The quadratic sieve factoring algorithm
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Factoring integers using SIMD sieves
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Applied cryptography (2nd ed.): protocols, algorithms, and source code in C
Applied cryptography (2nd ed.): protocols, algorithms, and source code in C
Improving functional density through run-time constant propagation
FPGA '97 Proceedings of the 1997 ACM fifth international symposium on Field-programmable gate arrays
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Handbook of Applied Cryptography
Handbook of Applied Cryptography
The Magic Words are Squeamish Ossifrage
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
RaPiD - Reconfigurable Pipelined Datapath
FPL '96 Proceedings of the 6th International Workshop on Field-Programmable Logic, Smart Applications, New Paradigms and Compilers
High-performance automatic target recognition through data-specific VLSI
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Reconfigurable computing: a survey of systems and software
ACM Computing Surveys (CSUR)
CAIRN 2: An FPGA Implementation of the Sieving Step in the Number Field Sieve Method
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
The input-aware dynamic adaptation of area and performance for reconfigurable accelerator
Proceedings of the ACM/SIGDA international symposium on Field programmable gate arrays
Hardware parallelism vs. software parallelism
HotPar'09 Proceedings of the First USENIX conference on Hot topics in parallelism
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Most advanced forms of security for electronic transactions rely on the public-key cryptosystems developed by Rivest, Shamir and Adleman. Unfortunately, these systems are only secure while it remains difficult to factor large integers. The fastest published algorithms for factoring large numbers have a common sieving step. These sieves collect numbers that are completely factored by a set of prime numbers that are known in advance. Furthermore, the time required to execute these sieves currently dominates the runtime of the factoring algorithms. We show how the sieving process can be mapped to the Mojave configurable computing architecture. The mapping exploits unique properties of the sieving algorithms to fully utilize the bandwidth of a multiple bank interleaved memory system. The sieve has been mapped to a single programmable hardware unit on the Mojave computer, and achieves a clock frequency of 16 MHz. The full system implementation sieves over 28 times faster than an UltraSPARC Workstation. A simple upgrade to 8ns SRAMs will result in a speedup factor of 160.