crypto_paper_from_chese

crypto_paper_from_chese - An End-to-End Systems Approach to...

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An End-to-End Systems Approach to Elliptic Curve Cryptography Nils Gura, Sheueling Chang Shantz, Hans Eberle, Sumit Gupta, Vipul Gupta, Daniel Finchelstein, Edouard Goupy, Douglas Stebila Sun Microsystems Laboratories { Nils.Gura, Sheueling.Chang, Hans.Eberle, Gupta.Sumit, Vipul.Gupta, Daniel.F.Finchelstein, Edouard.Goupy, Douglas.Stebila } @sun.com http://www.research.sun.com Abstract. Since its proposal by Victor Miller [17] and Neal Koblitz [15] in the mid 1980s, Elliptic Curve Cryptography (ECC) has evolved into a mature public-key cryptosystem. Offering the smallest key size and the highest strength per bit, its computational efficiency can benefit both client devices and server machines. We have designed a programmable hardware accelerator to speed up point multiplication for elliptic curves over binary polynomial fields GF (2 m ). The accelerator is based on a scalable architecture capable of handling curves of arbitrary field de- grees up to m = 255. In addition, it delivers optimized performance for a set of commonly used curves through hard-wired reduction logic. A prototype implementation running in a Xilinx XCV2000E FPGA at 66.4 MHz shows a performance of 6987 point multiplications per second for GF (2 163 ). We have integrated ECC into OpenSSL, today’s dominant implementation of the secure Internet protocol SSL, and tested it with the Apache web server and open-source web browsers. 1 Introduction Since its proposal by Victor Miller [17] and Neal Koblitz [15] in the mid 1980s, Elliptic Curve Cryptography (ECC) has evolved into a mature public-key cryp- tosystem. Extensive research has been done on the underlying math, its security strength, and efficient implementations. ECC offers the smallest key size and the highest strength per bit of any known public-key cryptosystem. This stems from the discrete logarithm problem in the group of points over an elliptic curve. Among the different fields that can un- derlie elliptic curves, integer fields F ( p ) and binary polynomial fields GF (2 m ) have shown to be best suited for cryptographical applications. In particular, bi- nary polynomial fields allow for fast computation in both software and hardware implementations. Small key sizes and computational efficiency of both public- and private-key operations make ECC not only applicable to hosts executing secure protocols over wired networks, but also to small wireless devices such as cell phones, PDAs and SmartCards. To make ECC commercially viable, its integration into secure
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protocols needs to be standardized. As an emerging alternative to RSA, the US government has adopted ECC for the Elliptic Curve Digital Signature Algorithm (ECDSA) and specified named curves for key sizes of 163, 233, 283, 409 and 571 bit [18]. Additional curves for commercial use were recommended by the Standards for Efficient Cryptography Group (SECG) [7]. However, only few ECC-enabled protocols have been deployed in commercial applications to date.
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.

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crypto_paper_from_chese - An End-to-End Systems Approach to...

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