{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:36:32Z","timestamp":1750307792459,"version":"3.41.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2008,6,1]],"date-time":"2008-06-01T00:00:00Z","timestamp":1212278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Reconfigurable Technol. Syst."],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p>The resistance against powerful index-calculus attacks makes Elliptic Curve Cryptosystems (ECC) an interesting alternative to conventional asymmetric cryptosystems, like RSA. Operands in ECC require significantly less bits at the same level of security, resulting in a higher computational efficiency compared to RSA. With growing computational capabilities and continuous technological improvements over the years, however, the question of the security of ECC against attacks based on special-purpose hardware arises. In this context, recently emerged low-cost FPGAs demand for attention in the domain of hardware-based cryptanalysis: the extraordinary efficiency of modern programmable hardware devices allow for a low-budget implementation of hardware-based ECC attacks---without the requirement of the expensive development of ASICs.<\/jats:p>\n          <jats:p>With focus on the aspect of cost-efficiency, this contribution presents and analyzes an FPGA-based architecture of an attack against ECC over prime fields. A multi-processing hardware architecture for Pollard's Rho method is described. We provide results on actually used key lengths of ECC (128 bits and above) and estimate the expected runtime for a successful attack.<\/jats:p>\n          <jats:p>As a first result, currently used elliptic curve cryptosystems with a security of 160 bit and above turn out to be infeasible to break with available computational and financial resources. However, some of the security standards proposed by the Standards for Efficient Cryptography Group (SECG) become subject to attacks based on low-cost FPGAs.<\/jats:p>","DOI":"10.1145\/1371579.1371580","type":"journal-article","created":{"date-parts":[[2009,1,13]],"date-time":"2009-01-13T13:15:48Z","timestamp":1231852548000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Special-Purpose Hardware for Solving the Elliptic Curve Discrete Logarithm Problem"],"prefix":"10.1145","volume":"1","author":[{"given":"Tim","family":"G\u00fcneysu","sequence":"first","affiliation":[{"name":"Horst-G\u00f6rtz Institute for IT Security, Ruhr University of Bochum, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"Paar","sequence":"additional","affiliation":[{"name":"Horst-G\u00f6rtz Institute for IT Security, Ruhr University of Bochum, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Pelzl","sequence":"additional","affiliation":[{"name":"Horst-G\u00f6rtz Institute for IT Security, Ruhr University of Bochum, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Blake I. Seroussi G. and Smart N. 1999. Elliptic Curves in Cryptography. Cambridge University Press.]]   Blake I. Seroussi G. and Smart N. 1999. Elliptic Curves in Cryptography . Cambridge University Press.]]","DOI":"10.1017\/CBO9781107360211"},{"key":"e_1_2_1_2_1","unstructured":"Certicom. 1997. Certicom ECC Challenge. http:\/\/www.certicom.com.]]  Certicom. 1997. Certicom ECC Challenge. http:\/\/www.certicom.com.]]"},{"key":"e_1_2_1_3_1","unstructured":"Certicom research. 2000a. Standards for Efficient Cryptography---SEC 1: Elliptic Curve Cryptography v1.0. http:\/\/www.secg.org\/secg_docs.htm.]]  Certicom research. 2000a. Standards for Efficient Cryptography---SEC 1: Elliptic Curve Cryptography v1.0. http:\/\/www.secg.org\/secg_docs.htm.]]"},{"key":"e_1_2_1_4_1","unstructured":"Certicom research. 2000b. Standards for Efficient Cryptography---SEC 1: Recommended Elliptic Curve Domain Parameters v1.0. http:\/\/www.secg.org\/secg_docs.htm.]]  Certicom research. 2000b. Standards for Efficient Cryptography---SEC 1: Recommended Elliptic Curve Domain Parameters v1.0. http:\/\/www.secg.org\/secg_docs.htm.]]"},{"key":"e_1_2_1_5_1","first-page":"5","article-title":"An FPGA implementation of a GF(p) ALU for encryption processors","volume":"28","author":"Daly A.","year":"2004","unstructured":"Daly , A. , Marnane , W. , Kerins , T. , and Popovici , E. 2004 . An FPGA implementation of a GF(p) ALU for encryption processors . Elsevier Microproces. Microsyst. 28 , 5 -- 6 , 253--260.]] Daly, A., Marnane, W., Kerins, T., and Popovici, E. 2004. An FPGA implementation of a GF(p) ALU for encryption processors. Elsevier Microproces. Microsyst. 28, 5--6, 253--260.]]","journal-title":"Elsevier Microproces. Microsyst."},{"key":"e_1_2_1_6_1","unstructured":"Daly A. Marnaney L. and Popovici E. 2004. Fast modular inversion in the Montgomery Domain on reconfigurable logic. Tech. rep. University College Cork Cork Ireland.]]  Daly A. Marnaney L. and Popovici E. 2004. Fast modular inversion in the Montgomery Domain on reconfigurable logic. Tech. rep. University College Cork Cork Ireland.]]"