Efficient indifferentiable hashing into ordinary elliptic curves

Eric Brier; Jean Sébastien Coron; Thomas Icart; David Madore; Hugues Randriam; Mehdi Tibouchi

doi:10.1007/978-3-642-14623-7_13

Efficient indifferentiable hashing into ordinary elliptic curves

Eric Brier, Jean Sébastien Coron, Thomas Icart, David Madore, Hugues Randriam, Mehdi Tibouchi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart's deterministic encoding from Crypto 2009. While almost as efficient as Icart's encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model. We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.

Original language	English
Title of host publication	Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings
Pages	237-254
Number of pages	18
DOIs	https://doi.org/10.1007/978-3-642-14623-7_13
Publication status	Published - 29 Sept 2010
Externally published	Yes
Event	30th Annual International Cryptology Conference, CRYPTO 2010 - Santa Barbara, CA, United States Duration: 15 Aug 2010 → 19 Aug 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6223 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	30th Annual International Cryptology Conference, CRYPTO 2010
Country/Territory	United States
City	Santa Barbara, CA
Period	15/08/10 → 19/08/10

Access to Document

10.1007/978-3-642-14623-7_13

Cite this

Brier, E., Coron, J. S., Icart, T., Madore, D., Randriam, H., & Tibouchi, M. (2010). Efficient indifferentiable hashing into ordinary elliptic curves. In Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings (pp. 237-254). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6223 LNCS). https://doi.org/10.1007/978-3-642-14623-7_13

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title = "Efficient indifferentiable hashing into ordinary elliptic curves",

abstract = "We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart's deterministic encoding from Crypto 2009. While almost as efficient as Icart's encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model. We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.",

author = "Eric Brier and Coron, \{Jean S{\'e}bastien\} and Thomas Icart and David Madore and Hugues Randriam and Mehdi Tibouchi",

year = "2010",

month = sep,

day = "29",

doi = "10.1007/978-3-642-14623-7\_13",

language = "English",

isbn = "3642146228",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "237--254",

booktitle = "Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings",

note = "30th Annual International Cryptology Conference, CRYPTO 2010 ; Conference date: 15-08-2010 Through 19-08-2010",

}

Brier, E, Coron, JS, Icart, T, Madore, D, Randriam, H & Tibouchi, M 2010, Efficient indifferentiable hashing into ordinary elliptic curves. in Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6223 LNCS, pp. 237-254, 30th Annual International Cryptology Conference, CRYPTO 2010, Santa Barbara, CA, United States, 15/08/10. https://doi.org/10.1007/978-3-642-14623-7_13

Efficient indifferentiable hashing into ordinary elliptic curves. / Brier, Eric; Coron, Jean Sébastien; Icart, Thomas et al.
Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings. 2010. p. 237-254 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6223 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Efficient indifferentiable hashing into ordinary elliptic curves

AU - Brier, Eric

AU - Coron, Jean Sébastien

AU - Icart, Thomas

AU - Madore, David

AU - Randriam, Hugues

AU - Tibouchi, Mehdi

PY - 2010/9/29

Y1 - 2010/9/29

N2 - We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart's deterministic encoding from Crypto 2009. While almost as efficient as Icart's encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model. We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.

AB - We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart's deterministic encoding from Crypto 2009. While almost as efficient as Icart's encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model. We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.

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DO - 10.1007/978-3-642-14623-7_13

M3 - Conference contribution

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SN - 9783642146220

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings

T2 - 30th Annual International Cryptology Conference, CRYPTO 2010

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ER -

Brier E, Coron JS, Icart T, Madore D, Randriam H, Tibouchi M. Efficient indifferentiable hashing into ordinary elliptic curves. In Advances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings. 2010. p. 237-254. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-14623-7_13

Efficient indifferentiable hashing into ordinary elliptic curves

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