{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:00:39Z","timestamp":1759147239682},"publisher-location":"Berlin, Heidelberg","reference-count":28,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540284741"},{"type":"electronic","value":"9783540319405"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11545262_16","type":"book-chapter","created":{"date-parts":[[2005,9,27]],"date-time":"2005-09-27T14:35:35Z","timestamp":1127831735000},"page":"211-225","source":"Crossref","is-referenced-by-count":5,"title":["Fast Truncated Multiplication for Cryptographic Applications"],"prefix":"10.1007","author":[{"given":"Laszlo","family":"Hars","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"16_CR1","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1109\/ARITH.1997.614900","volume-title":"13th IEEE Symposium on Computer Arithmetic (ARITH 13)","author":"J.-C. Bajard","year":"1997","unstructured":"Bajard, J.-C., Didier, L.-S., Kornerup, P.: An RNS Montgomery multiplication algorithm. In: 13th IEEE Symposium on Computer Arithmetic (ARITH 13), pp. 234\u2013239. IEEE Press, Los Alamitos (1997)"},{"key":"16_CR2","series-title":"Lecture Notes in Computer Science","first-page":"311","volume-title":"Advances in Cryptology - CRYPTO \u201986","author":"P.D. Barrett","year":"1987","unstructured":"Barrett, P.D.: Implementing the Rivest Shamir Adleman public key encryption algorithm on standard digital signal processor. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol.\u00a0263, pp. 311\u2013323. Springer, Heidelberg (1987)"},{"key":"16_CR3","unstructured":"Bernstein, D.J.: Fast Multiplication and its Applications, \n                    \n                      http:\/\/cr.yp.to\/papers.html#multapps"},{"key":"16_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/3-540-48329-2_16","volume-title":"Advances in Cryptology - CRYPTO \u201993","author":"A. Bosselaers","year":"1994","unstructured":"Bosselaers, A., Govaerts, R., Vandewalle, J.: Comparison of three modular reduction functions. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol.\u00a0773, pp. 175\u2013186. Springer, Heidelberg (1994)"},{"key":"16_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1007\/0-387-34805-0_34","volume-title":"Advances in Cryptology - CRYPTO \u201989","author":"E.F. Brickell","year":"1990","unstructured":"Brickell, E.F.: A Survey of Hardware Implementations of RSA. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol.\u00a0435, pp. 368\u2013370. Springer, Heidelberg (1990)"},{"key":"16_CR6","unstructured":"Burnikel, C., Ziegler, J.: Fast recursive division. MPI research report I-98-1-022"},{"key":"16_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1007\/10931455_18","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2003","author":"B. Chevallier-Mames","year":"2003","unstructured":"Chevallier-Mames, B., Joye, M., Paillier, P.: Faster Double-Size Modular Multiplication from Euclidean Multipliers. In: Walter, C.D., Ko\u00e7, \u00c7.K., Paar, C. (eds.) CHES 2003. LNCS, vol.\u00a02779, pp. 214\u2013227. Springer, Heidelberg (2003)"},{"key":"16_CR8","series-title":"Lecture Notes in Computer Science","first-page":"350","volume-title":"Smart Card. Research and Applications","author":"J.-F. Dhem","year":"2000","unstructured":"Dhem, J.-F., Quisquater, J.-J.: Recent results on modular multiplications for smart cards. In: Schneier, B., Quisquater, J.-J. (eds.) CARDIS 1998. LNCS, vol.\u00a01820, pp. 350\u2013366. Springer, Heidelberg (2000)"},{"key":"16_CR9","unstructured":"GNU Multiple Precision Arithmetic Library manual, \n                    \n                      http:\/\/www.swox.com\/gmp\/gmpman-4.1.2.pdf"},{"key":"16_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/3-540-36400-5_7","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2002","author":"W. Fischer","year":"2003","unstructured":"Fischer, W., Seifert, J.-P.: Increasing the bitlength of crypto-coprocessors via smart hardware\/software co-design. In: Kaliski Jr., B.S., Ko\u00e7, \u00c7.K., Paar, C. (eds.) CHES 2002. LNCS, vol.\u00a02523, pp. 71\u201381. Springer, Heidelberg (2003)"},{"key":"16_CR11","unstructured":"Hanrot, G., Quercia, M., Zimmermann, P.: The Middle Product Algorithm, I. Rapport de recherche No. 4664, December 2 (2002), \n                    \n                      http:\/\/www.inria.fr\/rrrt\/rr-4664.html"},{"key":"16_CR12","unstructured":"Hensel, K.: Theorie der algebraische Zahlen. Leipzig (1908)"},{"issue":"17","key":"16_CR13","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1049\/el:19890785","volume":"25","author":"J. Jedwab","year":"1989","unstructured":"Jedwab, J., Mitchell, C.J.: Minimum weight modified signed-digit representations and fast exponentiation. Electronics Letters\u00a025(17), 1171\u20131172 (1989)","journal-title":"Electronics Letters"},{"issue":"4","key":"16_CR14","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1145\/279232.279237","volume":"23","author":"A.H. Karp","year":"1997","unstructured":"Karp, A.H., Markstein, P.: High precision division and square root. ACM Transaction on Mathematical Software\u00a023(4), 561\u2013589 (1997)","journal-title":"ACM Transaction on Mathematical Software"},{"key":"16_CR15","unstructured":"Knuth, D.E.: The Art of Computer Programming. In: Seminumerical Algorithms, Algorithm 4.3.3R, vol.