Efficient Implementation of Elliptic Curve Cryptosystems on an ARM7 with Hardware Accelerator

This paper presents an efficient implementation of elliptic curve cryptosystems over a prime field on ARM7 with the help of a hardware accelerator. The hardware accelerator has two dedicated large number arithmetic units (LNAU's). Three different implementation platforms are considered: ARM7, ARM7 with one LNAU, and ARM7 with two LNAU's. The time costs for performing point multiplication are measured for all three platforms. On ARM7 with 2 LNAU's platform, we achieved the point multiplication in 18 ms with the chip running at 50 MHz clock frequency.

[1]  Paul C. Kocher,et al.  Differential Power Analysis , 1999, CRYPTO.

[2]  Arjen K. Lenstra,et al.  Selecting Cryptographic Key Sizes , 2000, Public Key Cryptography.

[3]  Gordon B. Agnew,et al.  An Implementation of Elliptic Curve Cryptosystems Over F2155 , 1993, IEEE J. Sel. Areas Commun..

[4]  J. Cassels LMSST: 24 Lectures on Elliptic Curves , 1991 .

[5]  Alfred Menezes,et al.  Software Implementation of Elliptic Curve Cryptography over Binary Fields , 2000, CHES.

[6]  P. L. Montgomery Modular multiplication without trial division , 1985 .

[7]  Alfred Menezes,et al.  The State of Elliptic Curve Cryptography , 2000, Des. Codes Cryptogr..

[8]  Christof Paar,et al.  Efficient Implementation of Elliptic Curve Cryptosystems on the TI MSP 430x33x Family of Microcontrollers , 2001, Public Key Cryptography.

[9]  Bart Preneel,et al.  On the Performance of Signature Schemes Based on Elliptic Curves , 1998, ANTS.

[10]  Atsushi Shimbo,et al.  Implementation of RSA Algorithm Based on RNS Montgomery Multiplication , 2001, CHES.

[11]  Mitsuru Matsui,et al.  A Practical Implementation of Elliptic Curve Cryptosystems over GF(p) on a 16-bit Microcomputer , 1998, Public Key Cryptography.

[12]  N. Koblitz Elliptic curve cryptosystems , 1987 .

[13]  Marc Joye,et al.  Hessian Elliptic Curves and Side-Channel Attacks , 2001, CHES.

[14]  Kazuhiro Yokoyama,et al.  Elliptic curve cryptosystem , 2000 .

[15]  Jean-Jacques Quisquater,et al.  TIMING ATTACK: WHAT CAN BE ACHIEVED BY A POWERFUL ADVERSARY? , 2000 .

[16]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[17]  Pil Joong Lee,et al.  Fast Implementation of Elliptic Curve Defined over GF(pm) on CalmRISC with MAC2424 Coprocessor , 2000, CHES.

[18]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

[19]  Christof Paar,et al.  Elliptic Curve Cryptography on Smart Cards without Coprocessors , 2001, CARDIS.

[20]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[21]  Alfred Menezes,et al.  Elliptic curve public key cryptosystems , 1993, The Kluwer international series in engineering and computer science.

[22]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[23]  Chae Hoon Lim,et al.  Fast Implementation of Elliptic Curve Arithmetic in GF(pn) , 2000, Public Key Cryptography.

[24]  Kouichi Itoh,et al.  Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201 , 1999, CHES.

[25]  Nigel P. Smart,et al.  The Hessian Form of an Elliptic Curve , 2001, CHES.

[26]  J. Cassels Lectures on elliptic curves , 1991 .

[27]  C. D. Walter,et al.  Distinguishing Exponent Digits by Observing Modular Subtractions , 2001, CT-RSA.

[28]  Servaas Vandenberghe,et al.  A Fast Software Implementation for Arithmetic Operations in GF(2n) , 1996, ASIACRYPT.

[29]  Christof Paar,et al.  Cryptographic Hardware and Embedded Systems - CHES 2006, 8th International Workshop, Yokohama, Japan, October 10-13, 2006, Proceedings , 2006, CHES.

[30]  Alfred Menezes,et al.  Software Implementation of the NIST Elliptic Curves Over Prime Fields , 2001, CT-RSA.

[31]  David Naccache,et al.  Topics in Cryptology — CT-RSA 2001 , 2001, Lecture Notes in Computer Science.