{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:00:37Z","timestamp":1759147237379,"version":"3.41.2"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[1996,1,1]],"date-time":"1996-01-01T00:00:00Z","timestamp":820454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1996,1,1]],"date-time":"1996-01-01T00:00:00Z","timestamp":820454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Designs, Codes and Cryptography"],"published-print":{"date-parts":[[1996,1]]},"DOI":"10.1023\/a:1018013116103","type":"journal-article","created":{"date-parts":[[2003,11,3]],"date-time":"2003-11-03T19:30:08Z","timestamp":1067887808000},"page":"135-151","source":"Crossref","is-referenced-by-count":1,"title":["Redundant Integer Representations and Fast Exponentiation"],"prefix":"10.1007","volume":"7","author":[{"given":"Dieter","family":"Gollmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfei","family":"Han","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris J.","family":"Mitchell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"102709_CR1","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1109\/12.238495","volume":"42","author":"S. Arno","year":"1993","unstructured":"S. Arno and F. S. Wheeler, Signed digit representations of minimal Hamming weight, IEEE Transactions on Computers, Vol. 42 (1993) pp. 1007\u20131010.","journal-title":"IEEE Transactions on Computers"},{"key":"102709_CR2","unstructured":"H. J. Beker and F. C. Piper, Cipher Systems, Van Nostrand Reinhold (1982)."},{"key":"102709_CR3","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1093\/qjmam\/4.2.236","volume":"4","author":"A. D. Booth","year":"1951","unstructured":"A. D. Booth, A signed binary multiplication technique, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 4 (1951) pp. 236\u2013240.","journal-title":"Quarterly Journal of Mechanics and Applied Mathematics"},{"key":"102709_CR4","doi-asserted-by":"crossref","unstructured":"E. F. Brickell, A fast modular multiplication algorithm with application to two key cryptography, Advances in Cryptology, Proceedings of Crypto '82 (1982) pp. 51\u201360.","DOI":"10.1007\/978-1-4757-0602-4_5"},{"key":"102709_CR5","first-page":"188","volume-title":"Proceedings of 1990 Bilkent International Conference on New Trends in Communication, Control, and Signal Processing","author":"O. Egecioglu","year":"1990","unstructured":"O. Egecioglu and C. K. Koc, Fast modular exponentiation, Proceedings of 1990 Bilkent International Conference on New Trends in Communication, Control, and Signal Processing, Elsevier Science Publishing Co., Ankara Turkey (1990) pp. 188\u2013194."},{"key":"102709_CR6","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.1049\/el:19940949","volume":"30","author":"L. K. Hui","year":"1994","unstructured":"L.C. K. Hui and K. Y. Lam, Fast square and multiply exponentiation for RSA, Electronics Letters, Vol. 30 (1994) pp. 1396\u20131397.","journal-title":"Electronics Letters"},{"key":"102709_CR7","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1049\/el:19890785","volume":"25","author":"J. Jedwab","year":"1989","unstructured":"J. Jedwab and C. J. Mitchell, Minimum weight modified signed digit representations and fast exponentiation, Electronic Letters, Vol. 25 (1989) pp. 1171\u20131172.","journal-title":"Electronic Letters"},{"key":"102709_CR8","volume-title":"The Art of Computer Programming, Volume 2: Seminumerical Algorithms","author":"D. E. Knuth","year":"1981","unstructured":"D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 2nd edition, Addison-Wesley, Reading, Mass. (1981).","edition":"2nd edition"},{"key":"102709_CR9","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/00207169108804009","volume":"40","author":"C. K. Koc","year":"1991","unstructured":"C. K. Koc. High-radix and bit recoding techniques for modular exponentiation. International Journal of Computer Mathematics, Vol. 40 (1991) pp. 139\u2013156.","journal-title":"International Journal of Computer Mathematics"},{"key":"102709_CR10","first-page":"312","volume":"24","author":"C. K. Koc","year":"1992","unstructured":"C. K. Koc and C. Y. Hung, Adaptive m-ary segmentation and canonical recoding algorithms for multiplication of large binary numbers, Computers Math. Applic., Vol. 24 (1992) pp. 312.","journal-title":"Computers Math. Applic."