Proceedings ArticleDOI
Montgomery modular exponentiation on reconfigurable hardware
T. Blum,Christof Paar +1 more
- pp 70-77
TLDR
This contribution proposes arithmetic architectures which are optimized for modern field programmable gate arrays (FPGAs) and shows that it is possible to implement modular exponentiation at secure bit lengths on a single commercially available FPGA.Abstract:
It is widely recognized that security issues will play a crucial role in the majority of future computer and communication systems. Central tools for achieving system security are cryptographic algorithms. For performance as well as for physical security reasons, it is often advantageous to realize cryptographic algorithms in hardware. In order to overcome the well-known drawback of reduced flexibility that is associated with traditional ASIC solutions, this contribution proposes arithmetic architectures which are optimized for modern field programmable gate arrays (FPGAs). The proposed architectures perform modular exponentiation with very long integers. This operation is at the heart of many practical public-key algorithms such as RSA and discrete logarithm schemes. We combine the Montgomery modular multiplication algorithm with a new systolic array design, which is capable of processing a variable number of bits per array cell. The designs are flexible, allowing any choice of operand and modulus. Unlike previous approaches, we systematically implement and compare several variants of our new architecture for different bit lengths. We provide absolute area and timing measures for each architecture. The results allow conclusions about the feasibility and time-space trade-offs of our architecture for implementation on Xilinx XC4000 series FPGAs. As a major practical result we show that it is possible to implement modular exponentiation at secure bit lengths on a single commercially available FPGA.read more
Citations
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[서평]「Applied Cryptography」
TL;DR: The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity.
Journal ArticleDOI
Montgomery exponentiation needs no final subtractions
TL;DR: Montgomery's modular multiplication algorithm is commonly used in implementations of the RSA cryptosystem and it has been observed that there is no need for extra cleaning up at the end of an exponentiation if the method is correctly set up.
Journal ArticleDOI
A scalable architecture for modular multiplication based on Montgomery's algorithm
TL;DR: A word-based version of MM is presented and used to explain the main concepts in the hardware design and gives enough freedom to select the word size and the degree of parallelism to be used, according to the available area and/or desired performance.
Journal ArticleDOI
Security on FPGAs: State-of-the-art implementations and attacks
TL;DR: This contribution provides a state-of-the-art description of security issues on FPGAs, both from the system and implementation perspectives, and summarizes both public and symmetric-key algorithm implementations on FGPAs.
References
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Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
New Directions in Cryptography
TL;DR: This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.
Journal ArticleDOI
A method for obtaining digital signatures and public-key cryptosystems
TL;DR: An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key.
Book
Handbook of Applied Cryptography
TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
Journal ArticleDOI
Elliptic curve cryptosystems
TL;DR: The question of primitive points on an elliptic curve modulo p is discussed, and a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point is given.