Root Computation in Finite Fields
نویسندگان
چکیده
منابع مشابه
Efficient Computation of Roots in Finite Fields
We present an algorithm to compute r-th roots in Fqm with complexity O((logm + r log q)m log q) for certain choices of m and q. This compares well to previously known algorithms, which need O(rm log q) steps.
متن کاملComplexity of computation in Finite Fields
Efficient implementation of arithmetic in finite fields is of primary importance for cryptography, coding theory, digital signal processing etc. (see, for example [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]). In this survey we consider only Boolean circuits for arithmetic operations in finite fields. Another term: bit-parallel circuits. Boolean circuits for multiplication and inversion in finite fields are...
متن کاملTheoretical Comparison of Root Computations in Finite Fields
In the paper [4], the authors generalized the CipollaLehmer method [2], [5] for computing square roots in finite fields to the case of r-th roots with r prime, and compared it with the AdlemanManders-Miller method [1] from the experimental point of view. In this paper, we compare these two methods from the theoretical point of view. key words: root computation, finite field, complexity
متن کاملOn the computation of discrete logarithms in finite prime fields
In this thesis we write about practical experience when solving congruences of the form a ≡ b mod p, a, b, p, x ∈ ZZ, p prime. This is referred to as the discrete logarithm problem in (ZZ/pZZ)∗. Many cryptographic protocols such as signature schemes, message encryption, key exchange and identification depend on the difficulty of this problem. We are concerned with the practicability of differen...
متن کاملCharacter Sums and Deterministic Polynomial Root Finding in Finite Fields
Let Fq be a finite field of q elements of characteristic p. The classical algorithm of Berlekamp [1] reduces the problem of factoring polynomials of degree n over Fq to the problem of factoring squarefree polynomials of degree n over Fp that fully split in Fp, see also [8, Chapter 14]. Shoup [15, Theorem 3.1] has given a deterministic algorithm that fully factors any polynomial of degree n over...
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: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
سال: 2013
ISSN: 0916-8508,1745-1337
DOI: 10.1587/transfun.e96.a.1081