A provably secure elliptic curve scheme with fast encryption

David Galindo; Sebastià Martín; Tsuyoshi Takagi; Jorge L. Villar

doi:10.1007/978-3-540-30556-9_20

A provably secure elliptic curve scheme with fast encryption

David Galindo, Sebastià Martín, Tsuyoshi Takagi, Jorge L. Villar

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We present a new elliptic curve cryptosystem with fast encryption and key generation, which is provably secure against passive adversaries in the standard model. The scheme uses arithmetic modulo n², where n is an USA modulus, and merges ideas from Paillier and Rabin related schemes. Despite the typical bit length of n, our encryption algorithm is the fastest elliptic curve based encryption algorithm to the best of our knowledge, even faster than El Gamal elliptic curve encryption. The one-wayness (OW-CPA) of the new cryptosystem is as hard as factoring n while the semantic security (IND-CPA) is proved under a reasonable decisional assumption. Two new length-preserving trapdoor permutations equivalent to factoring are also described. κ Springer-Verlag 2004.

Original language	English
Pages (from-to)	245-259
Number of pages	15
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3348
DOIs	https://doi.org/10.1007/978-3-540-30556-9_20
Publication status	Published - 2004

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-540-30556-9_20

Cite this

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title = "A provably secure elliptic curve scheme with fast encryption",

abstract = "We present a new elliptic curve cryptosystem with fast encryption and key generation, which is provably secure against passive adversaries in the standard model. The scheme uses arithmetic modulo n2, where n is an USA modulus, and merges ideas from Paillier and Rabin related schemes. Despite the typical bit length of n, our encryption algorithm is the fastest elliptic curve based encryption algorithm to the best of our knowledge, even faster than El Gamal elliptic curve encryption. The one-wayness (OW-CPA) of the new cryptosystem is as hard as factoring n while the semantic security (IND-CPA) is proved under a reasonable decisional assumption. Two new length-preserving trapdoor permutations equivalent to factoring are also described. κ Springer-Verlag 2004.",

author = "David Galindo and Sebasti{\`a} Mart{\'i}n and Tsuyoshi Takagi and Villar, {Jorge L.}",

note = "Funding Information: This work was partially supported by Sapanish Ministerio de Ciencia y Tecnolog{\'a} under project TSC 2003-008660. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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AU - Galindo, David

AU - Martín, Sebastià

AU - Takagi, Tsuyoshi

AU - Villar, Jorge L.

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AB - We present a new elliptic curve cryptosystem with fast encryption and key generation, which is provably secure against passive adversaries in the standard model. The scheme uses arithmetic modulo n2, where n is an USA modulus, and merges ideas from Paillier and Rabin related schemes. Despite the typical bit length of n, our encryption algorithm is the fastest elliptic curve based encryption algorithm to the best of our knowledge, even faster than El Gamal elliptic curve encryption. The one-wayness (OW-CPA) of the new cryptosystem is as hard as factoring n while the semantic security (IND-CPA) is proved under a reasonable decisional assumption. Two new length-preserving trapdoor permutations equivalent to factoring are also described. κ Springer-Verlag 2004.

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A provably secure elliptic curve scheme with fast encryption

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