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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. ...
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...
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...
Efficient Zero-Knowledge Arguments for Arithmetic Circuits in the Discrete Log Setting
Sigma-protocol zero-knowledge argument arithmetic circuit
2016/3/9
We provide a zero-knowledge argument for arithmetic circuit
satisfiability with a communication complexity that grows logarithmically
in the size of the circuit. The round complexity is also logarit...
Cryptanalysis of the $AA_{\beta}$ Cryptosystem based on Linear Diophantine Equation Discrete Log Problem
Public-Key Cryptosystem linear diophantine equation discrete log problem
2011/7/25
Very recently, Ariffin and Abu proposed a new version of the $AA_{\beta}$ cryptosystem based on linear diophantine equation discrete log problem. However, we give an efficient simple ciphertext-only a...
Let p be a odd prime such that 2 is a primitive element
of finite field Fp. In this short note we propose a new algorithm
for the computation of discrete logarithm in Fp.
On the Relations Between Non-Interactive Key Distribution, Identity-Based Encryption and Trapdoor Discrete Log Groups
Identity-based encryption identity-based non-interactive key distribution trapdoor discrete logs
2009/6/2
This paper investigates the relationships between identity-based
non-interactive key distribution (ID-NIKD) and identity-based encryption (IBE).
It provides a new security model for ID-NIKD, and a c...
Ramanujan Graphs and the Random Reducibility of Discrete Log on Isogenous Elliptic Curves
random reducibility discrete log elliptic curves
2009/4/1
Cryptographic applications using an elliptic curve over a finite field
filter curves for suitability using their order as the primary criterion:
e.g. checking that their order has a large prime divi...
ANOTHER LOOK AT NON-STANDARD DISCRETE LOG AND DIFFIE-HELLMAN PROBLEMS
Public Key Cryptography discrete log problem Diffie-Hellman
2008/5/21
Abstract. We examine several versions of the one-more-discrete-log
and one-more-Diffie-Hellman problems. In attempting to evaluate their
intractability, we find conflicting evidence of the rel...
On the Relations Between Non-Interactive Key Distribution,Identity-Based Encryption and Trapdoor Discrete Log Groups
Identity-based encryption identity-based non-interactive key distribution trapdoor dis-crete logs.
2008/5/21
We investigate the relationships between identity-based non-interactive key distribution and identity-based encryption. We provide constructions for these schemes that make use of general trapdoor di...