\u00a02. Addison-Wesley, Reading (1981)"},{"key":"16_CR16","unstructured":"Krandick, W., Johnson, J.R.: Efficient Multiprecision Floating Point Multiplication with Exact Rounding, Tech. Rep. 93-76, RISC-Linz. Johannes Kepler University, Linz, Austria (1993)"},{"key":"16_CR17","doi-asserted-by":"publisher","DOI":"10.1201\/9781439821916","volume-title":"Handbook of Applied Cryptography","author":"A. Menezes","year":"1996","unstructured":"Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)"},{"issue":"170","key":"16_CR18","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1090\/S0025-5718-1985-0777282-X","volume":"44","author":"P.L. Montgomery","year":"1985","unstructured":"Montgomery, P.L.: Modular Multiplication without Trial Division. Mathematics of Computation\u00a044(170), 519\u2013521 (1985)","journal-title":"Mathematics of Computation"},{"key":"16_CR19","unstructured":"Mulders, T.: On computing short products. Tech Report No. 276, Dept of CS, ETH Zurich (November 1997), \n                    \n                      http:\/\/www.inf.ethz.ch\/research\/publications\/data\/tech-reports\/2xx\/276.pdf"},{"key":"16_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/3-540-49162-7_18","volume-title":"Public Key Cryptography","author":"P. Paillier","year":"1999","unstructured":"Paillier, P.: Low-cost double-size modular exponentiation or how to stretch your cryptoprocessor. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol.\u00a01560, pp. 223\u2013234. Springer, Heidelberg (1999)"},{"issue":"5","key":"16_CR21","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1109\/71.382314","volume":"6","author":"K.C. Posh","year":"1995","unstructured":"Posh, K.C., Posh, R.: Modulo reduction in Residue Number Systems. IEEE Transactions on Parallel and Distributed Systems\u00a06(5), 449\u2013454 (1995)","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"16_CR22","unstructured":"Quisquater, J.-J.: Fast modular exponentiation without division. In: Rump session of Eurocrypt 1990, Arhus, Denmark (1990)"},{"issue":"2","key":"16_CR23","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R.L. Rivest","year":"1978","unstructured":"Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM\u00a021(2), 120\u2013126 (1978)","journal-title":"Communications of the ACM"},{"issue":"7","key":"16_CR24","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1016\/S0167-4048(99)80061-3","volume":"17","author":"J. Schwemmlein","year":"1998","unstructured":"Schwemmlein, J., Posh, K.C., Posh, R.: RNS modulo reduction upon a restricted base value set and its applicability to RSA cryptography. Computer & Security\u00a017(7), 637\u2013650 (1998)","journal-title":"Computer & Security"},{"key":"16_CR25","unstructured":"SNIA OSD Technical Work Group, \n                    \n                      http:\/\/www.snia.org\/tech_activities\/workgroups\/osd\/"},{"key":"16_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/3-540-46766-1_26","volume-title":"Advances in Cryptology - CRYPTO \u201991","author":"C.D. Walter","year":"1992","unstructured":"Walter, C.D.: Faster modular multiplication by operand scaling. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol.\u00a0576, pp. 313\u2013323. Springer, Heidelberg (1992)"},{"key":"16_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/978-3-540-28632-5_4","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2004","author":"L. Hars","year":"2004","unstructured":"Hars, L.: Long Modular Multiplication for Cryptographic Applications. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol.\u00a03156, pp. 45\u201361. Springer, Heidelberg (2004), \n                    \n                      http:\/\/eprint.iacr.org\/2004\/198\/"},{"key":"16_CR28","unstructured":"Hars, L.: Finding the Fastest Multiplication for Cryptographic Operand Lengths: Analytic and Experimental Comparisons (manuscript)"}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems \u2013 CHES 2005"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11545262_16.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T06:57:00Z","timestamp":1619506620000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11545262_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540284741","9783540319405"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/11545262_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}