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a) The remainder when 233 is divider by 17 is 16. b) 2 19 (mod 11) c) If n is odd, then n² = 1 (mod 8)

a) The remainder when 233 is divider by 17 is 16. b) 2 19 (mod 11) c) If n is odd, then n² = 1 (mod 8)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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a) The remainder when 233 is divider by 17 is 16. b) 2 19 (mod 11) c) If n is odd, then n² = 1 (mod 8) d) p(n-1)=n-2 if and only if n is prime. e) φ(120) = 32 f) Suppose p = 4k + 3 is prime and a is a quadratic residue modulo p. Then x = ak+1 will always satisfy the congruence x² = a (mod p). g) The AES was not designed to replace the Data Encryption Standard. h) Transposition is a mathematical operation that cannot be reversed. i) Let p be and odd prime and a an integer such that gcd(a, p) = 1. Then the congruence x² = 1 (mod p) has always two solutions. j) Bob received a digitally signed message from Alice; he should use his public key to verify the digital signature. k) An X.509v3 certificate is an IETF standard. 1) Transport mode provides protection to the entire IP packet. m) Using RSA, if an opponent can factor n into its two prime factors, enables him to figure out the private key. n) Firewalls cannot hide the internal destination port numbers and IP addresses. o) Alice and Bob cannot create a session key between themselves without using their public-key schemes.
Transcribed Image Text:a) The remainder when 233 is divider by 17 is 16. b) 2 19 (mod 11) c) If n is odd, then n² = 1 (mod 8) d) p(n-1)=n-2 if and only if n is prime. e) φ(120) = 32 f) Suppose p = 4k + 3 is prime and a is a quadratic residue modulo p. Then x = ak+1 will always satisfy the congruence x² = a (mod p). g) The AES was not designed to replace the Data Encryption Standard. h) Transposition is a mathematical operation that cannot be reversed. i) Let p be and odd prime and a an integer such that gcd(a, p) = 1. Then the congruence x² = 1 (mod p) has always two solutions. j) Bob received a digitally signed message from Alice; he should use his public key to verify the digital signature. k) An X.509v3 certificate is an IETF standard. 1) Transport mode provides protection to the entire IP packet. m) Using RSA, if an opponent can factor n into its two prime factors, enables him to figure out the private key. n) Firewalls cannot hide the internal destination port numbers and IP addresses. o) Alice and Bob cannot create a session key between themselves without using their public-key schemes.
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