Parallel cryptographic arithmetic using a redundant Montgomery representation

We describe how using a redundant Montgomery representation allows for high-performance SIMD-based implementations of RSA and elliptic curve cryptography. This is in addition to the known benefits of immunity from timing attacks afforded by the use of such a representation. We present some prelimina...

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Published in:IEEE transactions on computers Vol. 53; no. 11; pp. 1474 - 1482
Main Authors: Page, D., Smart, N.P.
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2004
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
algorithm design and analysis
Computer instructions
Index Terms- Public key cryptosystems
parallel and vector implementations
Parallel processing
performance measures
Pipeline arithmetic
Public key cryptography
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Abstract We describe how using a redundant Montgomery representation allows for high-performance SIMD-based implementations of RSA and elliptic curve cryptography. This is in addition to the known benefits of immunity from timing attacks afforded by the use of such a representation. We present some preliminary implementation timings using the SSE2 instruction set on a Pentium 4 processor and show that an SIMD parallel implementation of RSA can be around twice as fast as traditional sequential code. This is especially useful given the larger 2,048 bit RSA keys which are now being proposed for standard security levels. Finally, we remark on other application areas that improve the security of our work in the context of side-channel analysis while maintaining high performance.
AbstractList We describe how using a redundant Montgomery representation allows for high-performance SIMD-based implementations of RSA and elliptic curve cryptography. This is in addition to the known benefits of immunity from timing attacks afforded by the use of such a representation. We present some preliminary implementation timings using the SSE2 instruction set on a Pentium 4 processor and show that an SIMD parallel implementation of RSA can be around twice as fast as traditional sequential code. This is especially useful given the larger 2,048 bit RSA keys which are now being proposed for standard security levels. Finally, we remark on other application areas that improve the security of our work in the context of side-channel analysis while maintaining high performance.
Author Page, D.
Smart, N.P.
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SubjectTerms algorithm design and analysis
Computer instructions
Index Terms- Public key cryptosystems
parallel and vector implementations
Parallel processing
performance measures
Pipeline arithmetic
Public key cryptography
Title Parallel cryptographic arithmetic using a redundant Montgomery representation
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