Since 1999 specialized hardware architectures for factoring numbers of 1024 bit size with the Generalized Number Field Sieve (GNFS) have attracted a lot of attention ([Ber], [ST]). Concerns about the feasibility of giant monolytic ASIC architectures such as TWIRL have been raised. Therefore, we propose a parallelized lattice sieving device called SHARK,… (More)
The security of the most popular asymmetric cryptographic scheme RSA depends on the hardness of factoring large numbers. The best known method for factorization large integers is the General Number Field Sieve (GNFS). Recently, architectures for special purpose hardware for the GNFS have been proposed [5, 12]. One important step within the GNFS is the… (More)
CONTENTS We construct elliptic curves over Qof high Mordell-Weil rank, Introduction W \\h a nontrivial torsion subgroup. We improve the rank records 1.
The security of the most popular asymmetric cryptographic scheme RSA depends on the hardness of factoring large numbers. The best known method for this integer factorization is the General Number Field Sieve (GNFS). One important step within the GNFS is the factorization of mid-size numbers without small prime divisors. This can be done efficiently by the… (More)
— Hyperelliptic curve cryptography recently received a lot of attention , especially for constrained environments. Since there space is critical, compression techniques are interesting. In this note we propose a new method which avoids factoring the first representing polynomial. In the case of genus two the cost for decompression is, essentially, computing… (More)