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ACM International Collegiate Programming Contest

ACM International Collegiate Programming Contest

ACM International Collegiate Programming Contest. Banff Springs, Alberta April 6 – 10, 2008. Sep. 22 (local) Oct. 6 (Oswego – preliminary) Nov. 10 (RIT – regional final). stefanko@cs.rochester.edu Sep. 11, CBS 601, 4:15pm. Office hours. Instructor office hours (CSB 620)

By milt
(200 views)

网络安全技术

网络安全技术

网络安全技术. 刘振 上海交通大学 计算机科学与工程系 电信群楼 3-509 liuzhen@sjtu.edu.cn. Number Theory. We work on integers only. Divisors. Two integers: a and b (b is non-zero) b divides a if there exists some integer m such that a = m · b Notation: b|a eg . 1,2,3,4,6,8,12,24 divide 24

By stormy
(460 views)

Ancient Wisdom: Primes, Continued Fractions, The Golden Ratio, and Euclid’s GCD

Ancient Wisdom: Primes, Continued Fractions, The Golden Ratio, and Euclid’s GCD

Ancient Wisdom: Primes, Continued Fractions, The Golden Ratio, and Euclid’s GCD. Definition: A number > 1 is prime if it has no other factors, besides 1 and itself. Each number can be factored into primes in a unique way. [Euclid].

By walden
(228 views)

CS/ECE Advanced Network Security Dr. Attila Altay Yavuz

CS/ECE Advanced Network Security Dr. Attila Altay Yavuz

CS/ECE Advanced Network Security Dr. Attila Altay Yavuz. Topic 4 Basic Number Theory Credit: Prof. Dr. Peng Ning. Fall 2014. Outline. GCD Totient (Euler-Phi), relative primes Euclid and Extended Euclid Algorithm Little Fermat, Generalized Fermat Theorem

By thane
(90 views)

Modular (Remainder) Arithmetic

Modular (Remainder) Arithmetic

n = qk + r (for some k; r < k) eg 37 = (2)(17) + 3 Divisibility notation: 17 | 37 - 3. n mod k = r 37 mod 17 = 3. Modular (Remainder) Arithmetic. Sets of Remainders. x -2 (5 – 2) -1 (5 – 1) * 0 1 2 3 4 5 6 7 8. x mod 5 3 4 0 1 2 3 4 0 1 2 3.

By tiva
(1447 views)

CS 2210:0001Discrete Structures Modular Arithmetic and Cryptography

CS 2210:0001Discrete Structures Modular Arithmetic and Cryptography

CS 2210:0001Discrete Structures Modular Arithmetic and Cryptography. Fall 2017 Sukumar Ghosh. Preamble. Historically, number theory has been a beautiful area of study in pure mathematics . However, in modern times, number theory is very important in the area of security .

By omer
(370 views)

Announcements: Pass in Homework 5 now. Term project groups and topics due by Friday

Announcements: Pass in Homework 5 now. Term project groups and topics due by Friday

DTTF/NB479: Dszquphsbqiz Day 22. Announcements: Pass in Homework 5 now. Term project groups and topics due by Friday Can use discussion forum to find teammates HW6 posted Questions? This week: Primality testing, factoring Discrete Logs. 1.

By domani
(138 views)

RSA Cryptosystem

RSA Cryptosystem

RSA Cryptosystem. by Drs. Charles Tappert and Ron Frank The information presented here comes primarily from https ://en.wikipedia.org/wiki/RSA_(cryptosystem ) and http://www.math.uchicago.edu/~ may/VIGRE/VIGRE2007/ REUPapers /FINALAPP/Calderbank.pdf. RSA Cryptosystem.

By azura
(131 views)

DTTF/NB479: Dszquphsbqiz 		 Day 9

DTTF/NB479: Dszquphsbqiz Day 9

DTTF/NB479: Dszquphsbqiz Day 9. Announcements: Homework 2 due now Computer quiz Thursday on chapter 2 Questions? Today: Finish congruences Fermat’s little theorem Euler’s theorem Important for RSA public key crypto – pay careful attention!.

By Faraday
(177 views)

第三章 數學基礎

第三章 數學基礎

第三章 數學基礎 例如 數論 (Number Theory) ,資訊理論 (Information Theory) ,複雜度理論 (Complexity Theory) ,組合論 (Combinatoric Theory) ,機率 (Probability) 及線性代數 (Linear Algebra) 等等數學理論 數論應是近代密碼學中 ( 尤其是公開金匙密碼系統中 ) 最重要的數學基礎。 2.0 群 (Group): (G, *) G: a set; *: an operation Associativity: a*(b*c) = (a*b)*c

By cerise
(189 views)

公開鍵 暗号系

公開鍵 暗号系

公開鍵 暗号系. 2011/05/09. 公開鍵暗号. Diffie Hellman 鍵共有理論  1976 1978 年 R. L.  R ivest , A.  S hamir, L. M.  A dleman 実際には英国が最初に開発 GCHQ James Ellis 1969 Cliford Coks 1973 特徴 暗号化に必要な公開鍵 複合化に必要な秘密鍵 公開鍵と暗号化プロセス、複合化プロセスが分かっていても、秘密鍵を見つけるのは困難. RSA 暗号の原理. 素因数分解を応用 概念

