Arithmetic division in RNS using Galois Field GF(p)

Computers and Mathematics with Applications

Volumn 39, Issue 5-6, 2000, Pages 227-238

  Talahmeh, S ^a   Siy, P ^a  

^a Wayne State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); COMPUTATIONAL COMPLEXITY; CONFORMAL MAPPING; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; PARALLEL PROCESSING SYSTEMS; POLYNOMIALS; ROM; TABLE LOOKUP; THEOREM PROVING;

ARITHMETIC DIVISION; BASED EXTENSION OPERATION; COMPUTER ARITHMETIC; GALOIS FIELD; MODULAR ARITHMETIC; QUOTIENT ESTIMATION; RADIX CONVERSION; RECIPROCAL ESTIMATION;

NUMBER THEORY;

EID: 0034159175     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(00)00056-0     Document Type: Article

References (15)

1. N.S. Szabó and R.I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology, McGraw-Hill, New York, (1967).
2. C. Hung and B. Parhami, Fast RNS division algorithms for fixed divisors with application to RSA encryption, Information Processing Letters 51, 163-169 (1994).
3. C. Hung and B. Parhami, An approximate sign detection method for residue numbers and its application to RNS division, Computers Math. Applic. 27 (4), 23-35 (1994).
4. G.A. Julien, Residue number scaling and other operations using ROM arrays, IEEE Trans. Comput. C-27 (4), 325-336 (1978).
5. E.D. Claudio, F. Piazza and G. Orlandi, Fast combinatorial RNS processors for DSP applications, IEEE Trans. Comput. 44 (5), 624-633 (1995).
6. S. Waser and M.J. Flynn, Introduction to Arithmetic for Digital System Designers, Holt, Rinehart & Winston, New York, (1982).
7. F.J. Taylor, Residue arithmetic: A tutorial with examples, IEEE Comput. 17 (5), 50-62 (1984).
8. M. Lu and J. Chiang, A novel division algorithm for the residue number system, IEEE Trans. Comput. 41 (8), 1026-1032 (1992).
9. W.A. Chren, A new residue number system division algorithm, Computers Math. Applic. 19 (7), 13-29 (1990).
10. D.K. Banerji, T.Y. Cheung and V. Ganesan, A high-speed division method in residue arithmetic, IEEE Symp. Comput. Arithmetic. (5), 158-164 (1981).
11. M.A. Hits and E. Kaltofen, Integer division in residue number systems, IEEE Trans. Comput. 44 (8), 983-989 (1995).
12. E. Kinoshita, H. Kosako and Y. Kojima, General division in the symmetric residue number system, IEEE Trans. Comput. C-22, 134-142 (1973).
13. M.L. Lin, E. Leiss and B. McInnis, Division and sign detection algorithm for residue number systems, Computers Math. Applic. 10 (4/5), 331-342 (1984).
14. D. Radhakrishnan and Y. Yuan, Novel approaches to the design of VLSI RNS multipliers, IEEE Trans. Circuits and System - II 39 (1), 52-57 (1992).
15. W. Beyer, CRC-Standard Mathematical Tables and Formulae, Edition 91-101, CRC Press, (1991).