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An architecture for elliptic curve cryptograph computation

Published: 01 March 2005 Publication History

Abstract

It is known that several public key cryptosystems such as RSAs, ElGamals and elliptic curve cryptosystems [1], and also elliptic curve cryptosystems require smaller keys and more efficient operation than RSAs and ElGamals for same security. For example, elliptic curve cryptosystems with 160 bits key have same security as RSAs and ElGamals with 1024 bits key have. We focus elliptic curve cryptosystems and propose an architecture of computation unit for an elliptic curve cryptosystem with small hardware.

References

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N. Koblitz, A Course in Number Theory, Springer-Verlag, 1987.
[2]
J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.
[3]
P. L. Montgomery, "Speeding the Pollard and Elliptic Curve Methods of Factorization", Mathematics of computation, Vol. 48, No. 177, pp 243--264, 1987.
[4]
D. V. Bailey, C. Paar, "Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms", Advances in Cryptology--CRYPTO'98, LNCS 1462, pp 472--485, Springer, 1998.
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A. R. Omondi, Computer Arithmetic Systems, Prentice Hall, 1994.
[6]
Parthenon, http://www.kecl.ntt.co.jp/parthenon/html/intro.htm
[7]
K. Aoki, "How fast can an elliptic curve cryptosystem be?" (in Japanese), http://www.math.is.tohoku.ac.jp/~taya/sendaiNT/2000/aoki_m.pdf.
[8]
T. Kobayashi, H. Morita, K. Kobayashi, and F. Hoshino, "Fast Elliptic Curve Algorithm Combining Frobenius Map and Table Reference to Adapt to Higher Characteristic", Advances in Cryptology--EUROCRYPT'99, LNCS 1592, pp 176--189, Springer, 1999.

Cited By

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  • (2022)Field Programmable Gate Array based elliptic curve Menezes‐Qu‐Vanstone key agreement protocol realization using Physical Unclonable Function and true random number generator primitivesIET Circuits, Devices & Systems10.1049/cds2.1211116:5(382-398)Online publication date: 9-Feb-2022
  • (2018)Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards CurveACM Transactions on Reconfigurable Technology and Systems10.1145/323174311:2(1-19)Online publication date: 8-Nov-2018
  • (2007)An Elliptic Curve Cryptosystem Design Based on FPGA Pipeline FoldingProceedings of the 13th IEEE International On-Line Testing Symposium10.1109/IOLTS.2007.15(71-78)Online publication date: 8-Jul-2007

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Published In

cover image ACM SIGARCH Computer Architecture News
ACM SIGARCH Computer Architecture News  Volume 33, Issue 1
Special issue: Workshop on architectural support for security and anti-virus (WASSA)
March 2005
159 pages
ISSN:0163-5964
DOI:10.1145/1055626
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 2005
Published in SIGARCH Volume 33, Issue 1

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Cited By

View all
  • (2022)Field Programmable Gate Array based elliptic curve Menezes‐Qu‐Vanstone key agreement protocol realization using Physical Unclonable Function and true random number generator primitivesIET Circuits, Devices & Systems10.1049/cds2.1211116:5(382-398)Online publication date: 9-Feb-2022
  • (2018)Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards CurveACM Transactions on Reconfigurable Technology and Systems10.1145/323174311:2(1-19)Online publication date: 8-Nov-2018
  • (2007)An Elliptic Curve Cryptosystem Design Based on FPGA Pipeline FoldingProceedings of the 13th IEEE International On-Line Testing Symposium10.1109/IOLTS.2007.15(71-78)Online publication date: 8-Jul-2007

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