Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems

Narendran Narayanaswamy; Alexander Skavantzos; Thanos Stouraitis

doi:10.1109/ICECS.2010.5724506

Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems

Narendran Narayanaswamy, Alexander Skavantzos, Thanos Stouraitis

Electrical Engineering

Louisiana State University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this paper, specific modulus sets that offer efficient implementations of the New Chinese Remainder Theorems (CRT) are presented. Further, the resulting hardware is optimized for specific implementations. For n = 1,2,3,..., the utilized modulus sets are either the co-prime 4-modulus ones {2 ⁿ⁺²+3, 2ⁿ⁺¹+1, 2ⁿ+1, 2} and {2, 2 ⁿ+1, 2ⁿ⁺¹+1, 2ⁿ⁺²+3}, which can be used for the New CRT I and CRT II, or the non co-prime modulus set {2ⁿ⁺²+1, 2ⁿ⁺², 2ⁿ⁺¹+1, 2}, which can be used for the New CRT III. RNS implementations that use the special modulus sets eliminate the huge summations, inverse modulo operators, and dividers, while their further hardware optimization reduces the multiplication terms.

Original language	British English
Title of host publication	2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings
Pages	273-276
Number of pages	4
DOIs	https://doi.org/10.1109/ICECS.2010.5724506
State	Published - 2010
Event	2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Athens, Greece Duration: 12 Dec 2010 → 15 Dec 2010

Publication series

Name	2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings

Conference

Conference	2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010
Country/Territory	Greece
City	Athens
Period	12/12/10 → 15/12/10

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10.1109/ICECS.2010.5724506

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Narayanaswamy, N., Skavantzos, A., & Stouraitis, T. (2010). Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems. In 2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings (pp. 273-276). Article 5724506 (2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings). https://doi.org/10.1109/ICECS.2010.5724506

Narayanaswamy, Narendran ; Skavantzos, Alexander ; Stouraitis, Thanos. / Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems. 2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings. 2010. pp. 273-276 (2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings).

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abstract = "In this paper, specific modulus sets that offer efficient implementations of the New Chinese Remainder Theorems (CRT) are presented. Further, the resulting hardware is optimized for specific implementations. For n = 1,2,3,..., the utilized modulus sets are either the co-prime 4-modulus ones {2 n+2+3, 2n+1+1, 2n+1, 2} and {2, 2 n+1, 2n+1+1, 2n+2+3}, which can be used for the New CRT I and CRT II, or the non co-prime modulus set {2n+2+1, 2n+2, 2n+1+1, 2}, which can be used for the New CRT III. RNS implementations that use the special modulus sets eliminate the huge summations, inverse modulo operators, and dividers, while their further hardware optimization reduces the multiplication terms.",

author = "Narendran Narayanaswamy and Alexander Skavantzos and Thanos Stouraitis",

year = "2010",

doi = "10.1109/ICECS.2010.5724506",

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pages = "273--276",

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note = "2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 ; Conference date: 12-12-2010 Through 15-12-2010",

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Narayanaswamy, N, Skavantzos, A & Stouraitis, T 2010, Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems. in 2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings., 5724506, 2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings, pp. 273-276, 2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010, Athens, Greece, 12/12/10. https://doi.org/10.1109/ICECS.2010.5724506

Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems. / Narayanaswamy, Narendran; Skavantzos, Alexander; Stouraitis, Thanos.
2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings. 2010. p. 273-276 5724506 (2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper, specific modulus sets that offer efficient implementations of the New Chinese Remainder Theorems (CRT) are presented. Further, the resulting hardware is optimized for specific implementations. For n = 1,2,3,..., the utilized modulus sets are either the co-prime 4-modulus ones {2 n+2+3, 2n+1+1, 2n+1, 2} and {2, 2 n+1, 2n+1+1, 2n+2+3}, which can be used for the New CRT I and CRT II, or the non co-prime modulus set {2n+2+1, 2n+2, 2n+1+1, 2}, which can be used for the New CRT III. RNS implementations that use the special modulus sets eliminate the huge summations, inverse modulo operators, and dividers, while their further hardware optimization reduces the multiplication terms.

AB - In this paper, specific modulus sets that offer efficient implementations of the New Chinese Remainder Theorems (CRT) are presented. Further, the resulting hardware is optimized for specific implementations. For n = 1,2,3,..., the utilized modulus sets are either the co-prime 4-modulus ones {2 n+2+3, 2n+1+1, 2n+1, 2} and {2, 2 n+1, 2n+1+1, 2n+2+3}, which can be used for the New CRT I and CRT II, or the non co-prime modulus set {2n+2+1, 2n+2, 2n+1+1, 2}, which can be used for the New CRT III. RNS implementations that use the special modulus sets eliminate the huge summations, inverse modulo operators, and dividers, while their further hardware optimization reduces the multiplication terms.

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Narayanaswamy N, Skavantzos A, Stouraitis T. Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems. In 2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings. 2010. p. 273-276. 5724506. (2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings). doi: 10.1109/ICECS.2010.5724506

Optimal modulus sets for efficient residue-to-binary conversion using the new chinese remainder theorems

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