A few years ago a new kind of public key cryptosystems was proposed, called Identity Based Cryptography (IBC), which uses each user identity as his public key. IBC has had practical applications in e-mail communications and instant messengers. One of its most important goals is the efficient evaluation of cryptographically secure bilinear maps, as the Tate or Weil pairings. Most people in pairi...

Counting rational points on Jacobian varieties of hyperelliptic curves over finite fields is very important for constructing hyperelliptic curve cryptosystems (HCC), but known algorithms for general curves over given large prime fields need very long running times. In this article, we propose an extremely fast point counting algorithm for hyperelliptic curves of type y = x + ax over given large...