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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 ...
TRIFLE is a Round 1 candidate of the NIST Lightweight Cryptography Standardization process. In this paper, we present an interesting 1-round iterative differential characteristic of the underlying blo...
Faster Initial Splitting for Small Characteristic Composite Extension Degree Fields
Discrete Log Finite fields Function Field Sieve Cryptography
2019/3/21
Let pp be a small prime and n=n1n2>1n=n1n2>1 be a composite integer. For the function field sieve algorithm applied to FpnFpn, Guillevic (2019) had proposed an algorithm for initial splitting of the t...
Improved Attacks for Characteristic-2 Parameters of the Cubic ABC Simple Matrix Encryption Scheme
multivariate public key cryptography differential invariant MinRank
2017/3/6
In the last few years multivariate public key cryptography has experienced an infusion of new ideas for encryption. Among these new strategies is the ABC Simple Matrix family of encryption schemes whi...
Montgomery curves and their arithmetic: The case of large characteristic fields
Montgomery curve Montgomery ladder elliptic curve cryptography
2017/3/6
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundat...
Impossible differential attack is one of powerful methods for analyzing encryption algorithms. When designing cryptographic algorithms, it must be safe for impossible differential attacks. In case of ...
Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields
discrete logarithm problem bilinear pairings cryptanalysis, implementation
2016/12/9
Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasi-polynomial algorithm. In this paper, we re...
Automatic Search for a Maximum Probability Differential Characteristic in a Substitution-Permutation Network
Block ciphers Cryptanalysis
2016/6/27
The algorithm presented in this paper computes a maximum probability differential characteristic in a Substitution-Permutation Network (or SPN). Such characteristics can be used to prove that a cipher...
FourQ on FPGA: New Hardware Speed Records for Elliptic Curve Cryptography over Large Prime Characteristic Fields
Elliptic curves FourQ FPGA
2016/6/6
We present fast and compact implementations of FourQ (ASIACRYPT
2015) on field-programmable gate arrays (FPGAs), and demonstrate,
for the first time, the high efficiency of this new elliptic curve o...
The Adjacency Graphs of Linear Feedback Shift Registers with Primitive-like Characteristic Polynomials
feedback shift register adjacency graph De Bruijn sequence
2016/3/11
We consider the adjacency graphs of the linear feedback shift registers (LFSRs) with characteristic polynomials of the form l(x)p(x), where l(x) is a polynomial of small degree and p(x) is a primitive...
The Multiple Number Field Sieve for Medium and High Characteristic > Finite Fields
public-key cryptography discrete logarithm problem
2016/1/25
In this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve (NFS) based on numerous number fields. Our improv...
Secure Outsourced Computation of the Characteristic Polynomial and Eigenvalues of Matrix
Cloud Computing Outsourced computation Matrix
2016/1/9
Linear algebra plays an important role in computer science,
especially in cryptography.Numerous cryptog-raphic protocols, scientific
computations, and numerical computations are based on linear alge...
Summation polynomial algorithms for elliptic curves in characteristic two
ECDLP summation polynomials index calculus
2016/1/6
The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields
F2n of prime degree n. We consider practical issues about index calculus attacks using summat...
Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms - Simplified Setting for Small Characteristic Finite Fields
discrete logarithm problem finite fields
2016/1/6
In this paper, we revisit the recent small characteristic discrete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain ...
On the discrete logarithm problem in finite fields of fixed characteristic
discrete logarithm problem finite fields quasi-polynomial time algorithm
2015/12/29
For q a prime power, the discrete logarithm problem (DLP) in F×q consists in finding, for any g∈F×q and h∈⟨g⟩, an integer x such that gx=h. For each prime p we exhibit infinitely many ex...