Using an RSA Accelerator for Modular Inversion
We present a very simple new algorithm for modular inversion. Modular inversion can be done by the extended Euclidean algorithm. We substitute the extended Euclidean algorithm by a standard (non-extended) Euclidean algorithm that works on integers of approximately double the length of the modulus. T...
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| description | We present a very simple new algorithm for modular inversion. Modular inversion can be done by the extended Euclidean algorithm. We substitute the extended Euclidean algorithm by a standard (non-extended) Euclidean algorithm that works on integers of approximately double the length of the modulus. This substitution can be very useful on smart card coprocessors, since in some cases computations with longer numbers than necessary can be done at no extra cost. Many smart card coprocessors have been designed for the RSA algorithm of, say, 1024 bits length. On the other hand, elliptic curve algorithms work with much smaller numbers, and modular inversion is a much more important primitive in elliptic curve cryptography than in RSA cryptography. On one smart card coprocessor the new algorithm is more than twice as fast as the classical algorithm. |
| doi_str_mv | 10.1007/11545262_17 |
| format | Book Chapter |
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Modular inversion can be done by the extended Euclidean algorithm. We substitute the extended Euclidean algorithm by a standard (non-extended) Euclidean algorithm that works on integers of approximately double the length of the modulus. This substitution can be very useful on smart card coprocessors, since in some cases computations with longer numbers than necessary can be done at no extra cost. Many smart card coprocessors have been designed for the RSA algorithm of, say, 1024 bits length. On the other hand, elliptic curve algorithms work with much smaller numbers, and modular inversion is a much more important primitive in elliptic curve cryptography than in RSA cryptography. On one smart card coprocessor the new algorithm is more than twice as fast as the classical algorithm.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540284741</identifier><identifier>ISBN: 3540284745</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540319405</identifier><identifier>EISBN: 3540319409</identifier><identifier>DOI: 10.1007/11545262_17</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Cryptography ; Electronics ; Euclidean algorithm ; Exact sciences and technology ; Information, signal and communications theory ; Integrated circuits ; Integrated circuits by function (including memories and processors) ; Memory and file management (including protection and security) ; Memory organisation. Data processing ; modular inversion ; Semiconductor electronics. Microelectronics. Optoelectronics. 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On one smart card coprocessor the new algorithm is more than twice as fast as the classical algorithm.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Cryptography</subject><subject>Electronics</subject><subject>Euclidean algorithm</subject><subject>Exact sciences and technology</subject><subject>Information, signal and communications theory</subject><subject>Integrated circuits</subject><subject>Integrated circuits by function (including memories and processors)</subject><subject>Memory and file management (including protection and security)</subject><subject>Memory organisation. Data processing</subject><subject>modular inversion</subject><subject>Semiconductor electronics. Microelectronics. Optoelectronics. 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Data processing</topic><topic>modular inversion</topic><topic>Semiconductor electronics. Microelectronics. Optoelectronics. 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Modular inversion can be done by the extended Euclidean algorithm. We substitute the extended Euclidean algorithm by a standard (non-extended) Euclidean algorithm that works on integers of approximately double the length of the modulus. This substitution can be very useful on smart card coprocessors, since in some cases computations with longer numbers than necessary can be done at no extra cost. Many smart card coprocessors have been designed for the RSA algorithm of, say, 1024 bits length. On the other hand, elliptic curve algorithms work with much smaller numbers, and modular inversion is a much more important primitive in elliptic curve cryptography than in RSA cryptography. On one smart card coprocessor the new algorithm is more than twice as fast as the classical algorithm.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11545262_17</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Cryptographic Hardware and Embedded Systems – CHES 2005, 2005, p.226-236 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_17116121 |
| source | Springer Books |
| subjects | Applied sciences Computer science control theory systems Cryptography Electronics Euclidean algorithm Exact sciences and technology Information, signal and communications theory Integrated circuits Integrated circuits by function (including memories and processors) Memory and file management (including protection and security) Memory organisation. Data processing modular inversion Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices Signal and communications theory Smart card coprocessor Software Telecommunications and information theory |
| title | Using an RSA Accelerator for Modular Inversion |
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