WGU D344 Cryptosystems Exam with Questions and Answers

WGU D344 Cryptosystems Exam with Questions and Answers A fundamental concept in number theory states that two integers are coprime if their greatest common divisor equals 1. Which condition correctly defines when integers a and b are coprime? a) a + b = 1 b) gcd(a, b) = 0 c) gcd(a, b) = 1 d) a mod b = 1 Correct Answer: c Rationale: Two integers are coprime if and only if their greatest common divisor is 1. This means they share no positive integer factors other than 1, which is essential in cryptographic key generation and modular inverses. In modular arithmetic used in cryptography, a modular inverse of a number a modulo n exists only under a specific condition. When does the modular inverse of a modulo n exist? a) When a n b) When a is prime c) When a mod n = 0 d) When gcd(a, n) = 1 Correct Answer: d Rationale: A modular inverse exists only if a and n are coprime. This ensures that there is an integer x such that ax ≡ 1 (mod n), which is fundamental in RSA key operations.