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Computing Small Discrete Logarithms Faster [PDF]

, 2012
Computations of small discrete logarithms are feasible even in "secure" groups, and are used as subroutines in several cryptographic protocols in the literature. For example, the Boneh–Goh–Nissim degree-2-homomorphic public-key encryption system uses generic square-root discrete-logarithm methods for decryption.
Bernstein, D.J., Lange, T.
core   +5 more sources

Quantum computation of discrete logarithms in semigroups

Journal of Mathematical Cryptology, 2014
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines.
Childs Andrew M., Ivanyos Gábor
doaj   +2 more sources

Finding discrete logarithms with a set orbit distinguisher

Journal of Mathematical Cryptology, 2012
We consider finding discrete logarithms in a group of prime order p when the help of an algorithm D that distinguishes certain subsets of from each other is available.
Gallant Robert P.
doaj   +2 more sources

Computation of discrete logarithms in prime fields [PDF]

Designs, Codes and Cryptography, 1991
Let \(p\) be a prime and \(g\), \(x\) integers. The computation of \(y\) such that \(y\equiv g^ x(\mod p)\), \(0\leq y\leq p-1\), is referred to as discrete exponentiation. Given \(p\), \(g\) and \(y\) the computation of \(x\) is referred to as the discrete logarithm problem.
Brian A. LaMacchia, Andrew M. Odlyzko
openaire   +2 more sources

Concrete quantum cryptanalysis of binary elliptic curves

Transactions on Cryptographic Hardware and Embedded Systems, 2020
This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines.
Gustavo Banegas, Daniel J. Bernstein, Iggy van Hoof, Tanja Lange   +3 more
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Text Cryptography via Special Polynomial Technique

Journal of Kufa for Mathematics and Computer, 2022
Discrete cryptographic such as RSA, knapsack, and discrete logarithms are the oldest and best cryptographic techniques. They are worked during finite field. In this paper, an attempt to another branch of cryptography was introduced.
Adil Adil AL-Rammahi
doaj   +1 more source

Time-Memory Analysis of Parallel Collision Search Algorithms

Transactions on Cryptographic Hardware and Embedded Systems, 2021
Parallel versions of collision search algorithms require a significant amount of memory to store a proportion of the points computed by the pseudo-random walks.
Monika Trimoska, Sorina Ionica, Gilles Dequen   +2 more
doaj   +1 more source

Trace zero varieties in cryptography : optimal representation and index calculus [PDF]

, 2014
The trace zero variety associated to an elliptic or hyperelliptic curve is an abelian variety defined over a finite field F_q. Its F_q-rational points yield a finite group, the trace zero subgroup of the degree zero Picard group of the original curve ...
Massierer, Maike
core   +1 more source

On the Discrete Logarithmic Minkowski Problem [PDF]

International Mathematics Research Notices, 2015
If \(K\subset{\mathbb R}^n\) is a convex body (compact and convex set with non-empty interior) containing the origin as an interior point, the cone-volume measure of \(K\) is the Borel measure on the unit sphere \(S^{n-1}\) defined by \[ V_K(\omega)=\frac{1}{n}\int_{x\in\nu_K^{-1}(\omega)}x\cdot\nu_K(x)d\mathcal{H}^{n-1}(x), \quad \text{for each Borel }
Böröczky, Károly (Ifj.), Hegedus, P., Zhu, G.   +2 more
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Variational Quantum Algorithm for Solving Discrete Logarithms [PDF]

Jisuanji kexue
The discrete logarithm problem is a significant challenge in number theory,and due to the difficulty of solving it,classical computers lack efficient algorithms for this task.As a result,the discrete logarithm problem is widely used in public key ...
ZHANG Xinglan, RONG Xiaojun
doaj   +1 more source