On Shimura's elliptic curve over Q(29)

Efficient elliptic curve cryptosystems

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

Platform Independent Elliptic Curve Cryptography over

Elliptic curve cryptography has long since moved into several wellknown standards like IEEE’s 1363, SEC and X9.62. With its small key sizes it is just right for many crypto applications, in particular for mobile computing and communication devices. To make ECC easily available for all these different applications, a highly efficient and platformindependent implementation of ECC is necessary. Th...

On degree zero semistable bundles over an elliptic curve

Motivated by the study of heterotic string compactifications on elliptically fibered Calabi-Yau manifolds, we present a procedure for testing semistability and identifying the decomposition type of degree zero holomorphic vector bundles over a nonsingular elliptic curve. The algorithm requires explicit knowledge of a basis of sections of an associated ‘twisted bundle’. a [email protected]

Hardware for Collision Search on Elliptic Curve over GF(2)

In this last decade, Elliptic Curve Cryptography (ECC) has gain increasing acceptance in the industry and the academic community and has been the subject of several standards. This interest is mainly due to the high level of security with relatively small keys provided by ECC. Indeed, no sub-exponential algorithms are known to solve the underlying hard problem, namely the Elliptic Curve Discret...

Elliptic Curve Cryptography on FPGAs