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Can we Beat the Square Root Bound for ECDLP over Fp2 via Representations?     ECDLP  Square Root Bound       font style='font-size:12px;'> 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       font style='font-size:12px;'> 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 ...
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...
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...
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...
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...
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       font style='font-size:12px;'> 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       font style='font-size:12px;'> 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...
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...

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