IEICE TRANSACTIONS on Fundamentals
A High Performance FPGA Implementation of 256-bit Elliptic Curve Cryptography Processor Over GF(p)
Summary :
Field Programmable Gate Array (FPGA) implementation of Elliptic Curve Cryptography (ECC) over GF(p) is commonly not fast enough to meet the request of high-performance applications. There are three critical factors to determine the performance of ECC processor over GF(p): multiplication structure, modular multiplication algorithm, and scalar point multiplication scheduling. This work proposes a novel multiplication structure which is a two-stage pipeline on the basis of Karatsuba-Ofman algorithm. With the proposed multiplication structure, we design a 256-bit modular multiplier based on Improved Barret Modular Multiplication algorithm. Upon the modular multiplier, we finish the scalar point multiplication scheduling and implement a high-performance ECC processor on FPGA. Compared with the previous modular multipliers, our modular multiplier reduces the 256-bit modular multiplication time by 28% at least. Synthesis result on Altera Stratix II shows that our ECC processor can complete a 256-bit ECC scalar point multiplication in 0.51ms, which is at least 1.3 times faster than the currently reported FPGA ECC processors over GF(p).
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.3 pp.863-869
- Publication Date
- 2015/03/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E98.A.863
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Xiang FENG
Tsinghua University
Shuguo LI
Tsinghua University
Keyword
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Xiang FENG, Shuguo LI, "A High Performance FPGA Implementation of 256-bit Elliptic Curve Cryptography Processor Over GF(p)" in IEICE TRANSACTIONS on Fundamentals,
vol. E98-A, no. 3, pp. 863-869, March 2015, doi: 10.1587/transfun.E98.A.863.
Abstract: Field Programmable Gate Array (FPGA) implementation of Elliptic Curve Cryptography (ECC) over GF(p) is commonly not fast enough to meet the request of high-performance applications. There are three critical factors to determine the performance of ECC processor over GF(p): multiplication structure, modular multiplication algorithm, and scalar point multiplication scheduling. This work proposes a novel multiplication structure which is a two-stage pipeline on the basis of Karatsuba-Ofman algorithm. With the proposed multiplication structure, we design a 256-bit modular multiplier based on Improved Barret Modular Multiplication algorithm. Upon the modular multiplier, we finish the scalar point multiplication scheduling and implement a high-performance ECC processor on FPGA. Compared with the previous modular multipliers, our modular multiplier reduces the 256-bit modular multiplication time by 28% at least. Synthesis result on Altera Stratix II shows that our ECC processor can complete a 256-bit ECC scalar point multiplication in 0.51ms, which is at least 1.3 times faster than the currently reported FPGA ECC processors over GF(p).
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.863/_p
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@ARTICLE{e98-a_3_863,
author={Xiang FENG, Shuguo LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A High Performance FPGA Implementation of 256-bit Elliptic Curve Cryptography Processor Over GF(p)},
year={2015},
volume={E98-A},
number={3},
pages={863-869},
abstract={Field Programmable Gate Array (FPGA) implementation of Elliptic Curve Cryptography (ECC) over GF(p) is commonly not fast enough to meet the request of high-performance applications. There are three critical factors to determine the performance of ECC processor over GF(p): multiplication structure, modular multiplication algorithm, and scalar point multiplication scheduling. This work proposes a novel multiplication structure which is a two-stage pipeline on the basis of Karatsuba-Ofman algorithm. With the proposed multiplication structure, we design a 256-bit modular multiplier based on Improved Barret Modular Multiplication algorithm. Upon the modular multiplier, we finish the scalar point multiplication scheduling and implement a high-performance ECC processor on FPGA. Compared with the previous modular multipliers, our modular multiplier reduces the 256-bit modular multiplication time by 28% at least. Synthesis result on Altera Stratix II shows that our ECC processor can complete a 256-bit ECC scalar point multiplication in 0.51ms, which is at least 1.3 times faster than the currently reported FPGA ECC processors over GF(p).},
keywords={},
doi={10.1587/transfun.E98.A.863},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - A High Performance FPGA Implementation of 256-bit Elliptic Curve Cryptography Processor Over GF(p)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 863
EP - 869
AU - Xiang FENG
AU - Shuguo LI
PY - 2015
DO - 10.1587/transfun.E98.A.863
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2015
AB - Field Programmable Gate Array (FPGA) implementation of Elliptic Curve Cryptography (ECC) over GF(p) is commonly not fast enough to meet the request of high-performance applications. There are three critical factors to determine the performance of ECC processor over GF(p): multiplication structure, modular multiplication algorithm, and scalar point multiplication scheduling. This work proposes a novel multiplication structure which is a two-stage pipeline on the basis of Karatsuba-Ofman algorithm. With the proposed multiplication structure, we design a 256-bit modular multiplier based on Improved Barret Modular Multiplication algorithm. Upon the modular multiplier, we finish the scalar point multiplication scheduling and implement a high-performance ECC processor on FPGA. Compared with the previous modular multipliers, our modular multiplier reduces the 256-bit modular multiplication time by 28% at least. Synthesis result on Altera Stratix II shows that our ECC processor can complete a 256-bit ECC scalar point multiplication in 0.51ms, which is at least 1.3 times faster than the currently reported FPGA ECC processors over GF(p).
ER -
English
