'Mod 7' diaporamas de présentation

NUMBER THEORY AND ALGEBRA

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In particular, when p is a prime & k not a multiple of p, then gcd( k,p )=1.

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??????????? 4 ?

??????????? 4 ?. ???? ?????? kurosawa@mx.ibaraki.ac.jp. ??. m 2 ?. ? m 1 ,. E_K. E_K. Tag. CBC-MAC ???????? M=(m 1 , m 2 ), Tag ?????????. E k. E k. E k. E k. m 2. m 2 ?. ? m 1 ,. m 1 + Tag. m 1. Tag. Tag. ??????. ? k. ??? ?????? E. ?? ?????? D. ??? C. ?? m. m.

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PART?

PART?. ????????????. PART?-03. ????. ??. ???? (Information Security) ????????? (Cryptography) ?????????????? (Number Theory) ? ???????????????????????????????????????????. ???? ( ? ). ???? ???? ( Modular Arithmetic) ???????????????? (Modular Operation) ????????????????????

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Cryptography

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Chinese Remainder Theorem

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CSE 311 Foundations of Computing I

CSE 311 Foundations of Computing I. Lecture 10 Modular Arithmetic Spring 2013. Announcements. Reading assignments Modular Arithmetic: 4.1-4.2 7 th Edition 3.4-3.5 6 th Edition For Wednesday-Monday: 4.3-4.4 to page 277 7 th Edition 3.6-3.7 to page 236 6 th Edition

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CSE 311 Foundations of Computing I

CSE 311 Foundations of Computing I. Lecture 11 Modular Arithmetic Autumn 2012. Announcements. Reading assignments Today and Friday: 4.1-4.3 7 th Edition 3.5, 3.6 6 th Edition 2.5, 2.6 up to p. 191 5 th Edition Homework 4 Available now.

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IE MS5710 Introduction to Number Theory II

IE MS5710 Introduction to Number Theory II. 5 Feb 20 13 Prof. CHAN Yuen-Yan, Rosanna Department of Information Engineering The Chinese University of Hong Kong. Basic Number Theory Divisor. say a non-zero number b divides a if for some m have a=mb ( a,b,m all integers)

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CSE 311: Foundations of Computing

CSE 311: Foundations of Computing. Fall 2013 Lecture 10: Functions, Modular arithmetic. announcements. Reading assignment Modular arithmetic 4.1-4.2, 7 th edition 3.4-3.5, 6 th edition Homework 3 due now Graded Homework 2 and Solutions available Homework 4 out later today.

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CSE 311 Foundations of Computing I

CSE 311 Foundations of Computing I. Lecture 10 Divisibility and Modular Arithmetic Autumn 2011. Announcements. Reading assignments Today: 4.1-4.2 7 th Edition 3.4, 3.6 up to p. 227 6 th Edition 2.4, 2.5 up to p. 177 5 th Edition Homework 4

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CSE 311 Foundations of Computing I

CSE 311 Foundations of Computing I. Lecture 10 Divisibility and Modular Arithmetic Autumn 2011. Announcements. Reading assignments Today: 4.1-4.2 7 th Edition 3.4, 3.6 up to p. 227 6 th Edition 2.4, 2.5 up to p. 177 5 th Edition Homework 4

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CSE 321 Discrete Structures

CSE 321 Discrete Structures. Winter 2008 Lecture 8 Number Theory: Modular Arithmetic. Announcements. Readings Today: 3.4 (5 th Edition: 2.4) Monday and Wednesday: 3.5, 3.6, 3.7 (5 th Edition: 2.5, 2.6). Highlights from Lecture 7. Set Theory and ties to Logic

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Activity 2-11: Quadratic Reciprocity

www.carom-maths.co.uk. Activity 2-11: Quadratic Reciprocity. Modulo arithmetic is a helpful way to look at the properties of numbers. We say a ? b (mod c) if c divides a - b. Another way of putting it is that both a and b have the same remainder when divide by c. So 122 ? 45 (mod 11).

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Diffie-Hellman Key-Exchange Algorithm

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Friday the 13th

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