Mathematics for Computer Science

8.7. Arithmetic with an Arbitrary Modulus 213 mirrors the proof of Fermat’s Theorem. In particular, k 1
k 2


kr Drem.k 1
k;n ...

Chapter 8 Number Theory214 (a) Ifpis a prime, then.pk/Dpkpk^1 fork 1. (b) Ifaandbare relatively prime, then.ab/D.a/.b/. Her ...

8.8. The RSA Algorithm 215 The RSA Cryptosystem Beforehand The receiver creates a public key and a secret key as follows. Gener ...

Chapter 8 Number Theory216 receiver does using the Pulverizer —but it is not known how to factornintop andqin any reasonable amo ...

8.9. What has SAT got to do with it? 217 Class Problems Problem 8.2. A number isperfectif it is equal to the sum of its positive ...

Chapter 8 Number Theory218 Homework Problems Problem 8.5. Define the Pulverizer State machine to have: statesWWDN^6 start stateW ...

8.9. What has SAT got to do with it? 219 (b)Describe in general how to find the gcd.m;n/and lcm.m;n/from the prime factorization ...

Chapter 8 Number Theory220 Problem 8.11. At one time, the Guinness Book of World Records reported that the “greatest human calcu ...

8.9. What has SAT got to do with it? 221 prime,p. Find a solution to the congruences ym 1 xCb 1 .modp/ ym 2 xCb 2 .modp/ whenm ...

Chapter 8 Number Theory222 theChinese Remainder Theorem, which says that for allm;n, there is anxsuch that xmmoda; (8.16) xn m ...

8.9. What has SAT got to do with it? 223 (b)For any positive integer,k, letkbe the integers inŒ1;k/that are relatively prime to ...

Chapter 8 Number Theory224 k-bit pieces, using the hardware to perform the additions and multiplications on the pieces, and then ...

8.9. What has SAT got to do with it? 225 5 = All your base are belong to us. 6 = Someone onourteam thinks someone onyourteam i ...

Chapter 8 Number Theory226 In this problem we will examine theRabin cryptosystemthat does have such a security certification. Na ...

8.9. What has SAT got to do with it? 227 sy^2 .modp/.y^0 /^2 .modp/thenshas exactly four square roots, namely, s.xy/^2 .x^0 ...

Chapter 8 Number Theory228 (b)Conclude that 4 dividesx. (c)Show that if gcd.r;n/D 1 , thenrx1 .modn/: Asquare rootofmmodulonis ...

II Structures ...

...

Introduction Structure is fundamental in computer science. Whether you are writing code, solv- ing an optimization problem, or d ...

...