On provable security of some public key encryption schemes


Thesis Type: Doctorate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Turkey

Approval Date: 2012

Student: TURGUT HANOYMAK

Supervisor: ERSAN AKYILDIZ

Abstract:

In this thesis, we analyse the security criteria of some public key encryption schemes. In this respect, we present the notion of adversarial goals and adversarial capabilities. We give the definition of provably security by means of several games between the challenger and the adversary in some security models, namely the standard model and the random oracle model. We state the main differences between these two models and observe the advantage of the success probability of the adversary in breaking the cryptographic schemes. We search the ways of making more efficient and provably secure encryption schemes under weak assumptions. In this context, we examine the constructions of some public key encryption schemes such as RSA, ElGamal, Cramer-Shoup, Paillier, Damgard and finally Zheng-Seberry schemes and discuss under which circumstances they satisfy which security notions. Finally, we modify one of the schemes proposed by Zheng-Seberry -which is based on ElGamal signature- by adapting Schnorr signature in order to enhance the efficiency and give a rigorous proof of security in the random oracle model.