Suppose an RSA communication between two parties, of Alice and Bob....
Question
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.
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.
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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
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
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