{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T23:14:41Z","timestamp":1791414881723,"version":"4.3.3"},"publisher-location":"Berlin, Heidelberg","reference-count":40,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662483237","type":"print"},{"value":"9783662483244","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-662-48324-4_9","type":"book-chapter","created":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T10:27:48Z","timestamp":1441016868000},"page":"164-184","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Modular Hardware Architecture for Somewhat Homomorphic Function Evaluation"],"prefix":"10.1007","author":[{"given":"Sujoy","family":"Sinha Roy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kimmo","family":"J\u00e4rvinen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frederik","family":"Vercauteren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vassil","family":"Dimitrov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ingrid","family":"Verbauwhede","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,9,1]]},"reference":[{"key":"9_CR1","unstructured":"Xilinx 7 Series FPGAs Overview, DS180 (v1.16.1), 17 December 2014. http:\/\/www.xilinx.com\/support\/documentation\/data_sheets\/ds180_7Series_Overview.pdf"},{"key":"9_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1007\/978-3-662-46800-5_17","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"MR Albrecht","year":"2015","unstructured":"Albrecht, M.R., Rechberger, C., Schneider, T., Tiessen, T., Zohner, M.: Ciphers for MPC and FHE. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 430\u2013454. Springer, Heidelberg (2015)"},{"key":"9_CR3","doi-asserted-by":"crossref","unstructured":"Aysu, A., Patterson, C., Schaumont, P.: Low-cost and area-efficient FPGA Implementations of lattice-based cryptography. In: HOST, pp. 81\u201386. IEEE (2013)","DOI":"10.1109\/HST.2013.6581570"},{"key":"9_CR4","unstructured":"Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. Cryptology ePrint Archive, Report 2013\/404 (2013). http:\/\/eprint.iacr.org\/"},{"key":"9_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1007\/978-3-642-34961-4_14","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"J Borghoff","year":"2012","unstructured":"Borghoff, J., Canteaut, A., G\u00fcneysu, T., Kavun, E.B., Knezevic, M., Knudsen, L.R., Leander, G., Nikov, V., Paar, C., Rechberger, C., Rombouts, P., Thomsen, S.S., Yal\u00e7\u0131n, T.: PRINCE \u2013 a low-latency block cipher for pervasive computing applications. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 208\u2013225. Springer, Heidelberg (2012)"},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/978-3-642-45239-0_4","volume-title":"Cryptography and Coding","author":"JW Bos","year":"2013","unstructured":"Bos, J.W., Lauter, K., Loftus, J., Naehrig, M.: Improved security for a ring-based fully homomorphic encryption scheme. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 45\u201364. Springer, Heidelberg (2013)"},{"key":"9_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1007\/978-3-642-32009-5_50","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"Z Brakerski","year":"2012","unstructured":"Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868\u2013886. Springer, Heidelberg (2012)"},{"key":"9_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/978-3-642-22792-9_29","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"Z Brakerski","year":"2011","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505\u2013524. Springer, Heidelberg (2011)"},{"key":"9_CR9","unstructured":"Canteaut, A., Carpov, S., Fontaine, C., Lepoint, T., Naya-Plasencia, M., Paillier, P., Sirdey, R.: How to compress homomorphic ciphertexts. Cryptology ePrint Archive, Report 2015\/113 (2015). http:\/\/eprint.iacr.org\/"},{"key":"9_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/978-3-662-44774-1_14","volume-title":"Financial Cryptography and Data Security","author":"X Cao","year":"2014","unstructured":"Cao, X., Moore, C., O\u2019Neill, M., Hanley, N., O\u2019Sullivan, E.: High-speed fully homomorphic encryption over the integers. In: B\u00f6hme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014 Workshops. LNCS, vol. 8438, pp. 169\u2013180. Springer, Heidelberg (2014)"},{"key":"9_CR11","unstructured":"de Clercq, R., Sinha Roy, S., Vercauteren, F., Verbauwhede, I.: Efficient software implementation of ring-LWE encryption. Cryptology ePrint Archive, Report 2014\/725 (2014). http:\/\/eprint.iacr.org\/"},{"issue":"4","key":"9_CR12","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1147\/sj.294.0526","volume":"29","author":"PG Comba","year":"1990","unstructured":"Comba, P.G.: Exponentiation cryptosystems on the IBM PC. IBM Syst. J. 29(4), 526\u2013538 (1990)","journal-title":"IBM Syst. J."