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.
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
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.
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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
|Institution:||Queensland University of Technology|
|Copyright Owner:||Copyright Jaimee Brown|
|Deposited On:||03 Dec 2008 14:02|
|Last Modified:||29 Oct 2011 05:47|
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