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Can we Beat the Square Root Bound for ECDLP over Fp2 via Representations?
ECDLP Square Root Bound
2019/7/15
We give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field Fp2Fp2. Using the representation technique, we reduce ECDLP to a multivariate polynomial ...
Faster cofactorization with ECM using mixed representations
factoring Elliptic Curve Method cofactorization
2018/7/16
This paper introduces a novel implementation of the elliptic curve factoring method specifically designed for medium-size integers such as those arising by billions in the cofactorization step of the ...
A Fast Phase-Based Enumeration Algorithm for SVP Challenge through y-Sparse Representations of Short Lattice Vectors
public-key cryptography Lattice-based Xryptography
2016/1/5
In this paper, we propose a new phase-based enumeration algorithm based on two
interesting and useful observations for y-sparse representations of short lattice vectors in lattices
from SVP challeng...
An Attack Against Fixed Value Discrete Logarithm Representations
cryptographic protocols / attribute-based credentials revocation cryptanalysi discrete logarithm representation
2013/4/18
Attribute-based credentials (ABCs) are an important building block of privacy-enhancing identity management. Since non-identifying attributes can easily be abused as the anonymity they provide hides t...
A low-memory algorithm for finding short product representations in finite groups
A low-memory algorithm short product representations finite groups
2011/1/12
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence of elements S, our a...
A low-memory algorithm for finding short product representations in finite groups
finite group G applications
2012/3/30
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence of elements S, our a...
Unbalanced digit sets and the closest choice strategy for minimal weight integer representations
Unbalanced digit sets closest choice strategy minimal weight integer representations
2009/6/3
An online algorithm is presented that produces an optimal radix-2 representation of an
input integer n using digits from the set D`;u = fa 2 Z : ` a ug, where ` 0 and
u 1. The algorithm work...
Signed Binary Representations Revisited
signed binary elliptic curve cryptosystem efficient computation
2009/3/27
The most common method for computing exponentiation of
random elements in Abelian groups are sliding window schemes, which
enhance the efficiency of the binary method at the expense of some
precomp...
Some Analysis of Radix-r Representations
pairing-based cryptosystems radix-r representation gNAF wrNAF side channel attacks
2009/3/16
We deal with the radix-r representation used for the scalar multipli-
cation of pairing-based cryptosystems with characteristic r. Our goal of this paper
is to present some invariant properties abou...
Minimal Weight and Colexicographically Minimal Integer Representations
redundant number systems signed digits integer representations
2008/12/1
Redundant number systems (e.g., signed binary representations) have been utilized to efficiently
implement algebraic operations required by public-key cryptosystems, especially those based on ellipti...