A distributed approach to proving large numbers prime
A distributed approach to proving large numbers prime
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Efficient Construction of Cryptographically Strong Elliptic Curves
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
A Software Library for Elliptic Curve Cryptography
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Generating Elliptic Curves of Prime Order
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
ShortPK: A short-term public key scheme for broadcast authentication in sensor networks
ACM Transactions on Sensor Networks (TOSN)
Generating prime order elliptic curves: difficulties and efficiency considerations
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
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We present a variant of the complex multiplication method that generates elliptic curves of cryptographically strong order. Our variant is based on the computation ofWeber polynomials that require significantly less time and space resources than their Hilbert counterparts. We investigate the time efficiency and precision requirements for generating off-line Weber polynomials and its comparison to another variant based on the off-line generation of Hilbert polynomials. We also investigate the efficiency of our variant when the computation of Weber polynomials should be made on-line due to limitations in resources (e.g., hardware devices of limited space). We present trade-offs that could be useful to potential implementors of elliptic curve cryptosystems on resource-limited hardware devices.