In the PubVer phase, to compute the corresponding terms in the checking equation, the third party verifier needs to execute n times of pairing arithmetic, n times of exponential modulo arithmetic in [G.sub.T], and n times of multiplication arithmetic in [G.sub.T], respectively.
Modulo arithmetic and the one-time pad, explained through a combination of mathematics and text, are followed by descriptions of encrypting techniques using inverse numbers, prime numbers, factors of large numbers and one-way hash functions.