Cryptosystem

In our example of the affine cryptosystem family, deciphering is also accomplished by an affine map, namely P#92;equiva#123;-1#125;C-a#123;-1#125;b#92;bmodN, and so the deciphering transformation uses the same algorithm as the enciphering transformation, except with a different key, namely, the pair (a#123;-1#125;,-a#123;-1#125;b).

Our results show that many existing fast pseudomultiplication implementations (hitherto limited to applications in Diffie--Hellman key exchange) can be wrapped with simple and efficient pre-and post-computations to yield competitive full scalar multiplication algorithms, ready for use in more general discrete logarithm-based cryptosystems, including signature schemes.