Secure publickey encryption from factorisationrelated problems
Brown, Jaimee (2007) Secure publickey encryption from factorisationrelated problems. PhD thesis, Queensland University of Technology.

Jaimee Brown Thesis (PDF 1MB) 
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 publickey encryption schemes. This
thesis studies publickey 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 publickey encryption schemes are presented which
are secure in the sense of indistinguishability against chosenciphertext attack
in the standard model. These schemes are obtained by instantiating the two
previous paradigms for chosenciphertext 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 RSArelated 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 RSAtype assumptions. The motivating
observation is that RSAbased encryption schemes can be viewed as tagbased
encryption schemes, and as a result can be used as a building block in a previous
technique for obtaining chosenciphertext 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 selfescrowed publickey infrastructures is revisited,
and a security model is defined for selfescrowed 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 selfescrowed versions of ElGamal, RSA,
CramerShoup and KurosawaDesmedt encryption schemes are also presented,
and efficient instantiations are provided. In particular, one instantiation solves
the 'key doubling problem' observed in all previous selfescrowed encryption
schemes. Also, for another instantiation a mechanism is described for distributing
key recovery amongst a number of authorities.
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ID Code:  16386 

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, CramerShoup, RSA, selfescrowed encryption, key recovery 
Divisions:  Current > QUT Faculties and Divisions > Division of Research and Commercialisation Past > Institutes > Information Security Institute 
Department:  CrossFaculty 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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