NDLI: Verification of composite Galois field multipliers over GF $((2^{m})^{n})$ using computer algebra techniques

Content Provider	IEEE Xplore Digital Library
Author	Jinpeng Lv Kalla, P. Enescu, F.
Copyright Year	2011
Description	Author affiliation: Department of Mathematics and Statistics Georgia State University, Atlanta, GA 30302-4038 (Enescu, F.) \|\| Department of Electrical and Computer Eng. University of Utah, Salt Lake City, UT-84112 (Jinpeng Lv; Kalla, P.)
Abstract	Galois field computations abound in many applications, such as in cryptography, error correction codes, signal processing, among many others. Multiplication usually lies at the core of such Galois field computations, and is one of the most complex operations. Hardware implementations of such multipliers become very expensive. Therefore, there have been efforts to reduce the design complexity by decomposing the Galois field $GF(2^{k})$ as GF $((2^{m})^{n})$ where k = m × n. Such a decomposition introduces a hierarchical abstraction — lifting the ground field from GF (2) (bit-level) to GF $(2^{m})$ (word-level) — thus simplifying the design. This paper addresses the formal verification problem of such multipliers designed over GF $((2^{m})^{n}),$ using a computer algebra and algebraic geometry based approach. To prove that the composite field multiplier implementation matches the original specification, we hierarchically formulate the verification problem using the Hilbert's Nullstellensatz over Galois Fields. A Gröbner basis engine is employed as the underlying computational framework. Experiments are performed with various variable/term orders to demonstrate the efficacy of our approach. We can verify the correctness of upto 1024bit multipliers, whereas SAT/SMT-based approaches are in-feasible.
Starting Page	136
Ending Page	143
File Size	463463
Page Count	8
File Format	PDF
ISBN	9781457717444
ISSN	15526674
e-ISBN	9781457717437
DOI	10.1109/HLDVT.2011.6113989
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-11-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Galois fields Computers Integrated circuit modeling Mathematical model
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Formal Verification of Galois Field Multipliers Using Computer Algebra Techniques

Fast inversion in composite Galois fields GF((2/sup n/)/sup m/)

Verification of composite galois field multipliers over gf ((2m)n) using computer algebra techniques.

A low-area, high-speed, processor array architecture for field ALU over GF $(2^{m})$

Low complexity sequential normal basis multipliers over GF(2/sup m/)

Formal Design of Galois-Field Arithmetic Circuits Based on Polynomial Ring Representation

Reconfigurable implementation of bit-parallel multipliers over GF(2/sup m/) for two classes of finite fields

High speed galois fields $GF(2^{m})$ multipliers

A High-Speed, Low-Area Processor Array Architecture for Multiplication and Squaring over $GF(2^{m})$

Verification of composite Galois field multipliers over GF $((2^{m})^{n})$ using computer algebra techniques

Similar Documents

Formal Verification of Galois Field Multipliers Using Computer Algebra Techniques

Fast inversion in composite Galois fields GF((2/sup n/)/sup m/)

Verification of composite galois field multipliers over gf ((2m)n) using computer algebra techniques.

A low-area, high-speed, processor array architecture for field ALU over GF $(2^{m})$

Low complexity sequential normal basis multipliers over GF(2/sup m/)

Formal Design of Galois-Field Arithmetic Circuits Based on Polynomial Ring Representation

Reconfigurable implementation of bit-parallel multipliers over GF(2/sup m/) for two classes of finite fields

High speed galois fields $GF(2^{m})$ multipliers

A High-Speed, Low-Area Processor Array Architecture for Multiplication and Squaring over $GF(2^{m})$

Verification of composite Galois field multipliers over GF $((2^{m})^{n})$ using computer algebra techniques