Suppose an RSA communication between two parties, of Alice and Bob.
The Bob's public key is (187, 73).
The Alice encrypts a message m and sends to Bob in the following encrypted message (ciphertext) c = 42.
However, an eavesdropper, the Eve, monitors the communication channel and manages to read the encrypted message c.
Show how Eve can decrypt c and to acquire knowledge of the original message m.
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.
It is first useful to give an overview of the RSA algorithm and then apply for the provided numerical example.
n must decomposed in two prime factors p and q, thus n=p*q
It is computed φ(n)=(p-1)*(q-1)
We have e – the public exponent; it must be lower than φ(n) and GCD(e, φ(n))=1 (to be co-prime numbers).
It is computed the private exponent d, such way that to have d*e=1 mod φ(n)
The encryption process assumes that ciphertext c = m^e mod n, where m is the message in plaintext.
The decryption operation takes place like: m=c^d mod n...
This is only a preview of the solution. Please use the purchase button to see the entire solution