In the RSA cryptosystem, each individual has an encryption key (n, e) where n = pq, the modulus is the product of two large primes p and q, say with 200 digits each, and an exponent e that is relatively prime to (p 1)(q 1). To produce a usable key, two large primes must be found. This can be done quickly on a computer using probabilistic primality tests, referred to earlier in this section. However, the product of these primes n = pq, with approximately 400 digits, cannot, as far as is currently known, be factored in a reasonable length of time. As we will see, this is an important reason why decryption cannot, as far as is currently known, be done quickly without a separate decryption key. (

d) Encrypt the message ATTACK using the RSA system with n = 43 59 and e = 13, translating each letter into integers and grouping together pairs of integers.

(e) What is the original message encrypted using the RSA system with n = 43 59 and e = 13 if the encrypted message is 0667 1947 0671?