### 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 n ^{2}, 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 |
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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 |

Publication status | Published - Dec 1 2004 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*3348*, 245-259.