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Finite field arithmetic
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#	Item
21	Galois Field in Cryptography Christoforus Juan Benvenuto May 31, 2012 Abstract This paper introduces the basics of Galois Field as well as its implementation in storing data. This paper shows and helps visualizes that st Add to Reading List Source URL: www.math.washington.edu Language: English - Date: 2012-06-11 18:41:39 Finite fields Field theory Advanced Encryption Standard Finite field arithmetic Field Finite field Euclidean algorithm Multiplicative inverse GF Abstract algebra Mathematics Algebra
22	Feature Finite Field Arithmetic for Cryptography Erkay Savas¸ and Add to Reading List Source URL: www.cs.ucsb.edu Language: English - Date: 2010-05-29 22:43:04 Field theory Finite fields Linear algebra Cryptography Computer arithmetic Polynomial basis Finite field arithmetic XTR GF Abstract algebra Mathematics Algebra
23	Fast arithmetic and pairing evaluation on genus 2 curves David Freeman University of California, Berkeley [removed] November 6, 2005 Add to Reading List Source URL: theory.stanford.edu Language: English - Date: 2008-06-06 19:27:47 Group theory Polynomial Euclidean algorithm Finite fields Elliptic curves Integer factorization algorithms Lenstra elliptic curve factorization Factorization of polynomials over a finite field and irreducibility tests Abstract algebra Mathematics Algebra
24	A SCALABLE SYSTEM-ON-A-CHIP ARCHITECTURE FOR PRIME NUMBER VALIDATION Ray C.C. Cheung and Ashley Brown Department of Computing, Imperial College London, United Kingdom Abstract This paper presents a scalable SoC architect Add to Reading List Source URL: www.ashleybrown.co.uk Language: English - Date: 2010-09-16 09:55:04 Number theory Modular arithmetic Finite fields Probabilistic complexity theory Multiplication Miller–Rabin primality test Field-programmable gate array Montgomery reduction Randomized algorithm Mathematics Primality tests Cryptography
25	ON DEFINING INTEGERS AND PROVING ARITHMETIC CIRCUIT LOWER BOUNDS ¨rgisser Peter Bu Abstract. Let τ (n) denote the minimum number of arithmetic operations sufficient to build the integer n from the constant 1. We prove Add to Reading List Source URL: math-www.uni-paderborn.de Language: English - Date: 2007-06-22 04:55:31 Field theory Complexity classes Computational complexity theory Polynomials Integer sequences Circuit complexity NP Finite field Algebraic geometry Theoretical computer science Abstract algebra Mathematics
26	AN ABSTRACT OF THE THESIS OF Francisco Rodrguez-Henrquez for the degree of Doctor of Philosophy in Electrical & Computer Engineering presented on June 07, 2000. Title: New Algorithms and Architectures for Arithmetic Add to Reading List Source URL: delta.cs.cinvestav.mx Language: English - Date: 2005-02-12 19:20:36 Cryptography Finite fields Group theory Field theory Linear algebra Polynomial basis Elliptic curve cryptography Anatolii Alexeevitch Karatsuba Elliptic curve Abstract algebra Algebra Mathematics
27	Open Problems on Exponential and Character Sums Igor E. Shparlinski Department of Computing, Macquarie University Sydney, NSW 2109, Australia [removed] Add to Reading List Source URL: web.science.mq.edu.au Language: English - Date: 2013-04-07 21:19:17 Number theory Kloosterman sum Anatolii Alexeevitch Karatsuba Arithmetic function Character sum Exponential sum Prime number Prime-counting function Finite field Analytic number theory Mathematics Mathematical analysis
28	Optimal software-implemented Itoh–Tsujii inversion for F2m Jeremy Maitin-Shepard [removed] University of California at Berkeley Abstract Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2015-01-13 04:01:36 Field theory Finite fields Exponentials Computational complexity theory Computer arithmetic Exponentiation by squaring Polynomial basis Addition chain Elliptic curve cryptography Abstract algebra Mathematics Algebra
29	Working with Signed Numbers.pub Add to Reading List Source URL: www.cc.viu.ca Language: English - Date: 2013-08-06 19:32:44 Multiplication Addition Plus and minus signs Division 0 Negative number Finite field arithmetic Mathematics Elementary arithmetic Arithmetic
30	ON THE 4-RANK OF CLASS GROUPS OF QUADRATIC NUMBER FIELDS DJORDJO MILOVIC ´ ´ PARIS-SUD 11 ADVISOR: ETIENNE Add to Reading List Source URL: www.algant.eu Language: English - Date: 2013-07-05 07:44:32 Algebraic number theory Modular arithmetic Quadratic residue Finite fields Quadratic reciprocity Quadratic field Prime number XTR Quadratic form Abstract algebra Mathematics Number theory

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