Digital Signature Scheme: RSA vs ElGamal
What is the value of s in the RSA Digital Signature scheme given the public key (187, 101), private key 141, and message 47?
Calculating the RSA Digital Signature
Explanation:
In the RSA Digital Signature scheme, the value of s is calculated using the formula:
s = m^d mod n
Where:
- s is the value of the signature
- m is the message to be signed
- d is the private key
- n is the product of two prime numbers p and q, which are part of the public key
In this case, the public key is given as (187, 101), which means that n = 187. The private key is given as d = 141. The message to be signed is m = 47.
Substituting these values into the formula, we get:
s = 47^141 mod 187
To calculate the value of s, we can use modular exponentiation. By raising 47 to the power of 141 and taking the remainder when divided by 187, we can find the value of s.
This calculation leads to s = 61, which is the value of the signature for the given message in the RSA Digital Signature scheme.