Modern Terminology
In modern presentations, the algorithm is often simplified as follows
The hash function H is assumed to be a random oracle and the algorithm works as follows
- Key Generation
- The signer S chooses primes p,q each of size approximately k/2 bits, and computes the product
- The public key is n
- The private key is (p,q)
- Signing
- To sign a message m the signer S picks random padding U and calculates H(mU)
- If H(mU) is not a square modulo n, S picks a new pad U
- S solves the equation
- The signature on m is the pair (U,x)
- Verification
- Given a message m and a signature (U,x) the verifier V calculates x2 and H(mU) and verifies that they are equal
In some treatments, the random pad U is eliminated and instead we add two numbers a and b to the public key with and where denotes the legendre symbol. Then for any r modulo n exactly one of the four numbers will be a square, and the signer chooses that one for his signature.
Read more about this topic: Rabin Signature Algorithm
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