Mean Squared Length of Vectors in the Approximate Greatest Common Divisor Lattice
نویسنده
چکیده
This paper derives the mean squared length of vectors in a lattice relevant to the Approximate GCD problem and the related fully homomorphic encryption scheme.
منابع مشابه
A Lattice Solution to Approximate Common Divisors
The approximate common divisor problem(ACDP) is to find one or more divisors which is the greatest common divisor of the approximate numbers a and b of two given numbers a0 and b0. Howgrave-Graham[7] has considered the special case of b = b0 and gave a continued fraction approach and a lattice approach to find divisors. Furthermore he raised another lattice approach for ACDP based on Coppersmit...
متن کاملApproximate Polynomial GCD over Integers with Digits-wise Lattice
For the given coprime polynomials over integers, we change their coefficients slightly over integers so that they have a greatest common divisor (GCD) over integers. That is an approximate polynomial GCD over integers. There are only two algorithms known for this problem. One is based on an algorithm for approximate integer GCDs. The other is based on the well-known subresultant mapping and the...
متن کاملA New Upper Bound for the Minimum of an Integral Lattice of Determinant 1
Let A be an «-dimensional integral lattice of determinant 1. We show that, for all sufficiently large n , the minimal nonzero squared length in A does not exceed [(n + 6)/10]. This bound is a consequence of some new conditions on the theta series of these lattices; these conditions also enable us to find the greatest possible minimal squared length in all dimensions n < 33 . In particular, we s...
متن کاملApproximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation
The computation of the Greatest Common Divisor (GCD) of many polynomials is a nongeneric problem. Techniques defining “approximate GCD” solutions have been defined, but the proper definition of the “approximate” GCD, and the way we can measure the strength of the approximation has remained open. This paper uses recent results on the representation of the GCD of many polynomials, in terms of fac...
متن کاملApproximate Polynomial Common Divisor Problem Relates to Noisy Multipolynomial Reconstruction
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 to solve this problem, we present a simple method by using the polynomial lattice reduction algorithm and contain complete theoretical analyses. Further, we propose an improved lattice attack to red...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012