On Improving Integer Factorization and Discrete Logarithm Computation using Partial Triangulation

The number field sieve is the best-known algorithm for factoring integers and solving the discrete logarithm problem in prime fields. In this paper, we present some new improvements to various steps of the number field sieve. We apply these improvements on the current 768-bit discrete logarithm record and show that we are able to perform the overall computing time in about 1260 core$\cdot$years using these improvements instead of 2350 core$\cdot$years using the best known parameters for this problem. Moreover, we show that the pre-computation phase for a 768-bit discrete logarithm problem, that allows for example to build a massive decryption tool of IPsec traffic protected by the Oakley group~1, was feasible in reasonable time using technologies available before the year 2000

Analysis of Bernstein's factorization circuit

D.J. Bernstein has proposed a circuit-based implementation of the matrix step of the number field sieve factorization algorithm (see "Circuits for integer factorization: a proposal", http://cr.yp.to/papers.html#nfscircuit, 2001). These circuits offer an asymptotic cost reduction under the measure "construction cost × run time". We evaluate the cost of these circuits, in agreement with Bernstein, but argue that, compared to previously known methods, these circuits can factor integers that are 1.17 times larger, rather than 3.01 as claimed (and even this is only under the non-standard cost measure). We also propose an improved circuit design based on a new mesh routing algorithm, and show that, for factorization of 1024-bit integers, the matrix step can, under an optimistic assumption about the matrix size, be completed within a day by a device that costs a few thousand dollars. We conclude that from a practical standpoint, the security of RSA relies exclusively on the hardness of the relation collection step of the number field siev

Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control

The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Computational methods and software systems for dynamics and control of large space structures

This final report on computational methods and software systems for dynamics and control of large space structures covers progress to date, projected developments in the final months of the grant, and conclusions. Pertinent reports and papers that have not appeared in scientific journals (or have not yet appeared in final form) are enclosed. The grant has supported research in two key areas of crucial importance to the computer-based simulation of large space structure. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area, as reported here, involves massively parallel computers

13th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, CA, March 17-21, 1997, Conference Proceedings Volumes I & II

Includes Volumes 1 &

Research in Structures and Dynamics, 1984

A symposium on advanced and trends in structures and dynamics was held to communicate new insights into physical behavior and to identify trends in the solution procedures for structures and dynamics problems. Pertinent areas of concern were (1) multiprocessors, parallel computation, and database management systems, (2) advances in finite element technology, (3) interactive computing and optimization, (4) mechanics of materials, (5) structural stability, (6) dynamic response of structures, and (7) advanced computer applications