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# 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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### How does the order of Q affect the time it takes to solve ECDLP?

I use Sagemath's built-in function discrete_log() to solve ECDLP and according to the documentation it uses Pohling-Hellman algorithm to solve an ECDLP. This is ...
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### Question About ECC Primitives (GnuPG)

In version 2.1, GnuPG featured primitives that use elliptic curves. For encryption, one option was ECDH, which confused me. I thought ECDH was for key agreement, not public key encryption. How does ...
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### TLS 1.2 handshake ECDH premaster/master secret generation with C OpenSSL API [on hold]

I am doing a study on the TLS protocol as my degree thesis, but being completely inexperienced on this subject, I have many questions. I have to write C code and program a client that partecipates ...
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### Using (EC)DH to generate a signature

Say I have access to a system that is limited to performing (EC)DH, followed by key derivation to produce a secret key. This secret key can e.g. be used to generate a MAC. Is it possible to generate a ...
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### Have someone replaced Curve25519 in NaCL library? [migrated]

I am using NaCL library and I like it but I wonder if it is possible to replace Curve25519 with different stronger Curve if stronger encryption is needed. I do understand that new library would be ...
315 views

### Ed25519 key generation

the following rfc describes the key-pair generation mechanism for Ed25519; the first two steps are as follows: Hash the 32-byte private key using SHA-512, storing the digest in a 64-octet ...
29k views

### Explaining weakness of Dual EC DRBG to wider audience?

I have an audience of senior (non-technical) executives and senior technical people who are taking the backdoor in Dual_EC_DRBG and considering it as a weakness of Elliptic curves in general. I can ...
281 views

### What exactly could be accomplished with a backdoor in Dual_EC_DRBG?

Assume that some entity really holds the private key corresponding to the recommended/dubious constants of Dual_EC_DRBG. According to this presentation, they would be able to reconstruct the internal ...
16k views

### Who uses Dual_EC_DRBG?

Recent news articles have suggested that the NSA may be involved in trying to influence the cryptography in public standards or commercially deployed software, to enable the NSA to decrypt the ...
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### In Elliptic Curve, what does the point at infinity look like?

We know that for each point $P$ in curve $E$ there exists a minimum scalar $k$ such that $k*P$ equals the point at infinity. And the book Cryptography Theory and Practice by Douglas R. Stinson only ...
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### How to represent the point-at-infinity(Elliptic Curves) in code? [duplicate]

I am writing code for Elliptic Curve Cryptography. I have a class class EllipticCurvePoint. ...
2k views

### Difference between “ECDH with cofactor key” and “ECDH without cofactor key”?

I need to use “ECDH with a cofactor key” for generating symmetric key. I have a fair idea on how ECDH works, but I don’t understand the cofactor part. What is the difference between ”ECDH with a co-...
128 views

### Hash multiset to point on elliptic curve where $A = 0$

I want to hash a multiset to a point on the elliptic curve $y^2 = x^3 + 3$ over a finite field of some 254-bit prime order, where $P = 3 \pmod 4$. Moreover, I want this hash to be incremental, in that ...
439 views

### Does the backdoor in Dual_EC_DRBG work like that?

From what I read, the backdoor in Dual_EC_DRBG operates by using related $P$ and $Q$ points. Did I understand the idea correctly? Dual_EC_DRBG works by multiplying the $P$ point with the seed ...
39 views

### What are some use cases for white-box digital signatures?

There were 2 papers published in the last year, that describe 2 different white-box identity-based digital signature schemes: White-Box Implementation of the Identity-Based Signature Scheme in the ...
67 views

### Is it possible to derive the recipient's public key from libsodium's crypto_box?

Libsodium has "crypto_box_seal" which according to the documentation is used to "anonymously send messages to a recipient given its public key.", which hides the sender. But Is it possible for Eve to ...
2k views

### Can SRP be used with Elliptic Curves?

I'm sure it can, because SRP (secure remote protocol) can be implemented everywhere where Diffie-Hellman works, but I need a proof to put this aspect into Wikipedia. Edit: ok, can it be at least ...
71 views

### Diffie-Hellman Primitives in SP800-56A

I wonder if someone can give an explain about the different between two Diffie-Hellman Primitives defined in SP800-56A, CH5.7.1 5.7.1.1 Finite Field Cryptography Diffie-Hellman (FFC DH) Primitive 5.7....
700 views

### addition on finite elliptic curves

I tried to calculate the sum of two Points on an elliptic curve in a finite field. The Curve is defined as following: $$y^2 \equiv x^3 + x \mod 257$$ So the curve parameters are $a = 1,b = 0,p = 257$...
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### Problem on Elliptic Curve Point Doubling

Given an elliptical curve e.g. from “Understanding Cryptography” by Parr & Pelzl §9.2 Example 9.5: $y^2 = x^3 + 2x + 2~~~~ mod~17$ And given a primitive $P = (5, 1)$, the book indicates: We ...
45k views

### Should we trust the NIST-recommended ECC parameters?

Recent articles in the media, based upon Snowden documents, have suggested that the NSA has actively tried to enable surveillance by embedding weaknesses in commercially-deployed technology -- ...
249 views

### An efficient SPEKE protocol with curve25519

SPEKE is a very simple and elegant PAKE protocol. I think one of the reasons why PACE was invented and is now the ICAO protocol is that SPEKE was patented. Fortunately, the SPEKE patent expired in ...
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### Prevent a Man-In-The-Middle attack whilst transmitting a PSK for first time

I'm developing a network where two parties that want to join both compute ephemeral ECC keys for a key exchange, to create an encrypted connection. I plan to authenticate these keys by signing them ...
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### ECC order and modulus in EC [duplicate]

This question came from security.stackexchange.com. I have an error in reasoning regarding to the calculations on elliptic curves. The basic group operations are all calculated mod p. Ok right. Then ...