By lucine
(56 views)

情報セキュリティ特論( 6 )

情報セキュリティ特論( 6 )

情報セキュリティ特論( 6 ). 黒澤 馨 (茨城大学) kurosawa@mx.ibaraki.ac.jp. RSA 暗号    素因数分解の困難さ ElGamal 暗号    離散対数問題の困難さ. RSA 暗号    素因数分解の困難さ ElGamal 暗号    離散対数問題の困難さ   答えは、 x=3. 離散対数問題. y=a x mod p (= 素数)  となる x を求めよ、という問題。 p=1024 ビットのとき、 10 億年. mod 5 において. フェルマーの定理. 2 の位数は 4. mod 5 において.

By tirza
(218 views)

天津大学

天津大学

数论. 天津大学. 初等数论的概念. 整除性和约数: 假设 d 和 a 是整数, d|a (读作 d 整除 a ),意味着存在某个整数 k ,有 a=kd 。 如果 d|a ,并且 d≥0 ,则称 d 是 a 的约数。 每个整数 a 都可以被其平凡约数 1 和 a 整除, a 的非平凡约数也成为 a 的因子。. 初等数论的概念. 素数和和数 对于某个整数 a>1 ,如果它仅有平凡约束 1 和 a 则称 p 是素数。否则 p 是合数。 可以证明素数有无限多个。 筛法求素数。. 初等数论概念. 除法定理,余数和同模

By brandy
(172 views)

天津大学

天津大学

数论. 天津大学. 初等数论的概念. 整除性和约数: 假设 d 和 a 是整数, d|a (读作 d 整除 a ),意味着存在某个整数 k ,有 a=kd 。 如果 d|a ,并且 d≥0 ,则称 d 是 a 的约数。 每个整数 a 都可以被其平凡约数 1 和 a 整除, a 的非平凡约数也称为 a 的因子。. 初等数论的概念. 素数和和数 对于某个整数 a>1 ,如果它仅有平凡约数 1 和 a 则称 p 是素数。否则 p 是合数。 可以证明素数有无限多个。 筛法求素数。. 初等数论概念. 除法定理,余数和同模

By gage
(161 views)

IS 2150 / TEL 2810 Introduction to Security

IS 2150 / TEL 2810 Introduction to Security

IS 2150 / TEL 2810 Introduction to Security. James Joshi Associate Professor, SIS Lecture 7 Oct 20, 2009 Basic Cryptography Network Security. Objectives. Understand/explain/employ the basic cryptographic techniques Review the basic number theory used in cryptosystems Classical system

By abril
(122 views)

Some Number Theory

Some Number Theory

Some Number Theory. Modulo Operation: Question: What is 12 mod 9? Answer: 12 mod 9  3 or 12  3 mod 9 Definition: Let a , r , m   (where  is a set of all integers) and m  0. We write a  r mod m if m divides r – a. m is called the modulus.

By feryal
(125 views)

VIL CRHF from FIL CRHF: adding IV

VIL CRHF from FIL CRHF: adding IV

x[1]. x[2]. …. x[l]. VIL CRHF from FIL CRHF: adding IV. Build VIL CRHF h:{0,1} *  {0,1} m from FIL CRHF c:{0,1} n  {0,1} m 1 st Idea: use iterative process, compressing block by block 2 nd idea: use a fixed IV as first block y 0 =IV {0,1} m

By watson
(85 views)

第4章 公钥密码

第4章 公钥密码

第4章 公钥密码. 4.1 密码学中一些常用的数学知识 4.2 公钥密码体制的基本概念 4.3 RSA 算法 4.4 背包密码体制 4.5 Rabin 密码体制 4.6 椭圆曲线密码体制 习题. 4.1 密码学中一些常用的数学知识. 4.1. 2 素数和互素数. 1. 因子 设 a,b ( b ≠0) 是两个整数,如果存在另一整数 m , 使得 a = mb , 则称 b 整除 a , 记为 b|a , 且称 b 是 a 的因子。. 整数具有以下性质: ① a |1, 那么 a =±1。

By tilly
(167 views)

Authors: K. W. Kim, E. K. Ryu and K. Y. Yoo Authors: K. J. Lee and B. J. Lee

Authors: K. W. Kim, E. K. Ryu and K. Y. Yoo Authors: K. J. Lee and B. J. Lee

Cryptanalysis of Lee-Lee authenticated key agreement scheme Cryptanalysis of the modified authenticated key agreement scheme. Authors: K. W. Kim, E. K. Ryu and K. Y. Yoo Authors: K. J. Lee and B. J. Lee Source: Applied Mathematics and Computation, 2005 Reporter: Chun-Ta Li ( 李俊達 ). Outline.

By thelma
(140 views)

Aritmética Computacional

Aritmética Computacional

Aritmética Computacional. Francisco Rodríguez Henríquez CINVESTAV e-mail: francisco@cs.cinvestav.mx. Fairy Tale : Chinese Emperor used to count his army by giving a series of tasks. All troops should form groups of 3. Report back the number of soldiers that were not able to do this.

By stacie
(160 views)

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