},{"key":"9_CR13","unstructured":"Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. http:\/\/staff.ustc.edu.cn\/ csli\/graduate\/algorithms\/book6\/toc.htm"},{"key":"9_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-642-54631-0_18","volume-title":"Public-Key Cryptography \u2013 PKC 2014","author":"J-S Coron","year":"2014","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: Scale-invariant fully homomorphic encryption over the integers. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 311\u2013328. Springer, Heidelberg (2014)"},{"key":"9_CR15","doi-asserted-by":"crossref","unstructured":"Cousins, D.B., Rohloff, K., Peikert, C., Schantz, R.: SIPHER: scalable implementation of primitives for homomorphic encryption \u2013 FPGA implementation using Simulink. In: Proceedings of the 15th Annual Workshop on High Performance Embedded Computing (HPEC 2011) (2011)","DOI":"10.1109\/HPEC.2012.6408672"},{"key":"9_CR16","doi-asserted-by":"crossref","unstructured":"Cousins, D.B., Rohloff, K., Peikert, C., Schantz, R.: An update on SIPHER (scalable implementation of primitives for homomorphic encryption) \u2013 FPGA implementation using Simulink. In: Proceedings of the 2012 IEEE High Performance Extreme Computing Conference (HPEC 2012), pp. 1\u20135 (2012)","DOI":"10.1109\/HPEC.2012.6408672"},{"key":"9_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-642-13190-5_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"M Dijk van","year":"2010","unstructured":"van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24\u201343. Springer, Heidelberg (2010)"},{"key":"9_CR18","doi-asserted-by":"crossref","unstructured":"Dor\u00f6z, Y., \u00d6zt\u00fcrk, E., Sunar, B.: Evaluating the hardware performance of a million-bit multiplier. In: Proceedings of the 16th Euromicro Conference on Digital System Design (DSD 2013), pp. 955\u2013962 (2013)","DOI":"10.1109\/DSD.2013.108"},{"key":"9_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/978-3-662-44774-1_17","volume-title":"Financial Cryptography and Data Security","author":"Y Dor\u00f6z","year":"2014","unstructured":"Dor\u00f6z, Y., Shahverdi, A., Eisenbarth, T., Sunar, B.: Toward practical homomorphic evaluation of block ciphers using prince. In: B\u00f6hme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014 Workshops. LNCS, vol. 8438, pp. 208\u2013220. Springer, Heidelberg (2014)"},{"key":"9_CR20","unstructured":"Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. Cryptology ePrint Archive, Report 2012\/144 (2012). http:\/\/eprint.iacr.org\/"},{"key":"9_CR21","volume-title":"Modern Computer Algebra","author":"J Gathen von zur","year":"1999","unstructured":"von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, New York (1999)"},{"key":"9_CR22","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st ACM Symposium on Theory of Computing (STOC 2009), pp. 169\u2013178 (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"9_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/978-3-642-20465-4_9","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"C Gentry","year":"2011","unstructured":"Gentry, C., Halevi, S.: Implementing Gentry\u2019s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129\u2013148. Springer, Heidelberg (2011)"},{"key":"9_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1007\/978-3-642-32009-5_49","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"C Gentry","year":"2012","unstructured":"Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 850\u2013867. Springer, Heidelberg (2012)"},{"key":"9_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-642-40041-4_5","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"C Gentry","year":"2013","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75\u201392. Springer, Heidelberg (2013)"},{"key":"9_CR26","volume-title":"Guide to Elliptic Curve Cryptography","author":"D Hankerson","year":"2003","unstructured":"Hankerson, D., Menezes, A.J., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer-Verlag New York Inc., Secaucus (2003)"},{"issue":"4","key":"9_CR27","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1145\/279232.279237","volume":"23","author":"AH Karp","year":"1997","unstructured":"Karp, A.H., Markstein, P.: High-precision division and square root. ACM Trans. Math. Softw. 23(4), 561\u2013589 (1997)","journal-title":"ACM Trans. Math. Softw."