Constructing hash function from plaintext to Huff curves

YU Wei; WANG Kunpeng; LI Bao

doi:10.3969/j.issn.0253-2778.2014.10.006

JUSTC > 2014 > 44(10): 835-838. > DOI: 10.3969/j.issn.0253-2778.2014.10.006 CSTR: 32290.14.j.issn.0253-2778.2014.10.006

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Open Access JUSTC Original Paper

Constructing hash function from plaintext to Huff curves

1.
Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China
2.
Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230027, China

Cite this: JUSTC, 2014, 44(10): 835-838

https://doi.org/10.3969/j.issn.0253-2778.2014.10.006

CSTR: 32290.14.j.issn.0253-2778.2014.10.006

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Received Date: September 09, 2013
Revised Date: April 30, 2014
Accepted Date: April 30, 2014
Published Date: October 29, 2014

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Abstract

Abstract

A deterministic function with its time complexity being O(log3q) was constructed for the first time from a finite field Fq to Huff curves. Based on this function, construct a hash function from plaintext into Huff curves. The Hash function laid the foundation for identity-based protocols on elliptic curves and its experimental time cost on the elliptic curve of the Chinese elliptic curve standard SM2 is 5578 μs.

Abstract

A deterministic function with its time complexity being O(log3q) was constructed for the first time from a finite field Fq to Huff curves. Based on this function, construct a hash function from plaintext into Huff curves. The Hash function laid the foundation for identity-based protocols on elliptic curves and its experimental time cost on the elliptic curve of the Chinese elliptic curve standard SM2 is 5578 μs.

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References (21)

References

[1]	Koblitz N. Elliptic curve cryptosystems[J]. Mathematics of Computation, 1987, 48(177):203-209.
[2]	Miller V S. Uses of elliptic curves in cryptography[C]// Proceedings of Advances in Cryptology-CRYPTO85. Santa Barbara, USA: Springer, 1986:417-428.
[3]	Joye M, Tibouchi M, Vergnaud D. Huffs model for elliptic curves[C]// Lecture Notes in Computer Science. Brussels, Belgium: Springer-Verlag, 2010, 6234: 234-250.
[4]	Devigne J, Joye M. Binary Huff curves[C]// Lecture Notes in Computer Science, CT-RSA. San Francisco, USA: Springer, 2011, 6558: 340-355.
[5]	Elmegaard-Fessel L. Efficient scalar multiplication and security against power analysis in cryptosystemsbased on the nist elliptic curves over prime fields[EB/OL]. http://eprint.iacr.org/2006/313.
[6]	Wu H F, Feng R Q. Elliptic curves in Huffs model[J]. Wuhan University Journal of Natural Sciences, 2012, 17(6): 473-480.
[7]	Boneh D, Franklin M K. Identity-based encryption from the Weil pairing[C]// 21st Annual International Cryptology Conference. Santa Barbara, USA: Springer, 2001, 2139: 213-229.
[8]	Horwitz J, Lynn B. Toward hierarchical identity-based encryption[C]// Lecture Notes in Computer Science, Amsterdam, Netherlands: Springer, 2002, 2332: 466-481.
[9]	Boneh D, Gentry C, Lynn B, et al. Aggregate and verifiably encrypted signatures from bilinear maps[C]// International Conference on the Theory and Applications of Cryptographic Techniques. Warsaw, Poland: Springer, 2003, 2656: 416-432.
[10]	Cha J C, Cheon J H. An identity-based signature from gap Diffie-Hellman groups[C]// Proceedings of 6th International Workshop on Practice and Theory in Public Key Cryptography. Miami, USA: Springer, 2003, 2567: 18-30.
[11]	Zhang F G, Kim K. Id-based blind signature and ring signature from pairings[C]// Proceedings of 8th International Conference on the Theory and Application of Cryptology and Information Security. Queenstown, New Zealand: Springer, 2002: 533-547.
[12]	Boyen X. Multipurpose identity-based signcryption: A Swiss army knife for identity-based cryptography[C]// Proceedings of the 23rd International Conference on Advances in Cryptology. Santa Barbara, USA: Springer, 2003: 383-399.
[13]	Libert B, Quisquater J J. Efficient signcryption with key privacy from gap Diffie-Hellman groups[C]// Proceedings of 7th International Workshop on Theory and Practice in Public Key Cryptography. Singapore: Springer, 2004: 187-200.
[14]	Lindell Y. Highly-efficient universally-composable commitments based on the DDH assumption[C]// 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques. Tallinn, Estonia: Springer, 2011: 446-466.
[15]	Shallue A, van de Woestijne C E. Construction of rational points on elliptic curves over finite fields[C]// Proceedings of 7th International Symposium. Berlin, Germany: Springer, 2006: 510-524.
[16]	Icart T. How to hash into elliptic curves[C]// 29th Annual International Cryptology Conference. Santa Barbara, USA: Springer, 2009: 303-316.
[17]	Brier E, Coron J S, Icart T, et al. Efficient indifferentiable hashing into ordinary elliptic curves[C]// Proceedings of 30th Annual Cryptology Conference. Santa Barbara, USA: Springer, 2010: 237-254.
[18]	Farashahi R R, Fouque P A, Shparlinski I E, et al. Indifferentiable deterministic hashing to elliptic and hyperelliptic curves[J]. Mathematics of Computation, 2013, 82(281): 491-512.
[19]	Farashahi R R. Hashing into Hessian curves[C]// Lecture Notes in Computer Science. Dakar, Senegal: Springer, 2011: 278-289.
[20]	Yu W, Wang K, Li B, et al. About hash into Montgomery form elliptic curves[C]// Proceedings of the 9th International Conference on Information Security Practice and Experience. Lanzhou, China: Springer, 2013: 147-159.
[21]	Shoup V. A new polynomial factorization algorithm and its implementation[J]. Journal of Symbolic Computation, 1995, 20(4): 363-397.

