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Speeding Up the Discrete Log Computation on Curves With Automorphisms
, 1999
"... We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on ABC elliptic curves. This includes the first known attack on CM (hyper)elliptic curves, as well as most of the hyperelliptic curves described in the literature. ..."
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Cited by 30 (2 self)
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We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on ABC elliptic curves. This includes the first known attack on CM (hyper)elliptic curves, as well as most of the hyperelliptic curves described in the literature.
On the performance of hyperelliptic cryptosystems
, 1999
"... In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to generate suitable curves for use in cryptography. This paper presents a practical comparison between the performance of ellip ..."
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Cited by 30 (5 self)
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In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to generate suitable curves for use in cryptography. This paper presents a practical comparison between the performance of elliptic curve based digital signature schemes and schemes based on hyperelliptic curves. We conclude that, at present, hyperelliptic curves offer no performance advantage over elliptic curves.
EPOC: Efficient Probabilistic PublicKey Encryption
"... We describe a novel publickey cryptosystem, EPOC (Efficient Probabilistic PublicKey Encryption), which has three versions: EPOC1, EPOC2 and EPOC3. EPOC1 is a publickey encryption system that uses a oneway trapdoor function and a random function (hash function). EPOC2 and EPOC3 are public ..."
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Cited by 2 (0 self)
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We describe a novel publickey cryptosystem, EPOC (Efficient Probabilistic PublicKey Encryption), which has three versions: EPOC1, EPOC2 and EPOC3. EPOC1 is a publickey encryption system that uses a oneway trapdoor function and a random function (hash function). EPOC2 and EPOC3 are publickey encryption systems that use a oneway trapdoor function, two random functions (hash functions) and a symmetrickey encryption (e.g., onetime padding and blockciphers).
A RAPID GENERATION SCHEME OF LARGE PRIMES
"... RSA is by far the most widely adopted standard in public key cryptography algorithm. Its security depends on the Integer Factorization Problem, that it is very easy to calculate the product of two large prime numbers, but the decomposition the product and get the prime factors are very difficult. Th ..."
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RSA is by far the most widely adopted standard in public key cryptography algorithm. Its security depends on the Integer Factorization Problem, that it is very easy to calculate the product of two large prime numbers, but the decomposition the product and get the prime factors are very difficult. Therefore, the generations of large primes are important research field. This paper presented a rapid generation scheme of it, and the techniques for the related software implementation were presented. To speed up the modular multiplication and squaring, Montgomery's algorithms were used with sliding window method. Three pretreatments were also described in details. In view of prime generation of RSA, a series of design methods for software implementation was proposed and give the optimization programs.