搜索结果: 1-15 共查到“Discrete logarithms”相关记录31条 . 查询时间(0.093 秒)
Low Weight Discrete Logarithms and Subset Sum in 20.65n with Polynomial Memory
Low weight dlog subset sum representations Nested Rho
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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...
Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
discrete logarithm problem finite field
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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 ...
The Proof is in the Pudding: Proofs of Work for Solving Discrete Logarithms
Proofs of work discrete logarithm problem Pollard rho
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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 ...
A new perspective on the powers of two descent for discrete logarithms in finite fields
foundations discrete logarithm problem
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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 ...
Computing Low-Weight Discrete Logarithms
discrete logarithm problem number theory baby-step giant-step
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2017/7/28
We propose some new baby-step giant-step algorithms for computing "low-weight" discrete logarithms; that is, for computing discrete logarithms in which the radix-b representation of the exponent is kn...
Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms
Quantum cryptanalysis elliptic curve cryptography elliptic curve discrete logarithm problem
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2017/6/22
We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate netwo...
Multivariate Cryptography with Mappings of Discrete Logarithms and Polynomials
Public key cryptography and digital signature Digital certificates Multivariate analysis
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2016/12/10
In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite rin...
Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields
discrete logarithm problem bilinear pairings cryptanalysis, implementation
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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...
Faster individual discrete logarithms in non-prime finite fields with the NFS and FFS algorithms
finite field discrete logarithm number field sieve
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2016/7/13
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms known are the Number Field Sieve and its variants in large and medium characteristic fields (e.g. ...
Solving discrete logarithms on a 170-bit MNT curve by pairing reduction
Discrete logarithm finite field number field sieve
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2016/5/26
Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finit...
Faster discrete logarithms on FPGAs
attacks FPGAs ECC
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2016/4/18
This paper accelerates FPGA computations of discrete logarithms on elliptic curves over binary fields. As an illustration, this paper reports successful completion of an attack against the SECG standa...
Computing Discrete Logarithms in F_{3^{6*137}} and F_{3^{6*163}} using Magma
discrete logarithm problem small-characteristic finite fields
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2016/1/26
We show that a Magma implementation of Joux’s L[1/4 +
o(1)] algorithm can be used to compute discrete logarithms in the 1303-
bit finite field F36·137 and the 1551-bit finite field F36·163 with very...
Breaking `128-bit Secure' Supersingular Binary Curves (or how to solve discrete logarithms in ${\mathbb F}_{2^{4 \cdot 1223}}$ and ${\mathbb F}_{2^{12 \cdot 367}}$)
Discrete logarithm problem finite fields supersingular binary curves,
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2016/1/25
In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of
small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasipolynomial
tim...
Computing Individual Discrete Logarithms Faster in $GF(p^n)$
Discrete logarithm finite field number field sieve
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2015/12/30
The Number Field Sieve (NFS) algorithm is the best known method to compute discrete logarithms (DL) in large characteristic finite fields \FFpn, with p large and n≥1 small. This algorithm comprises fo...
Computing Elliptic Curve Discrete Logarithms with Improved Baby-step Giant-step Algorithm
baby-step giant-step elliptic curve discrete logarithm negation map
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2015/12/29
The negation map can be used to speed up the computation
of elliptic curve discrete logarithms using either the baby-step-giant-step
algorithm (BSGS) or Pollard rho. Montgomery’s simultaneous modula...