Cryptographic implications of Hess' generalized GHS attack
Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil...
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Gespeichert in:
| Autor*in: |
Menezes, Alfred [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2005 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2005 |
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| Übergeordnetes Werk: |
Enthalten in: Applicable algebra in engineering, communication and computing - Springer-Verlag, 1990, 16(2005), 6 vom: 17. Nov., Seite 439-460 |
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| Übergeordnetes Werk: |
volume:16 ; year:2005 ; number:6 ; day:17 ; month:11 ; pages:439-460 |
| Links: |
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| DOI / URN: |
10.1007/s00200-005-0186-8 |
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| Katalog-ID: |
OLC2075497222 |
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| 520 | |a Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. | ||
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| 700 | 1 | |a Teske, Edlyn |4 aut | |
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10.1007/s00200-005-0186-8 doi (DE-627)OLC2075497222 (DE-He213)s00200-005-0186-8-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Menezes, Alfred verfasserin aut Cryptographic implications of Hess' generalized GHS attack 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. Elliptic curve cryptography Weil descent Isogenies Teske, Edlyn aut Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 16(2005), 6 vom: 17. Nov., Seite 439-460 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:16 year:2005 number:6 day:17 month:11 pages:439-460 https://doi.org/10.1007/s00200-005-0186-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_100 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4324 AR 16 2005 6 17 11 439-460 |
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10.1007/s00200-005-0186-8 doi (DE-627)OLC2075497222 (DE-He213)s00200-005-0186-8-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Menezes, Alfred verfasserin aut Cryptographic implications of Hess' generalized GHS attack 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. Elliptic curve cryptography Weil descent Isogenies Teske, Edlyn aut Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 16(2005), 6 vom: 17. Nov., Seite 439-460 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:16 year:2005 number:6 day:17 month:11 pages:439-460 https://doi.org/10.1007/s00200-005-0186-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_100 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4324 AR 16 2005 6 17 11 439-460 |
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10.1007/s00200-005-0186-8 doi (DE-627)OLC2075497222 (DE-He213)s00200-005-0186-8-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Menezes, Alfred verfasserin aut Cryptographic implications of Hess' generalized GHS attack 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. Elliptic curve cryptography Weil descent Isogenies Teske, Edlyn aut Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 16(2005), 6 vom: 17. Nov., Seite 439-460 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:16 year:2005 number:6 day:17 month:11 pages:439-460 https://doi.org/10.1007/s00200-005-0186-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_100 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4324 AR 16 2005 6 17 11 439-460 |
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10.1007/s00200-005-0186-8 doi (DE-627)OLC2075497222 (DE-He213)s00200-005-0186-8-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Menezes, Alfred verfasserin aut Cryptographic implications of Hess' generalized GHS attack 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. Elliptic curve cryptography Weil descent Isogenies Teske, Edlyn aut Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 16(2005), 6 vom: 17. Nov., Seite 439-460 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:16 year:2005 number:6 day:17 month:11 pages:439-460 https://doi.org/10.1007/s00200-005-0186-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_100 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4324 AR 16 2005 6 17 11 439-460 |
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10.1007/s00200-005-0186-8 doi (DE-627)OLC2075497222 (DE-He213)s00200-005-0186-8-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Menezes, Alfred verfasserin aut Cryptographic implications of Hess' generalized GHS attack 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. Elliptic curve cryptography Weil descent Isogenies Teske, Edlyn aut Enthalten in Applicable algebra in engineering, communication and computing Springer-Verlag, 1990 16(2005), 6 vom: 17. Nov., Seite 439-460 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:16 year:2005 number:6 day:17 month:11 pages:439-460 https://doi.org/10.1007/s00200-005-0186-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_100 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4324 AR 16 2005 6 17 11 439-460 |
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Enthalten in Applicable algebra in engineering, communication and computing 16(2005), 6 vom: 17. Nov., Seite 439-460 volume:16 year:2005 number:6 day:17 month:11 pages:439-460 |
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Enthalten in Applicable algebra in engineering, communication and computing 16(2005), 6 vom: 17. Nov., Seite 439-460 volume:16 year:2005 number:6 day:17 month:11 pages:439-460 |
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Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. © Springer-Verlag Berlin Heidelberg 2005 |
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Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. © Springer-Verlag Berlin Heidelberg 2005 |
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Abstract A finite field K is said to be weak for elliptic curve cryptography if all instances of the discrete logarithm problem for all elliptic curves over K can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. By considering the GHS Weil descent attack, it was previously shown that characteristic two finite fields are weak. In this paper, we examine characteristic two finite fields for weakness under Hess' generalization of the GHS attack. We show that the fields are potentially partially weak in the sense that any instance of the discrete logarithm problem for half of all elliptic curves over , namely those curves E for which is divisible by 4, can likely be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We also show that the fields are partially weak, that the fields are potentially weak, and that the fields are potentially partially weak. Finally, we argue that the other fields where N is not divisible by 3, 5, 6, 7 or 8, are not weak under Hess' generalized GHS attack. © Springer-Verlag Berlin Heidelberg 2005 |
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