High-Speed Design of Montgomery Inverse Algorithm over GF(2<SUP><I>m</I></SUP>)

Ming-Der SHIEH; Jun-Hong CHEN; Chien-Ming WU

doi:10.1093/ietfec/e89-a.2.559

High-Speed Design of Montgomery Inverse Algorithm over GF(2^m)

Ming-Der SHIEH, Jun-Hong CHEN, Chien-Ming WU

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Montgomery algorithm has demonstrated its effectiveness in applications like cryptosystems. Most of the existing works on finding the Montgomery inverse of an element over the Galois field are based on the software implementation, which is then extended to derive the scalable hardware architecture. In this work, we consider a fundamental change at the algorithmic level and eliminate the potential problems in hardware implementation which makes the resulting modified Montgomery inverse algorithm over GF(2^m) very suitable for hardware realization. Due to its structural simplicity, the modified algorithm can be easily mapped onto a high-speed and possibly low-complexity circuit. Experimental results show that our development can achieve both the area and speed advantages over the previous work when the inversion operation over GF(2^m) is under consideration and the improvement becomes more significant when we increase the value of m as in the applications of cryptosystems. The salient property of our development sustains the high-speed operation as well as low hardware complexity over a wide range of m for commercial cryptographic applications and makes it suitable for both the scalable architecture and direct hardware implementation.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.2 pp.559-565

Publication Date: 2006/02/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.2.559

Type of Manuscript: PAPER

Category: Information Security

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Ming-Der SHIEH, Jun-Hong CHEN, Chien-Ming WU, "High-Speed Design of Montgomery Inverse Algorithm over GF(2m)" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 2, pp. 559-565, February 2006, doi: 10.1093/ietfec/e89-a.2.559.
Abstract: Montgomery algorithm has demonstrated its effectiveness in applications like cryptosystems. Most of the existing works on finding the Montgomery inverse of an element over the Galois field are based on the software implementation, which is then extended to derive the scalable hardware architecture. In this work, we consider a fundamental change at the algorithmic level and eliminate the potential problems in hardware implementation which makes the resulting modified Montgomery inverse algorithm over GF(2^m) very suitable for hardware realization. Due to its structural simplicity, the modified algorithm can be easily mapped onto a high-speed and possibly low-complexity circuit. Experimental results show that our development can achieve both the area and speed advantages over the previous work when the inversion operation over GF(2^m) is under consideration and the improvement becomes more significant when we increase the value of m as in the applications of cryptosystems. The salient property of our development sustains the high-speed operation as well as low hardware complexity over a wide range of m for commercial cryptographic applications and makes it suitable for both the scalable architecture and direct hardware implementation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.2.559/_p

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@ARTICLE{e89-a_2_559,
author={Ming-Der SHIEH, Jun-Hong CHEN, Chien-Ming WU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={High-Speed Design of Montgomery Inverse Algorithm over GF(2m)},
year={2006},
volume={E89-A},
number={2},
pages={559-565},
abstract={Montgomery algorithm has demonstrated its effectiveness in applications like cryptosystems. Most of the existing works on finding the Montgomery inverse of an element over the Galois field are based on the software implementation, which is then extended to derive the scalable hardware architecture. In this work, we consider a fundamental change at the algorithmic level and eliminate the potential problems in hardware implementation which makes the resulting modified Montgomery inverse algorithm over GF(2^m) very suitable for hardware realization. Due to its structural simplicity, the modified algorithm can be easily mapped onto a high-speed and possibly low-complexity circuit. Experimental results show that our development can achieve both the area and speed advantages over the previous work when the inversion operation over GF(2^m) is under consideration and the improvement becomes more significant when we increase the value of m as in the applications of cryptosystems. The salient property of our development sustains the high-speed operation as well as low hardware complexity over a wide range of m for commercial cryptographic applications and makes it suitable for both the scalable architecture and direct hardware implementation.},
keywords={},
doi={10.1093/ietfec/e89-a.2.559},
ISSN={1745-1337},
month={February},}

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TY - JOUR
TI - High-Speed Design of Montgomery Inverse Algorithm over GF(2m)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 559
EP - 565
AU - Ming-Der SHIEH
AU - Jun-Hong CHEN
AU - Chien-Ming WU
PY - 2006
DO - 10.1093/ietfec/e89-a.2.559
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2006
AB - Montgomery algorithm has demonstrated its effectiveness in applications like cryptosystems. Most of the existing works on finding the Montgomery inverse of an element over the Galois field are based on the software implementation, which is then extended to derive the scalable hardware architecture. In this work, we consider a fundamental change at the algorithmic level and eliminate the potential problems in hardware implementation which makes the resulting modified Montgomery inverse algorithm over GF(2^m) very suitable for hardware realization. Due to its structural simplicity, the modified algorithm can be easily mapped onto a high-speed and possibly low-complexity circuit. Experimental results show that our development can achieve both the area and speed advantages over the previous work when the inversion operation over GF(2^m) is under consideration and the improvement becomes more significant when we increase the value of m as in the applications of cryptosystems. The salient property of our development sustains the high-speed operation as well as low hardware complexity over a wide range of m for commercial cryptographic applications and makes it suitable for both the scalable architecture and direct hardware implementation.
ER -