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74735-2_26"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1976.1055638"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1985.1057074"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/11545262_9"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1216919.1216953"},{"key":"e_1_2_1_12_1","unstructured":"Hankerson D. Menezes A. and Vanstone S. 2004. Guide to Elliptic Curve Cryptography. Springer Verlag Berlin Germany.]]   Hankerson D. Menezes A. and Vanstone S. 2004. Guide to Elliptic Curve Cryptography . Springer Verlag Berlin Germany.]]"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1987-0866109-5"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/11894063_9"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-001-0009-4"},{"key":"e_1_2_1_16_1","unstructured":"Menezes A. J. van Oorschot P. C. and Vanstone S. A. 1996. Handbook of Applied Cryptography. CRC Press New York NY.]]   Menezes A. J. van Oorschot P. C. and Vanstone S. A. 1996. Handbook of Applied Cryptography . CRC Press New York NY.]]"},{"volume-title":"Advances in Cryptology---(CRYPTO'85)","author":"Miller V.","key":"e_1_2_1_17_1","unstructured":"Miller , V. 1986. Uses of elliptic curves in cryptography . In Advances in Cryptology---(CRYPTO'85) , H. C. Williams, Ed. Vol. Lecture Notes in Computer Science, 218. Springer , 417--426.]] Miller, V. 1986. Uses of elliptic curves in cryptography. In Advances in Cryptology---(CRYPTO'85), H. C. Williams, Ed. Vol. Lecture Notes in Computer Science, 218. Springer, 417--426.]]"},{"volume-title":"Proceedings of Workshop on Cryptograpic Hardware and Embedded Systems (CHES'01)","author":"Orlando G.","key":"e_1_2_1_18_1","unstructured":"Orlando , G. and Paar , C . 2001. A scalable GF(p) elliptic curve processor architecture for programmable hardware . In Proceedings of Workshop on Cryptograpic Hardware and Embedded Systems (CHES'01) . 356--371.]] Orlando, G. and Paar, C. 2001. A scalable GF(p) elliptic curve processor architecture for programmable hardware. In Proceedings of Workshop on Cryptograpic Hardware and Embedded Systems (CHES'01). 356--371.]]"},{"volume-title":"Proceedings of the Application-Specific Systems, Architectures, and Processors (ASAP), 433--443","author":"\u00d6rs S.","key":"e_1_2_1_19_1","unstructured":"\u00d6rs , S. , Batina , L. , Preneel , B. , and Vandewalle , J . 2003. Hardware implementation of elliptic curve processor over GF(p) . In Proceedings of the Application-Specific Systems, Architectures, and Processors (ASAP), 433--443 .]] \u00d6rs, S., Batina, L., Preneel, B., and Vandewalle, J. 2003. Hardware implementation of elliptic curve processor over GF(p). In Proceedings of the Application-Specific Systems, Architectures, and Processors (ASAP), 433--443.]]"},{"volume-title":"Monte Carlo methods for index computation mod","author":"Pollard J.","key":"e_1_2_1_20_1","unstructured":"Pollard , J. 1978. Monte Carlo methods for index computation mod p. Math. Comput . 32, 143, 918--924.]] Pollard, J. 1978. Monte Carlo methods for index computation mod p. Math. Comput. 32, 143, 918--924.]]"},{"key":"e_1_2_1_21_1","volume-title":"Lecture Notes in Computer Science","volume":"2729","author":"Shamir A.","unstructured":"Shamir , A. and Tromer , E . 2003. Factoring large numbers with the TWIRL device. In Advances in Cryptology---(Crypto'03) . Lecture Notes in Computer Science , vol. 2729 . Springer, 1--26.]] Shamir, A. and Tromer, E. 2003. Factoring large numbers with the TWIRL device. In Advances in Cryptology---(Crypto'03). Lecture Notes in Computer Science, vol. 2729. Springer, 1--26.]]"},{"key":"e_1_2_1_22_1","doi-asserted-by":"crossref","unstructured":"Teske E. 1998. Speeding up Pollard's rho method for computing discrete logarithms. Algorithmic Number Theory Seminar (ANTS-III) 541--554.]]   Teske E. 1998. Speeding up Pollard's rho method for computing discrete logarithms. Algorithmic Number Theory Seminar (ANTS-III) 541--554.]]","DOI":"10.1007\/BFb0054891"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00003816"}],"container-title":["ACM Transactions on Reconfigurable Technology and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1371579.1371580","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1371579.1371580","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:56:21Z","timestamp":1750254981000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1371579.1371580"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1145\/1371579.1371580"],"URL":"https:\/\/doi.org\/10.1145\/1371579.1371580","relation":{},"ISSN":["1936-7406","1936-7414"],"issn-type":[{"type":"print","value":"1936-7406"},{"type":"electronic","value":"1936-7414"}],"subject":[],"published":{"date-parts":[[2008,6]]},"assertion":[{"value":"2007-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-06-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}