  The El-Gamal AA_{\beta} Public Key Cryptosystem is a new asymmetric
cryptosystem based on the piecewise AA_{\beta}-function. The
AA_{\beta}-function which is essentially a one way Boolean function was
motivated by the squaring and multiplying process while computing g^a (mod p)
in the Diffie Hellman key exchange procedure and also computing C \equiv M^e
(mod N) and M \equiv C^d (mod N) in the RSA cryptosystem. It was also motivated
by the add and double point operation E=kG in the elliptic curve cryptosystem.
The hard mathematical problem surrounding this newly designed asymmetric
cryptosystem is the NP-complete problem known as the subset sum problem. The
El-Gamal AA_{\beta} Public Key Cryptosystem mimics the El-Gamal Cryptosystem
and the Elliptic Curve Cryptosystem by sending a two parameter ciphertext to
the recipient.
