Verifiable Quantum Advantage Based on Polynomials with Planted Structures

A central question in the theory of quantum advantage is whether there are quantum advantage protocols with similar resource requirements as random circuit sampling that are also verifiable just from the classical outputs of the quantum computation. Here, we develop the idea of simulation secrets...

PT-2026-65408

Name of the Vulnerable Software and Affected Versions Bouncy Castle for Java versions 1.73 through 1.77 Description Three ML-KEM CRYSTALS-Kyber routines perform non-constant-time division of secret-derived polynomial coefficients by the modulus q. The affected routines are Poly.toMsg, which decod...

RUSTSEC-2024-0398 Bias of Polynomial Coefficients in Secret Sharing

Affected versions of this crate allowed for a bias when generating random polynomials for Shamir Secret Sharing, where instead of being within the range 0, 255 they were instead in the range 1, 255. A description from Cure53, who originally found the issue, is available: The correct method to...

PT-2024-40944

Name of the Vulnerable Software and Affected Versions sharks affected versions not specified Description The issue concerns a bias in generating random polynomials for Shamir Secret Sharing. Instead of coefficients being in the range 0, 255, they were in the range 1, 255. This allows an attacker ...

AZL-78531 CVE-2024-9143 affecting package openssl-fips-provider 3.1.2-2

Issue summary: Use of the low-level GF2^m elliptic curve APIs with untrusted explicit values for the field polynomial can lead to out-of-bounds memory reads or writes. Impact summary: Out of bound memory writes can lead to an application crash or even a possibility of a remote code execution,...

UBUNTU-CVE-2024-9143

Issue summary: Use of the low-level GF2^m elliptic curve APIs with untrusted explicit values for the field polynomial can lead to out-of-bounds memory reads or writes. Impact summary: Out of bound memory writes can lead to an application crash or even a possibility of a remote code execution,...

CVE-2024-9143 Low-level invalid GF(2^m) parameters lead to OOB memory access

Issue summary: Use of the low-level GF2^m elliptic curve APIs with untrusted explicit values for the field polynomial can lead to out-of-bounds memory reads or writes. Impact summary: Out of bound memory writes can lead to an application crash or even a possibility of a remote code execution,...

Enough Polynomials and Linear Algebra to Implement Kyber

I was once talking with a mathematician and trying to explain elliptic curve cryptography. Eventually, something clicked and they went "oh, that! I think there was a chapter about it in the book. You made a whole field out of it?" Yes, in cryptography we end up focusing on a very narrow slice of...

CVE-2019-7167

Zcash, before the Sapling network upgrade 2018-10-28, had a counterfeiting vulnerability. A key-generation process, during evaluation of polynomials related to a to-be-proven statement, produced certain bypass elements. Availability of these elements allowed a cheating prover to bypass a...

CVE-2019-7167

Zcash, before the Sapling network upgrade 2018-10-28, had a counterfeiting vulnerability. A key-generation process, during evaluation of polynomials related to a to-be-proven statement, produced certain bypass elements. Availability of these elements allowed a cheating prover to bypass a...