{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T18:10:57Z","timestamp":1778263857009,"version":"3.51.4"},"publisher-location":"Boston, MA","reference-count":19,"publisher":"Springer US","isbn-type":[{"value":"9781441959058","type":"print"},{"value":"9781441959065","type":"electronic"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-1-4419-5906-5_49","type":"book-chapter","created":{"date-parts":[[2011,10,27]],"date-time":"2011-10-27T09:53:32Z","timestamp":1319709212000},"page":"795-798","source":"Crossref","is-referenced-by-count":0,"title":["Modular Arithmetic"],"prefix":"10.1007","author":[{"given":"Scott","family":"Contini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c7etin","family":"Kaya Ko\u00e7","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Colin D.","family":"Walter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"49_CR1_49","unstructured":"Barrett P (1987) Implementing the rivest shamir and adleman public key encryption algorithm on a standard digital signal processor. In: Odlyzko AM (ed) Advances in Cryptology\u00a0\u2013 CRYPTO \u201986, Lecture Notes in Computer Science, vol 263. Springer, New york, pp 311\u2013323. http:\/\/www.springerlink.com\/content\/c4f3rqbt5dxxyad4\/"},{"key":"49_CR2_49","unstructured":"Diffie W, Hellman ME (1976) New directions in cryptography. IEEE Trans Inform Theory 22(6):644\u2013654. http:\/\/citeseer.ist.psu.edu\/diffie76new.html"},{"key":"49_CR3_49","unstructured":"ElGamal T (1985) A public-key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inform Theory 31(4):469\u2013472. http:\/\/ieeexplore.ieee.org\/xpl\/freeabs_all.jsp?arnumber=1057074"},{"key":"49_CR4_49","unstructured":"Fiat A, Shamir A (1987) How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko AM (ed) Advances in Cryptology\u00a0\u2013 CRYPTO \u201986, Lecture Notes in Computer Science, vol 263. Springer, Berlin, pp 186\u2013194. http:\/\/citeseerx.ist.psu.edu\/viewdoc\/summary?doi=10.1.1.13.8796"},{"key":"49_CR5_49","unstructured":"Knuth DE (1998) The art of computer programming, vol 2, Seminumerical Algorithms, 3rd edn. Addison-Wesley, Reading, ISBN 0-201-89684-2. http:\/\/www.informit.com\/title\/0201896842"},{"key":"49_CR6_49","unstructured":"Koblitz N (1987) Elliptic curve cryptosystems. Math Comput 48(177):203\u2013209. http:\/\/www.jstor.org\/pss\/2007884"},{"key":"49_CR7_49","unstructured":"Koblitz N (1994) A course in number theory and cryptography, Graduate Texts in Mathematics, vol 114, 2nd edn. Springer, New York, ISBN 978-0-387-94293-3. http:\/\/www.springer.com\/math\/numbers\/book\/978-0-387-94293-3"},{"key":"49_CR8_49","unstructured":"Kocher P (1996) Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In: Koblitz N (ed) Advances in Cryptology\u00a0\u2013 CRYPTO \u201996, Lecture Notes in Computer Science, vol 1109, Springer, Berlin, 104\u2013113. http:\/\/www.springerlink.com\/content\/4el17cvre3gxt4gd\/"},{"key":"49_CR9_49","unstructured":"Kocher P, Jaffe J, Jun B (1999) Differential power analysis. In: Wiener M (ed) Advances in Cryptology\u00a0\u2013 CRYPTO \u201999, Lecture Notes in Computer Science, vol 1666, Springer, Berlin, pp\u00a0388\u2013397. http:\/\/www.springerlink.com\/content\/kx35ub53vtrkh2nx\/"},{"key":"49_CR10_49","unstructured":"Lidl R, Niederreiter H (1994) Introduction to finite fields and their applications, 2nd edn. Cambridge University Press, Cambridge, ISBN 9780521460941. http:\/\/www.cambridgeuniversitypress.com\/catalogue\/catalogue.asp?isbn=9780521460941"},{"key":"49_CR11_49","unstructured":"Miller GL (1976) Riemann\u2019s hypothesis and tests for primality. J Comput Syst Sci 13(3):300\u2013317. http:\/\/www.cs.cmu.edu\/~glmiller\/Publications\/b2hd-Mi76.html"},{"key":"49_CR12_49","unstructured":"Miller V (1986) Uses of elliptic curves in cryptography. In: Williams HC (ed) Advances in Cryptology\u00a0\u2013 CRYPTO \u201985: Proceedings, Lecture Notes in Computer Science, vol 218, Springer, Berlin, pp 417\u2013426. http:\/\/www.springerlink.com\/content\/4lfhkd08684v3wyl\/"},{"key":"49_CR13_49","unstructured":"Montgomery PL (1985) Modular multiplication without trial division. Math Comput 44(170):519\u2013521. http:\/\/www.jstor.org\/pss\/2007970"},{"key":"49_CR14_49","unstructured":"Quisquater J-J, Couvreur C (1982) Fast decipherment algorithm for RSA Publickey cryptosystem. Electron Lett 18(21):905\u2013907. http:\/\/ieeexplore.ieee.org\/xpl\/freeabs_all.jsp?arnumber=4246955"},{"key":"49_CR15_49","unstructured":"Quisquater J-J, Samyde D (2001) ElectroMagnetic analysis (EMA): measures and counter-measures for smart cards. In: Attali I, Jensen T (eds) Smart card programming and security (e-Smart 2001), Lecture Notes in Computer Science, vol 2140, Springer, Cannes, pp 200\u2013210. http:\/\/www.springerlink.com\/content\/chmydkq8x5tgdrce\/"},{"key":"49_CR16_49","unstructured":"Rabin MO (1980) Probabilistic algorithm for testing primality. J Number Theory 12(1):128\u2013138. http:\/\/dx.doi.org\/10.1016\/0022-314X(80)90084-0"},{"key":"49_CR17_49","unstructured":"Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120\u2013126. http:\/\/citeseerx.ist.psu.edu\/viewdoc\/summary?doi=10.1.1.40.5588"},{"key":"49_CR18_49","unstructured":"Schnorr CP (1991) Efficient signature generation by smart cards. J Cryptol 4:161\u2013174. http:\/\/www.springerlink.com\/content\/w037127811042441\/"},{"key":"49_CR19_49","unstructured":"Stinson DR (2005) Cryptography: theory and practice, 3rd edn. CRC Press, New York, ISBN 9781584885085. http:\/\/www.crcpress.com\/product\/isbn\/9781584885085"}],"container-title":["Encyclopedia of Cryptography and Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4419-5906-5_49","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T17:44:01Z","timestamp":1778262241000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4419-5906-5_49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9781441959058","9781441959065"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-1-4419-5906-5_49","relation":{},"subject":[],"published":{"date-parts":[[2011]]}}}