},{"key":"9_CR28","doi-asserted-by":"crossref","unstructured":"Ko\u00e7, C.K. (ed.): Cryptographic Engineering 1st. Springer Publishing Company (2008)","DOI":"10.1007\/978-0-387-71817-0_1"},{"key":"9_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1007\/978-3-319-06734-6_20","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2014","author":"T Lepoint","year":"2014","unstructured":"Lepoint, T., Naehrig, M.: A comparison of the homomorphic encryption schemes $$\\sf FV$$ FV and $$\\sf YASHE$$ YASHE . In: Pointcheval, D., Vergnaud, D. (eds.) AFRICACRYPT. LNCS, vol. 8469, pp. 318\u2013335. Springer, Heidelberg (2014)"},{"key":"9_CR30","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing, pp. 1219\u20131234. ACM, New York, NY, USA (2012)","DOI":"10.1145\/2213977.2214086"},{"key":"9_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1007\/978-3-642-41320-9_16","volume-title":"Financial Cryptography and Data Security","author":"C Moore","year":"2013","unstructured":"Moore, C., Hanley, N., McAllister, J., O\u2019Neill, M., O\u2019Sullivan, E., Cao, X.: Targeting FPGA DSP slices for a large integer multiplier for integer based FHE. In: Adams, A.A., Brenner, M., Smith, M. (eds.) FC 2013. LNCS, vol. 7862, pp. 226\u2013237. Springer, Heidelberg (2013)"},{"key":"9_CR32","doi-asserted-by":"crossref","unstructured":"Naehrig, M., Lauter, K., Vaikuntanathan, V.: Can homomorphic encryption be practical? In: Proceedings of the 3rd ACM Workshop on Cloud Computing Security Workshop (CCSW 2011), pp. 113\u2013124. ACM (2011)","DOI":"10.1145\/2046660.2046682"},{"key":"9_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1007\/978-3-662-43414-7_4","volume-title":"Selected Areas in Cryptography \u2013 SAC 2013","author":"T P\u00f6ppelmann","year":"2014","unstructured":"P\u00f6ppelmann, T., G\u00fcneysu, T.: Towards practical lattice-based public-key encryption on reconfigurable hardware. In: Lange, T., Lauter, K., Lison\u011bk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 68\u201386. Springer, Heidelberg (2014)"},{"issue":"11","key":"9_CR34","first-page":"169","volume":"4","author":"RL Rivest","year":"1978","unstructured":"Rivest, R.L., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. Found. Secure Comput. 4(11), 169\u2013180 (1978)","journal-title":"Found. Secure Comput."},{"key":"9_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/978-81-322-1786-2","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2014","author":"S Sinha Roy","year":"2014","unstructured":"Sinha Roy, S., Vercauteren, F., Mentens, N., Chen, D.D., Verbauwhede, I.: Compact ring-LWE cryptoprocessor. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 371\u2013391. Springer, Heidelberg (2014)"},{"key":"9_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1007\/978-3-642-13013-7_25","volume-title":"Public Key Cryptography \u2013 PKC 2010","author":"NP Smart","year":"2010","unstructured":"Smart, N.P., Vercauteren, F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420\u2013443. Springer, Heidelberg (2010)"},{"issue":"1","key":"9_CR37","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10623-012-9720-4","volume":"71","author":"N Smart","year":"2014","unstructured":"Smart, N., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Cryptogr. 71(1), 57\u201381 (2014)","journal-title":"Des. Codes Cryptogr."},{"key":"9_CR38","doi-asserted-by":"crossref","unstructured":"Wang, W., Hu, Y., Chen, L., Huang, X., Sunar, B.: Accelerating fully homomorphic encryption using GPU. In: IEEE Conference on High Performance Extreme Computing (HPEC 2012), pp. 1\u20135 (2012)","DOI":"10.1109\/HPEC.2012.6408660"},{"key":"9_CR39","doi-asserted-by":"crossref","unstructured":"Wang, W., Huang, X.: FPGA implementation of a large-number multiplier for fully homomorphic encryption. In: IEEE International Symposium on Circuits and Systems (ISCAS 2013), pp. 2589\u20132592 (2013)","DOI":"10.1109\/ISCAS.2013.6572408"},{"issue":"9","key":"9_CR40","doi-asserted-by":"publisher","first-page":"1879","DOI":"10.1109\/TVLSI.2013.2281786","volume":"22","author":"W Wang","year":"2014","unstructured":"Wang, W., Huang, X.: VLSI design of a large-number multiplier for fully homomorphic encryption. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 22(9), 1879\u20131887 (2014)","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems -- CHES 2015"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-48324-4_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T09:25:39Z","timestamp":1748597139000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-48324-4_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783662483237","9783662483244"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-48324-4_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"1 September 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}