# RSA decryption problem knowing public key and ciphertext [closed]

new member here.

I am taking a course in computer security, and we just got introduced in Cryptography and especially in RSA Algorithm. Although i got the 'basic idea' behind the RSA algorithm and the prime numbers needed for the keys, we have an assignment. Roughly the content of the exercise, is this : Suppose an RSA commmunication between Alice and Bob. Bob got his public key which is the following (187,73). Alice encrypts a message "m" and sends to Bob the following encrypted ciphertext c = 42. An eavesdropper (Eve) monitors the communication and somehow manages to read the encrypted message c Show how Eve can decrypt c and acquire knowledge of the original message m

I mean, reading this my first thought goes to factoring the numbers in Bob's key in order to continue ?

• Yes factorization of the public modulus (187) allows to compute a private exponent and decipher. Another method is to re-encipher the ciphertext iteratively until getting back at the ciphertext, which here happens at the fourth re-encryption. The last value encrypted, that encrypts to the ciphertext, is the plaintext. Neither method would work for a realistically large public modulus, which has several hundreds of decimal digits, rather than three. This post was closed as homework (and easy)
– fgrieu
Dec 7, 2022 at 18:12