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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)

- Jan Pelzl, Martin Šimka, +5 authors Viktor Fischer
- 2005

Since the introduction of public key cryptography, the problem of factoring large composites has been of increased interest. The security of the most popular asymmetric cryptographic scheme RSA depends on the hardness of factoring large numbers. The best known method for factoring large integers is the general number field sieve (GNFS). One important step… (More)

- Martin Simka, Jan Pelzl, +5 authors Viktor Fischer
- 13th Annual IEEE Symposium on Field-Programmable…
- 2005

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. One important step within the GNFS is the factorization… (More)

- Thorsten Kleinjung, Claus Diem, Arjen K. Lenstra, Christine Priplata, Colin Stahlke
- IACR Cryptology ePrint Archive
- 2017

- Jens Franke, Thorsten Kleinjung, +4 authors Colin Stahlke
- 2005

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)

- Colin Stahlke
- IACR Cryptology ePrint Archive
- 2004

— 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)

- Leopoldo Kulesz, Colin Stahlke
- Experimental Mathematics
- 2001

In order to find elliptic curves over Q with large rank, J.-F. Mestre [1991] constructed an infinite family of elliptic curves with rank at least 12. Then K. Nagao [1994] and S. Kihara [1997b] found infinite subfamilies of rank 13 and 14, respectively. By specialization, elliptic curves of rank at least 21 [Nagao and Kouya 1994], 22 [Fermigier 1997], and 23… (More)

- Jan Pelzl, Colin Stahlke
- 2005

Project co-funded by the European Commission within the 6th Framework Programme Dissemination Level PU Public X PP Restricted to other programme participants (including the Commission services) RE Restricted to a group specified by the consortium (including the Commission services) CO Confidential, only for members of the consortium (including the… (More)

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