Families of genus 2 curves with small embedding degree
In cryptographic applications, hyperelliptic curves of small genus have the advantage of providing a group of comparable size to that of elliptic curves, while working over a field of smaller size. Pairing-friendly hyperelliptic curves are those for which the order of the Jacobian is divisible by a...
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| Format: | Article |
| Language: | English |
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De Gruyter
2009-05-01
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| Series: | Journal of Mathematical Cryptology |
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| Online Access: | https://doi.org/10.1515/JMC.2009.002 |
| _version_ | 1811279407221833728 |
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| author | Hitt Laura |
| author_facet | Hitt Laura |
| author_sort | Hitt Laura |
| collection | DOAJ |
| description | In cryptographic applications, hyperelliptic curves of small genus have the advantage of providing a group of comparable size to that of elliptic curves, while working over a field of smaller size. Pairing-friendly hyperelliptic curves are those for which the order of the Jacobian is divisible by a large prime, whose embedding degree is small enough for pairing computations to be feasible, and whose minimal embedding field is large enough for the discrete logarithm problem in it to be difficult. We give a sequence of 𝔽q-isogeny classes for a family of Jacobians of genus 2 curves over 𝔽q, for q = 2m, and the corresponding small embedding degrees. We give examples of the parameters for such curves with embedding degree k < (log q)2, such as k = 8, 13, 16, 23, 26. |
| first_indexed | 2024-04-13T00:54:07Z |
| format | Article |
| id | doaj.art-290fceaf444742b086db29a9c380f55f |
| institution | Directory Open Access Journal |
| issn | 1862-2976 1862-2984 |
| language | English |
| last_indexed | 2024-04-13T00:54:07Z |
| publishDate | 2009-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Mathematical Cryptology |
| spelling | doaj.art-290fceaf444742b086db29a9c380f55f2022-12-22T03:09:45ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842009-05-0131193610.1515/JMC.2009.002Families of genus 2 curves with small embedding degreeHitt Laura0321 Abbey Drive, Austin, TX 78737, USA. Email: hitt36@gmail.comIn cryptographic applications, hyperelliptic curves of small genus have the advantage of providing a group of comparable size to that of elliptic curves, while working over a field of smaller size. Pairing-friendly hyperelliptic curves are those for which the order of the Jacobian is divisible by a large prime, whose embedding degree is small enough for pairing computations to be feasible, and whose minimal embedding field is large enough for the discrete logarithm problem in it to be difficult. We give a sequence of 𝔽q-isogeny classes for a family of Jacobians of genus 2 curves over 𝔽q, for q = 2m, and the corresponding small embedding degrees. We give examples of the parameters for such curves with embedding degree k < (log q)2, such as k = 8, 13, 16, 23, 26.https://doi.org/10.1515/JMC.2009.002embedding degreegenus 2hyperelliptic curvesbinary curvespairing-based cryptography |
| spellingShingle | Hitt Laura Families of genus 2 curves with small embedding degree Journal of Mathematical Cryptology embedding degree genus 2 hyperelliptic curves binary curves pairing-based cryptography |
| title | Families of genus 2 curves with small embedding degree |
| title_full | Families of genus 2 curves with small embedding degree |
| title_fullStr | Families of genus 2 curves with small embedding degree |
| title_full_unstemmed | Families of genus 2 curves with small embedding degree |
| title_short | Families of genus 2 curves with small embedding degree |
| title_sort | families of genus 2 curves with small embedding degree |
| topic | embedding degree genus 2 hyperelliptic curves binary curves pairing-based cryptography |
| url | https://doi.org/10.1515/JMC.2009.002 |
| work_keys_str_mv | AT hittlaura familiesofgenus2curveswithsmallembeddingdegree |