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A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
Intersection of Curves Grobner Basis Vanishing Ideals
2019/9/19
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Compact and Scalable Arbitrary-centered Discrete Gaussian Sampling over Integers
Lattice-based crypto discrete Gaussian sampling implementation
2019/9/16
The arbitrary-centered discrete Gaussian sampler is a fundamental subroutine in implementing lattice trapdoor sampling algorithms. However, existing approaches typically rely on either a fast implemen...
Efficient zero-knowledge arguments in the discrete log setting, revisited
zero-knowledge argument quadratic equations arithmetic circuit satisfiability
2019/8/20
This work revisits zero-knowledge proofs in the discrete logarithm setting. First, we identify and carve out basic techniques (partly being used implicitly before) to optimize proofs in this setting. ...
Low Weight Discrete Logarithms and Subset Sum in 20.65n with Polynomial Memory
Low weight dlog subset sum representations Nested Rho
2019/8/19
We propose two polynomial memory collision finding algorithms for the low Hamming weight discrete logarithm problem in any abelian group GG. The first one is a direct adaptation of the Becker-Coron-Jo...
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms
discrete logarithm problem finite fields elliptic representation
2019/7/10
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by sever...
Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
discrete logarithm problem finite field
2019/6/26
We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can ...
Polar Sampler: Discrete Gaussian Sampling over the Integers Using Polar Codes
Discrete Gaussian sampling Polar codes Integer lattice
2019/6/10
Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post quantum public key cryptography. As the standardization process takes place, o...
Pushing the speed limit of constant-time discrete Gaussian sampling. A case study on Falcon
Post-quantum signature Falcon constant-time
2019/3/6
Sampling from discrete Gaussian distribution has applications in lattice-based post-quantum cryptography. Several efficient solutions have been proposed in recent years. However, making a Gaussian sam...
Short Discrete Log Proofs for FHE and Ring-LWE Ciphertexts
Zero-Knowledge Proofs Bulletproofs FHE
2019/1/26
In applications of fully-homomorphic encryption (FHE) that involve computation on encryptions produced by several users, it is important that each user proves that her input is indeed well-formed. Thi...
FACCT: FAst, Compact, and Constant-Time Discrete Gaussian Sampler over Integers
Lattice-based crypto Discrete Gaussian sampling Constant-time
2019/1/2
The discrete Gaussian sampler is one of the fundamental tools in implementing lattice-based cryptosystems. However, a naive discrete Gaussian sampling implementation suffers from side-channel vulnerab...
Faster Homomorphic Discrete Fourier Transforms and Improved FHE Bootstrapping
Discrete Fourier Transform Homomorphic Encryption Bootstrapping
2018/11/12
In this work, we propose a faster homomorphic linear transform algorithm for structured matrices such as the discrete Fourier transform (DFT) and linear transformations in bootstrapping.
The Proof is in the Pudding: Proofs of Work for Solving Discrete Logarithms
Proofs of work discrete logarithm problem Pollard rho
2018/11/7
We propose a proof of work protocol that computes the discrete logarithm of an element in a cyclic group. Individual provers generating proofs of work perform a distributed version of the Pollard rho ...
An Optimal Distributed Discrete Log Protocol with Applications to Homomorphic Secret Sharing
Homomorphic secret sharing share conversion fully homomorphic encryption
2018/8/10
The distributed discrete logarithm (DDL) problem was introduced by Boyle et al. at CRYPTO 2016. A protocol solving this problem was the main tool used in the share conversion procedure of their homomo...
A new perspective on the powers of two descent for discrete logarithms in finite fields
foundations discrete logarithm problem
2018/7/9
A new proof is given for the correctness of the powers of two descent method for computing discrete logarithms. The result is slightly stronger than the original work, but more importantly we provide ...
Quantum Lattice Enumeration and Tweaking Discrete Pruning
Lattices Quantum algorithms Enumeration
2018/6/5
Enumeration is a fundamental lattice algorithm used in challenge records. We show how to speed up enumeration on a quantum computer, which affects the security estimates of several lattice-based submi...