},{"key":"102709_CR11","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1090\/S0025-5718-1985-0777282-X","volume":"44","author":"P. L. Montgomery","year":"1985","unstructured":"P. L. Montgomery, Modular multiplication without trial division, Mathematics of Computation, Vol. 44 (1985) pp. 519\u2013521.","journal-title":"Mathematics of Computation"},{"key":"102709_CR12","first-page":"151","volume":"31","author":"M. J. Norris","year":"1981","unstructured":"M. J. Norris and G. J. Simmons, Algorithms for high-speed modular arithmetics. Congressus Numerantium, Vol. 31 (1981) pp. 151\u2013163.","journal-title":"Congressus Numerantium"},{"key":"102709_CR13","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1109\/71.382314","volume":"6","author":"K. C. Posch","year":"1995","unstructured":"K. C. Posch and R. Posch, Modulo reduction in residue number systems, IEEE Transactions on Parallel and Distributed Systems, Vol. 6 (1995) pp. 449\u2013454.","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"102709_CR14","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1049\/el:19820617","volume":"18","author":"J.\u2013J. Quisquater","year":"1982","unstructured":"J.\u2013J. Quisquater and C. Couvreur, Fast decipherment algorithm for RSA public-key cryptosystem, Electronic Letters, Vol. 18 (1982) pp. 905\u2013907.","journal-title":"Electronic Letters"},{"key":"102709_CR15","first-page":"232","volume-title":"Advances in Computers I","author":"G. W. Reitwiesner","year":"1960","unstructured":"G. W. Reitwiesner, Binary arithmetic, Advances in Computers I, (F. L. Alt ed.), Academic, New York (1960) pp. 232\u2013308."},{"key":"102709_CR16","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R. L. Rivest","year":"1978","unstructured":"R. L. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, Vol. 21 (1978) pp. 120\u2013126.","journal-title":"Communications of the ACM"},{"key":"102709_CR17","first-page":"166","volume":"136","author":"A. Selby","year":"1989","unstructured":"A. Selby and C. Mitchell, Algorithms for software implementations of RSA, Proceedings of the IEE. Part E, Vol. 136 (1989) pp. 166\u2013170.","journal-title":"Proceedings of the IEE. Part E"},{"key":"102709_CR18","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1109\/12.256444","volume":"41","author":"N. Takagi","year":"1992","unstructured":"N. Takagi and S. Yajima, Modular multiplication hardware algorithms with a redundant representation and their application to RSA cryptosystem, IEEE Transactions on Computers, Vol. 41 (1992) pp. 887\u2013891.","journal-title":"IEEE Transactions on Computers"},{"key":"102709_CR19","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/TC.1985.1676634","volume":"C-34","author":"N. Takagi","year":"1985","unstructured":"N. Takagi, H. Yasuura, and S. Yajima, High-speed VLSI multiplication algorithm with a redundant binary addition tree, IEEE transactions on Computers, Vol. C-34 (1985) pp. 789\u2013796.","journal-title":"IEEE transactions on Computers"},{"key":"102709_CR20","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0898-1221(93)90295-7","volume":"25","author":"C. N. Zhang","year":"1993","unstructured":"C. N. Zhang, An improved binary algorithm for RSA, Computers Math. Applic., Vol. 25 (1993) pp. 15\u201324.","journal-title":"Computers Math. Applic."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018013116103.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1018013116103\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018013116103.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T03:48:03Z","timestamp":1753760883000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1018013116103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,1]]},"references-count":20,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["102709"],"URL":"https:\/\/doi.org\/10.1023\/a:1018013116103","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[1996,1]]}}}