Modular arithmetic

Ebook BigNum math: Implementing cryptographic multiple precision arithmetic presents the following content: Chapter 1 introduction, chapter 2 getting started, chapter 3 basic operations, chapter 4 basic arithmetic, chapter 5 multiplication and squaring, chapter 6 modular reduction, chapter 7 exponentiation, chapter 8 higher level algorithms, chapter 9 number theoretic algorithms.

315p zizaybay1103 29-05-2024 3 2   Download

The paper extends author’s method of modular distributions to arithmetic automorphic L functions on general classical groups. Main resultat gives a p-adic interpolation of their critical L values in the form of integrals of distributions constructed from a given eigen function of Hecke algebras by applying BGG modules.

26p vioracle 25-09-2023 7 2   Download

Lecture Discrete mathematics: Chapter 4 provide students with content about: divisibility and modular arithmetic; integer representations and algorithms; primes and greatest common divisors; solving congruences; applications of congruences;... Please refer to the detailed lecture content!

84p diepkhinhchau 18-09-2023 6 3   Download

Advanced Algorithms Analysis and Design - Lecture 40: Chinese remainder theorem & RSA cryptosystem. In this lecture we will cover the following: modular arithmetic; solving modular linear equations; Chinese remainder theorem; unique representation of a number by CRT;...

27p andromedashun 26-05-2022 10 1   Download

Lecture Cryptography and network security: Chapter 2 after studying this section will help you understand: To review integer arithmetic, concentrating on divisibility and finding the greatest common divisor using the Euclidean algorithm; To understand how the extended Euclidean algorithm can be used to solve linear Diophantine equations, to solve linear congruent equations, and to find the multiplicative inverses;...

82p hoathachthao090 10-02-2022 19 4   Download

In this chapter, the following content will be discussed: Equivalence classes, equivalence classes of congruence modulo 3, equivalence of congruence modulo n, properties of congruence modulo n, modular arithmetic, partial order relations, hasse diagram.

33p larachdumlanat122 26-11-2020 6 1   Download

This chapter presents the following content: Number theory, divisibility & GCD, modular arithmetic with integers, Euclid’s algorithm for GCD & inverse, the AES selection process, the details of Rijndael – the AES cipher, looked at the steps in each round out of four AES stages.

52p koxih_kothogmih3 24-08-2020 11 3   Download

This chapter presents the following content: Number theory, divisibility & GCD, modular arithmetic with integers, Euclid’s algorithm for GCD & inverse, Group, Ring, Field, finite fields GF(p), polynomial arithmetic in general and in GF(2n).

51p koxih_kothogmih3 24-08-2020 39 3   Download

This chapter presents the following content: Number theory, divisibility & GCD, modular arithmetic with integers, Euclid’s algorithm for GCD & inverse, the AES selection process, the details of Rijndael – the AES cipher, looked at the steps in each round out of four AES stages, last two are discussed: MixColumns, AddRoundKey.

55p koxih_kothogmih3 24-08-2020 14 2   Download

Lecture Notes for transition to advanced has contents: Logic and proof, set theory and induction, relations, functions, cardnality, modular arithmetic, algebra, basic logical operations, definitions for our toy examples

115p bautroibinhyen19 02-03-2017 37 2   Download

Bài giảng "Nhập môn an toàn thông tin - Chương 2c: Toán học dùng cho mật mã" có cấu trúc gồm 2 phần cung cấp cho người học các kiến thức: Số học số nguyên (Integer Arithmetic), số học đồng dư (Modular Arithmetic). Mời các bạn cùng tham khảo.

118p thangnamvoiva20 20-09-2016 119 13   Download

Cùng tham khảo tài liệu Modular Arithmetic sau đây. Tài liệu tham khảo cho những ai yêu thích và muốn tìm hiểu về Toán học.

3p choninview 26-08-2015 43 4   Download

In the underlying finite field arithmetic of an elliptic curve cryptosystem, field multiplication is the next computational costly operation other than field inversion. We present two novel algorithms for efficient implementation of field multiplication and modular reduction used frequently in an elliptic curve cryptosystem defined over GF (2n ).

10p dunglh2013 02-04-2014 53 0   Download

We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus.

15p dunglh2013 02-04-2014 56 0   Download

The paper discusses some public key algorithms such as DH, RSA, DSA, ECDH and ECDSA and also gives mathematical explanations on the working of these algorithms. The paper also gives a brief introduction to modular arithmetic, which is the core arithmetic of almost all public key algorithms.

14p dunglh2013 02-04-2014 54 1   Download

This book contains 104 of the best problems used in the training and testing of the U.S. International Mathematical Olympiad (IMO) team. It is not a collection of very difficult, and impenetrable questions. Rather, the book gradually builds students’ number-theoretic skills and techniques. The first chapter provides a comprehensive introduction to number theory and its mathematical structures. This chapter can serve as a textbook for a short course in number theory.

213p retcl83 28-02-2013 120 36   Download

Let us first discuss some issues related, directly ,indirectly, to error detection and correction. Types of ErrorsRedundancyDetection Versus CorrectionForward Error Correction Versus RetransmissionCoding Modular Arithmetic

93p trada85 22-01-2013 89 8   Download

Elliptic units, which are obtained by evaluating modular units at quadratic imaginary arguments of the Poincar´e upper half-plane, provide us with a rich source of arithmetic questions and insights. They allow the analytic construction of abelian extensions of imaginary quadratic fields, encode special values of zeta functions through the Kronecker limit formula, and are a prototype for Stark’s conjectural construction of units in abelian extensions of number fields.

47p noel_noel 17-01-2013 47 8   Download

Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

266p chipmoon 19-07-2012 88 14   Download

Over half of the students who enrol on economics degree courses have not studied mathematics beyond GCSE or an equivalent level. These include many mature students whose last encounter with algebra, or any other mathematics beyond basic arithmetic, is now a dim and distant memory. It is mainly for these students that this book is intended. It aims to develop their mathematical ability up to the level required for a general economics degree course (i.e. one not specializing in mathematical economics) or for a modular degree course in economics and related subjects, such as business studies.

535p conrepcon 12-04-2012 103 38   Download