ESIGN
As a researcher, you should never dismiss a method, even though it isn’t currently used. There are often opportunities to bring back methods, as has been shown with post-quantum cryptography (PQC) and lightweight cryptography. So let’s look at a smart little signature scheme called ESIGN (Efficient digital SIGNature). The method involves the generation of two random prime numbers (p and q), and generates a value of n=p²q. It was created by Fujioka et al [1], and is defined as a fast method of creating signatures, and where the difficulty relates to the factorization of integers [here]:
In this method, we generate two prime numbers p and q and then compute:
n=p²q
Next, we select a positive integer (k) and which must be greater than or equal to four. Alice’s public key is then (n,k) and her private key is (p,q).
Signature generation
First, we take a message (M) and compute its hash:
Next, we generate a random number x and which is between zero and pq, and then we compute:
