An optimally secure relativized cryptosystem

V. K. Zadiraka, Антон Михайлович Кудін, I. A. Kudin +1 more

The problem of assessing the stability of cryptographic transformations in modern cryptography, which is usually implemented using an axiomatic or proof-based approach, is considered. Since the quantum computing model changes the complexity of certain computational problems (for example, integer factorization problems), cryptography studies classes of algorithms that will remain stable in the quantum computing model—the so-called “post-quantum cryptographic algorithms.” A generalization of this problem statement is the study of computational models containing cryptanalysis algorithms, the best of which has exponential complexity or complexity close to it. The generalization of the problem of the existence of cryptosystems that are secure in the post-quantum world, namely, cryptosystems that are secure in certain computational models, as well as the possibility of practical application of such models, is considered. The main result of the work is the creation of a universal computational model that generalizes a whole class of promising computational models, including quantum ones, and the construction of a cryptosystem that is stable within such a computational model. Keywords: post-quantum cryptography, relativized cryptography, computing models, genetic algorithms, reversible computing, blockchain.

Mordechai M. Yung

Yong Wang

Yu‐Fang Chung, Zhen Yu Wu, Feipei Lai +1 more

Most cryptographic works these days have employed mathematical concepts to design cryptosystems and algorithms.Therefore, mathematical concepts have become critical in the designing of cryptosystems, and are generally used to analyze cryptosystems and protocols, supporting the allegation that the intended cryptosystem is secure.In earlier cryptosystems, most algorithms were based on either factorization or discrete logarithm problem.This system has an overtly simple mathematical background and so, requires extensive secondary index computation.Therefore, a securer method must be developed to protect system security and to optimize system efficiency.Quantum cryptography detects intrusion and wiretapping.In quantum mechanics, a wiretap is not external or passive, but the opposite-changing its entity according to the internal component of the system.The status of the system changes once a wiretap is detected.Therefore, only the designer of the system can determine the quantum status of the system; eavesdroppers can neither determine the quantum status nor duplicate the system.Since quantum cryptosystem can reach unconditional security, it actually guarantees secure communication.Accordingly, this study examines quantum cryptography and contributes to secure quantum cryptography.

Abhishek Parakh

Over the past four decades, computational power and algorithmic strategies have advanced tremendously resulting in an enormous increase in the key sizes required for secure cryptosystems such as RSA. At the same time, the electronic devices have grown smaller and portable requiring algorithms running on them to be optimized in size and efficiency while providing security, at least, equivalent to that provided on a typical desktop computer. As a result, the industry is moving towards newer cryptosystems such as ECC and NTRU that are well suited for resource constrained environments. While, ECC claims to provide security equivalent to that of RSA for a fraction of key size, NTRU is inherently suited for embedded systems technology. However, implementation of new cryptosystems requires the development of protocols analogous to those developed using older cryptosystems. In this thesis, we fulfill a part of this requirement by providing protocols for Oblivious Transfer using ECC and NTRU. Oblivious Transfer, in turn, has applications in simultaneous contract signing, digital certified mail, simultaneous exchange of secrets, secure multiparty computations, private information retrieval, etc. Furthermore, we introduce the idea of basing Oblivious Transfer on public-key exchange protocols. The presentation in the thesis uses Diffie-Hellman Key Exchange, but the scheme is generalizable to any cryptosystem that has a public-key exchange strategy. In fact, our proposal may especially be suited for Quantum Cryptography where the security of key exchange protocols has been proven.

Stefan Wolf