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Algorithms for CRT-variant of Approximate Greatest Common Divisor Problem
CCK-ACD Lattice orthogonal lattice attack
2019/3/1
The approximate greatest common divisor problem (ACD) and its variants have been used to construct many cryptographic primitives. In particular, variants of the ACD problem based on Chinese remainder ...
Revisiting Orthogonal Lattice Attacks on Approximate Common Divisor Problems and their Applications
Fully homomorphic encryption approximate common divisor problem implicit factorization problem
2018/12/20
In this paper, we revisit three existing types of orthogonal lattice (OL) attacks and propose optimized cases to solve approximate common divisor (ACD) problems. In order to reduce both space and time...
Approximate Polynomial Common Divisor Problem Relates to Noisy Multipolynomial Reconstruction
Approximate polynomial common divisor problem noisy multipolynomial reconstruction polynomial lattice
2017/4/17
In this paper, we investigate the hardness of the approximate polynomial common divisor problem, which is regarded as a polynomial analogy of the approximate integer common divisor problem. In order t...
Algorithms for the Approximate Common Divisor Problem
Approximate common divisors lattice attacks orthogonal lattice
2016/3/1
The security of homomorphic encryption over the integers and its variants
depends on the hardness of the Approximate Common Divisor (ACD) problem.
In this paper we review and compare existing algori...
Co-Z Divisor Addition Formulae in Jacobian of Genius 2 Hyperelliptic Curves over Prime Fields
hyperelliptic curve divisor Jacobian addition formulae exponentiation projective representation
2010/9/29
In this paper we proposed a new approach to divisor scalar multiplication in Jacobian of genus 2 hyperelliptic curves over fields with odd characteristic, without field inversion. It based on improved...
Approximate Integer Common Divisor Problem relates to Implicit Factorization
Greatest Common Divisor Factorization Integer Approximations
2009/12/29
In CaLC 2001, Howgrave-Graham presented a technique to calculate GCD (Greatest Common
Divisor) of two large integers when the integers are not exactly known, but some approximation
of those integers...
A Complete Divisor Class Halving Algorithm for Hyperelliptic Curve Cryptosystems of Genus Two
hyperelliptic curve cryptosystems scalar multiplication divisor class halving
2009/3/31
We deal with a divisor class halving algorithm on hyperelliptic
curve cryptosystems (HECC), which can be used for scalar multiplication,
instead of a doubling algorithm. It is not obvious how to con...
Efficient Divisor Class Halving on Genus Two Curves
hyperelliptic curve divisor class halving binary fields
2008/12/9
Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the featur...