EC

i'm building a low-power wireless sensor network in which each slave node has a public/private ECC key pair -- generated by the node itself during manufacturing.... the slave node is also provisioned ...
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### ECDSA - why is the first part of the signature used in the second?

Using the terminology of https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm Why is the second part of the ECDSA signature defined as: $s = k^{-1}(z+rd_A)\text{ mod n}$ ...
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### Why doesn't the JOSE suite/JWA include ECIES?

The JOSE suite specifics use of RSA-OAEP (for when one party has an RSA key) and ECDH (for when two parties have EC keys) in JWA. Why doesn't it include ECIES? It seems like a way to derive a key ...
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### Reason for including the public key of the key agreement in the KDF

I found the following text when looking up KDFs: In comparison, the so-called DHAES mode in IEEE 1363a mandates to use the binary representation of the sender’s public key as an input parameter. ...
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### Patterns in elliptic curve division polynomials

While looking at division polynomials of elliptic curves in relation to this and this questions, I noticed some patterns. I am wondering if anyone knows of general formulas the describe these patterns....
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### Is it necessary to transmit two or three points of an elliptic curve?

Are there cryptographic protocols, where a party should transmit by communication channel simultaneously two or three $\mathbb{F}_q$-points of an elliptic curve over a finite field $\mathbb{F}_q$? ...
1answer
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### Authentication protocol for communication with Arduino Uno

I am using an ECDH key exchange to establish a shared secret between an Arduino Uno and an Android device. For this purpose I am using this library and more specifically Curve25519. This is the ...
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### Security of BLS under additional information on the secret key

Question A Is the BLS signature scheme still secure if an adversary in addition to the public key $pk = g_2 \, sk \in \mathbb{G}_2$ also obtains additional information on the private key $sk$, ...
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### HW wallet and multisignaters in ECC

I need to design a system where there is a secure device (a.k.a. HW wallet), with the following functionality: Deterministic key generation for key parameters (speaking simply: key ID). Never expose/...
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### What does the absence of Abelian group actions on supersingular isogenies implicate?

There are no Abelian group actions on supersingular isogenies. Why does this make them secure? - motivated by De Feo's Paper on mathematics of IBS
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### Preserving location privacy

What are cryptographic techniques that could be used so that if I wanna to enable a server to send message to certain nodes in a network with preserving the privacy location for them ??
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### What should I change in my implementation to pass from a curve $y^2=x^3+1$ to $y^2=x^3+x$

I tried to change my implementation of pairing in curves $y^2 = x^3 + 1$ to use curves of the type $y^2 = x^3 + x$ but it didn't work. I thought the only thing I had to change in my code was the ...
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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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### Implementing key mapping across different elliptic curves

From this answer I understood how to prove key equivalence across two elliptic curves. Now, I'm trying to figure out some more practical aspects of implementing this. Before jumping into questions, ...
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### Elliptical Curve Cryptography benchmark test

I have built web app that implement Elliptical Curve Cryptography. During testing using data set that i chose on my own, it already run well.. But, for now, i want to test it in some benchmark test, ...
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### what does the m parameter in XML Signatures for gnBasis characteristic-two curves represent?

https://www.w3.org/TR/xmldsig-core/#sec-ECParameters defines the same three characters two-field basis's that http://www.secg.org/sec1-v2.pdf#page=107 defines: GN (Gaussian Normal, I guess) TP (...
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### trying to understand the elliptic curve format for XML Signatures

https://www.w3.org/TR/xmldsig-core/#sec-ECKeyValue gives the following example of an ECDSA key: ...
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### Can someone give me an idea of active areas relating to pairing based cryptography, and what they involve?

Apologies if this isn't the place to ask this question. I'm an undergraduate math student and I've been reading about elliptic curves. I've learned about the Weil and Tate pairings as well as Miller's ...
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### What's wrong with this construction? ECDHE+AES

Let's say I want to use ECs to do asymmetric encryption. Suppose both sides have generated EC keypairs and have exchanged their public keys. I run ECDHE, and get a derived secret. I would then either ...
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### How can I split a packed Ed25519 public signing key into its X and Y coordinates?

I'm using the Curve25519 code (from http://www.dlbeer.co.nz/oss/c25519.html), and trying to convert from a public signing key (Edwards form) to a public key-exchange key (Montgomery form). There's ...
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### how researchers extract encryption times when randomness is involved?

I have seen some research papers where they compare encryption/signature times on elliptic curves.But when i have implemented the algorithms and calculated encryption times but each time i get some ...
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### Lower bound for the size of prime factors?

We all know classic RSA and that we should pick moduli of at least 2048-bit length to get decent (112 bit) security. Now there's also multi-prime RSA, which can yield significant speed-ups using the ...