Results 1  10
of
19
An EndtoEnd Systems Approach to Elliptic Curve Cryptography
 In Cryptographic Hardware and Embedded Systems (CHES
, 2002
"... Since its proposal by Victor Miller [17] and Neal Koblitz [15] in the mid 1980s, Elliptic Curve Cryptography (ECC) has evolved into a mature publickey cryptosystem. Offering the smallest key size and the highest strength per bit, its computational efficiency can benefit both client devices and serv ..."
Abstract

Cited by 32 (4 self)
 Add to MetaCart
(Show Context)
Since its proposal by Victor Miller [17] and Neal Koblitz [15] in the mid 1980s, Elliptic Curve Cryptography (ECC) has evolved into a mature publickey 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 degrees up to m = 255. In addition, it delivers optimized performance for a set of commonly used curves through hardwired 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 opensource web browsers.
Generic implementations of elliptic curve cryptography using partial reduction
 Proc. ACM Computer and Communications Security
, 2002
"... ABSTRACT Elliptic Curve Cryptography (ECC) is evolving as an attractive alternative to other publickey schemes such as RSA by offering the smallest key size and the highest strength per bit. The importance of ECC has been recognized by the US government and the standards bodies NIST and SECG. Stan ..."
Abstract

Cited by 18 (5 self)
 Add to MetaCart
(Show Context)
ABSTRACT Elliptic Curve Cryptography (ECC) is evolving as an attractive alternative to other publickey schemes such as RSA by offering the smallest key size and the highest strength per bit. The importance of ECC has been recognized by the US government and the standards bodies NIST and SECG. Standards for preferred elliptic curves over prime fields GF (p) and binary polynomial fields GF (2 m ) as well as the Elliptic Curve Digital Signature Algorithm (ECDSA) have been created. A security protocol based on ECC requires support for different curves representing different security levels. This is particularly true for server applications that are exposed to requests for secure connections with different parameters generated by a multitude of client devices. Reported implementations of ECC over GF (2 m ) typically choose to implement each curve as a special case so that modular reduction can be optimized, thus improving the overall performance. In contrast, this paper focuses on generic implementations of ECC point multiplication for arbitrary curves over GF (2 m ). We present a novel reduction algorithm that allows hardware and software implementations for variable field degrees m. Though not as high in performance as an implementation optimized for a specific curve, it offers an attractive solution to supporting infrequently used curves or curves not known at the time of the implementation.
Customizable elliptic curve cryptosystems
 IEEE Transactions on Very Large Scale Integration (VLSI) Systems
, 2005
"... Abstract—This paper presents a method for producing hardware designs for elliptic curve cryptography (ECC) systems over the finite field qp@P A, using the optimal normal basis for the representation of numbers. Our field multiplier design is based on a parallel architecture containing multiplebit s ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
(Show Context)
Abstract—This paper presents a method for producing hardware designs for elliptic curve cryptography (ECC) systems over the finite field qp@P A, using the optimal normal basis for the representation of numbers. Our field multiplier design is based on a parallel architecture containing multiplebit serial multipliers; by changing the number of such serial multipliers, designers can obtain implementations with different tradeoffs in speed, size and level of security. A design generator has been developed which can automatically produce a customised ECC hardware design that meets userdefined requirements. To facilitate performance characterization, we have developed a parametric model for estimating the number of cycles for our generic ECC architecture. The resulting hardware implementations are among the fastest reported: for a key size of 270 bits, a point multiplication in a Xilinx XC2V6000 FPGA at 35 MHz can run over 1000 times faster
FPGA Implementation of Point Multiplication on Koblitz Curves using Kleinian Integers
 In Cryptographic Hardware and Embedded Systems, CHES 2006
, 2006
"... Abstract. We describe algorithms for point multiplication on Koblitz curves using multiplebase expansions of the form k = ∑ ±τ a (τ − 1) b and k = ∑ ±τ a (τ − 1) b (τ 2 − τ − 1) c. We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first p ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
Abstract. We describe algorithms for point multiplication on Koblitz curves using multiplebase expansions of the form k = ∑ ±τ a (τ − 1) b and k = ∑ ±τ a (τ − 1) b (τ 2 − τ − 1) c. We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first provably sublinear point multiplication algorithm on Koblitz curves. For the first type, we conjecture that the number of terms is sublinear and provide numerical evidence demonstrating that the number of terms is significantly less than that of τadic nonadjacent form expansions. We present details of an innovative FPGA implementation of our algorithm and performance data demonstrating the efficiency of our method. 1
On Parallelization of HighSpeed Processors for Elliptic Curve Cryptography
 IEEE Transaction on Very Large
"... permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or pr ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
(Show Context)
permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubspermissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Provably Sublinear Point Multiplication on Koblitz Curves and its Hardware Implementation
 IEEE Transaction on Computers
, 2008
"... Reprinted with permission. ..."
Contents lists available at ScienceDirect Computers and Electrical Engineering
"... journal homepage: www.elsevier.com/locate/compeleceng An area/performance tradeoff analysis of a GF(2 m) multiplier architecture ..."
Abstract
 Add to MetaCart
(Show Context)
journal homepage: www.elsevier.com/locate/compeleceng An area/performance tradeoff analysis of a GF(2 m) multiplier architecture