Faster Polynomial Multiplication over Finite Fields
نویسندگان
چکیده
منابع مشابه
Private Multiplication over Finite Fields
The notion of privacy in the probing model, introduced by Ishai, Sahai, and Wagner in 2003, is nowadays frequently involved to assess the security of circuits manipulating sensitive information. However, provable security in this model still comes at the cost of a significant overhead both in terms of arithmetic complexity and randomness complexity. In this paper, we deal with this issue for ci...
متن کاملMultiplication of Polynomials over Finite Fields
We prove the 2.5n − o (n ) lower bound on the number of multiplications/divisions required to compute the coefficients of the product of two polynomials of degree n over a finite field by means of straight-line algorithms.
متن کاملLinearized polynomial maps over finite fields
We consider polynomial maps described by so-called (multivariate) linearized polynomials. These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps without mixed terms over a characteristic zero field, we will only obtain (up to a linear transformation of the variables) triangular maps, which are the most b...
متن کاملOn Sparse Polynomial Interpolation over Finite Fields
We present a Las Vegas algorithm for interpolating a sparse multivariate polynomial over a finite field, represented with a black box. Our algorithm modifies the algorithm of BenOr and Tiwari in 1988 for interpolating polynomials over rings with characteristic zero to characteristic p by doing additional probes. One of the best algorithms for sparse polynomial interpolation over a finite field ...
متن کاملUnivariate Polynomial Factorization Over Finite Fields
This paper shows that a recently proposed approach of D. Q. Wan to bivariate factorization over finite fields, the univariate factoring algorithm of V. Shoup, and the new bound of this paper for the average number of irreducible divisors of polynomials of a given degree over a finite field can be used to design a bivariate factoring algorithm that is polynomial for "almost all" bivariate polyno...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2017
ISSN: 0004-5411,1557-735X
DOI: 10.1145/3005344