Question

Encryption Stage Take two primes p and q. (In practice, p and q are very large primes. In this worksheet, we use small number for simplicity.). Set n=pq and pick an e that is relatively prime to (p−1)(q−1). The value pair (n,e) is the public encryption key. You can give this to anyone, and they can encrypt data as follows: - Take any integer 0

Answer 1

The question involves the creation of a public key for encryption using prime numbers in mathematics, specifically within cryptography. A pair of primes is chosen, and their product along with another number relatively prime to (p-1)(q-1) forms the public key (n, e), used for encrypting messages.

Step-by-step explanation:

The question describes the initial steps of setting up a public key encryption system, which is a concept in cryptography within the field of mathematics and computer science. The process involves choosing two prime numbers, p and q, then computing their product n=pq to form part of the public key.

The other part of the public key is an integer e, chosen such that it is relatively prime to (p-1)(q-1), which means e and (p-1)(q-1) share no divisors other than 1. The public key consisting of (n, e) can then be used to encrypt messages.

For example, if we select p = 5 and q = 11, then n = 55, and (p - 1)(q - 1) = 40. We could choose e = 3 because 3 is relatively prime to 40. Hence, our public key is (55, 3). This key can be used to encrypt data using a specific encryption algorithm, typically the RSA algorithm in this kind of cryptographic system.