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References

[1]	Koblitz N. Elliptic curve cryptosystems[J]. Mathematics of Computation, 1987, 48(177):203-209.
[2]	Miller V S. Uses of elliptic curves in cryptography[C]// Proceedings of Advances in Cryptology-CRYPTO85. Santa Barbara, USA: Springer, 1986:417-428.
[3]	Joye M, Tibouchi M, Vergnaud D. Huffs model for elliptic curves[C]// Lecture Notes in Computer Science. Brussels, Belgium: Springer-Verlag, 2010, 6234: 234-250.
[4]	Devigne J, Joye M. Binary Huff curves[C]// Lecture Notes in Computer Science, CT-RSA. San Francisco, USA: Springer, 2011, 6558: 340-355.
[5]	Elmegaard-Fessel L. Efficient scalar multiplication and security against power analysis in cryptosystemsbased on the nist elliptic curves over prime fields[EB/OL]. http://eprint.iacr.org/2006/313.
[6]	Wu H F, Feng R Q. Elliptic curves in Huffs model[J]. Wuhan University Journal of Natural Sciences, 2012, 17(6): 473-480.
[7]	Boneh D, Franklin M K. Identity-based encryption from the Weil pairing[C]// 21st Annual International Cryptology Conference. Santa Barbara, USA: Springer, 2001, 2139: 213-229.
[8]	Horwitz J, Lynn B. Toward hierarchical identity-based encryption[C]// Lecture Notes in Computer Science, Amsterdam, Netherlands: Springer, 2002, 2332: 466-481.
[9]	Boneh D, Gentry C, Lynn B, et al. Aggregate and verifiably encrypted signatures from bilinear maps[C]// International Conference on the Theory and Applications of Cryptographic Techniques. Warsaw, Poland: Springer, 2003, 2656: 416-432.
[10]	Cha J C, Cheon J H. An identity-based signature from gap Diffie-Hellman groups[C]// Proceedings of 6th International Workshop on Practice and Theory in Public Key Cryptography. Miami, USA: Springer, 2003, 2567: 18-30.
[11]	Zhang F G, Kim K. Id-based blind signature and ring signature from pairings[C]// Proceedings of 8th International Conference on the Theory and Application of Cryptology and Information Security. Queenstown, New Zealand: Springer, 2002: 533-547.
[12]	Boyen X. Multipurpose identity-based signcryption: A Swiss army knife for identity-based cryptography[C]// Proceedings of the 23rd International Conference on Advances in Cryptology. Santa Barbara, USA: Springer, 2003: 383-399.
[13]	Libert B, Quisquater J J. Efficient signcryption with key privacy from gap Diffie-Hellman groups[C]// Proceedings of 7th International Workshop on Theory and Practice in Public Key Cryptography. Singapore: Springer, 2004: 187-200.
[14]	Lindell Y. Highly-efficient universally-composable commitments based on the DDH assumption[C]// 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques. Tallinn, Estonia: Springer, 2011: 446-466.
[15]	Shallue A, van de Woestijne C E. Construction of rational points on elliptic curves over finite fields[C]// Proceedings of 7th International Symposium. Berlin, Germany: Springer, 2006: 510-524.
[16]	Icart T. How to hash into elliptic curves[C]// 29th Annual International Cryptology Conference. Santa Barbara, USA: Springer, 2009: 303-316.
[17]	Brier E, Coron J S, Icart T, et al. Efficient indifferentiable hashing into ordinary elliptic curves[C]// Proceedings of 30th Annual Cryptology Conference. Santa Barbara, USA: Springer, 2010: 237-254.
[18]	Farashahi R R, Fouque P A, Shparlinski I E, et al. Indifferentiable deterministic hashing to elliptic and hyperelliptic curves[J]. Mathematics of Computation, 2013, 82(281): 491-512.
[19]	Farashahi R R. Hashing into Hessian curves[C]// Lecture Notes in Computer Science. Dakar, Senegal: Springer, 2011: 278-289.
[20]	Yu W, Wang K, Li B, et al. About hash into Montgomery form elliptic curves[C]// Proceedings of the 9th International Conference on Information Security Practice and Experience. Lanzhou, China: Springer, 2013: 147-159.
[21]	Shoup V. A new polynomial factorization algorithm and its implementation[J]. Journal of Symbolic Computation, 1995, 20(4): 363-397.

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