# Secure public-key encryption from factorisation-related problems

Brown, Jaimee
(2007)
*Secure public-key encryption from factorisation-related problems.*
PhD
thesis,
Queensland University of Technology.

## Abstract

Public key encryption plays a vital role in securing sensitive data in practical

applications. The security of many encryption schemes relies on mathematical

problems related to the difficulty of factoring large integers. In particular,

subgroup problems in composite order groups are a general class of problems

widely used in the construction of secure public-key encryption schemes. This

thesis studies public-key encryption schemes that are provably secure based on

the difficulty of subgroup or other integer factorisation related problems in the

standard model.

Firstly, a number of new public-key encryption schemes are presented which

are secure in the sense of indistinguishability against chosen-ciphertext attack

in the standard model. These schemes are obtained by instantiating the two

previous paradigms for chosen-ciphertext security by Cramer and Shoup, and

Kurosawa and Desmedt, with three previously studied subgroup membership

problems. The resulting schemes are very efficient, and are comparable if not

superior in terms of efficiency when compared to previously presented instantiations.

Secondly, a new approach is presented for constructing RSA-related public

key encryption schemes secure in the sense of indistinguishability against chosenciphertext

attack without random oracles. This new approach requires a new

set of assumptions, called the Oracle RSA-type assumptions. The motivating

observation is that RSA-based encryption schemes can be viewed as tag-based

encryption schemes, and as a result can be used as a building block in a previous

technique for obtaining chosen-ciphertext security. Two example encryption

schemes are additionally presented, each of which is of comparable efficiency to

other public key schemes of similar security.

Finally, the notion of self-escrowed public-key infrastructures is revisited,

and a security model is defined for self-escrowed encryption schemes. The security definitions proposed consider adversarial models which reflect an attacker's

ability to recover private keys corresponding to public keys of the attacker's

choice. General constructions for secure self-escrowed versions of ElGamal, RSA,

Cramer-Shoup and Kurosawa-Desmedt encryption schemes are also presented,

and efficient instantiations are provided. In particular, one instantiation solves

the 'key doubling problem' observed in all previous self-escrowed encryption

schemes. Also, for another instantiation a mechanism is described for distributing

key recovery amongst a number of authorities.

Impact and interest:

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ID Code: | 16386 |
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Item Type: | QUT Thesis (PhD) |

Supervisor: | Gonzalez Nieto, Juan, Boyd, Colin, Dawson, Edward, & Montague, Paul |

Keywords: | public key encryption, subgroup membership problems, provable security, chosenciphertext security, Cramer-Shoup, RSA, self-escrowed encryption, key recovery |

Divisions: | Current > QUT Faculties and Divisions > Division of Research and Commercialisation Past > Institutes > Information Security Institute |

Department: | Cross-Faculty Collaboration |

Institution: | Queensland University of Technology |

Copyright Owner: | Copyright Jaimee Brown |

Deposited On: | 03 Dec 2008 04:02 |

Last Modified: | 28 Oct 2011 19:47 |

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