This paper briefly deals with a wide range of topics in information-theoretic cryptography. First, we focus on the results on symmetric-key encryption and authentication codes, since these protocols are fundamental in the field and well studied in the frameworks by Shannon and Simmons, respectively. Secondly, we explain several existing assumptions and security criteria whose merit mainly lies in realizing cryptographic protocols with short/weak shared secret-keys, correlated weak secret-keys, or no shared secrets. Thirdly, we consider research themes by three aspects for further development of information-theoretic cryptography. Finally, we refer to trends of technical approaches in information-theoretic cryptography and explain our recent results brought by using the approach.
This paper briefly deals with a wide range of topics in information-theoretic cryptography. First, we focus on the results on symmetric-key encryption and authentication codes, since these protocols are fundamental in the field and well studied in the frameworks by Shannon and Simmons, respectively. Secondly, we explain several existing assumptions and security criteria whose merit mainly lies in realizing cryptographic protocols with short/weak shared secret-keys, correlated weak secret-keys, or no shared secrets. Thirdly, we consider research themes by three aspects for further development of information-theoretic cryptography. Finally, we refer to trends of technical approaches in information-theoretic cryptography and explain our recent results brought by using the approach.
This book offers a mathematical foundation for modern cryptography. It is primarily intended as an introduction for graduate students. Readers should have basic knowledge of probability theory, but familiarity with computational complexity is not required. Starting from Shannon's classic result on secret key cryptography, fundamental topics of cryptography, such as secret key agreement, authentication, secret sharing, and secure computation, are covered. Particular attention is drawn to how correlated randomness can be used to construct cryptographic primitives. To evaluate the efficiency of such constructions, information-theoretic tools, such as smooth min/max entropies and information spectrum, are developed. The broad coverage means the book will also be useful to experts as well as students in cryptography as a reference for information-theoretic concepts and tools.
This paper analyzes the formalizations of information-theoretic security for the fundamental primitives in cryptography: symmetric-key encryption and key agreement. Revisiting the previous results, we can formalize information-theoretic security using different methods, by extending Shannon's perfect secrecy, by information-theoretic analogues of indistinguishability and semantic security, and by the frameworks for composability of protocols. We show the relationships among the security formalizations and obtain the following results. First, in the case of encryption, there are significant gaps among the formalizations, and a certain type of relaxed perfect secrecy or a variant of information-theoretic indistinguishability is the strongest notion. Second, in the case of key agreement, there are significant gaps among the formalizations, and a certain type of relaxed perfect secrecy is the strongest notion. In particular, in both encryption and key agreement, the formalization of composable security is not stronger than any other formalizations. Furthermore, as an application of the relationships in encryption and key agreement, we simultaneously derive a family of lower bounds on the size of secret keys and security quantities required under the above formalizations, which also implies the importance and usefulness of the relationships.
Abstract. In this paper, information theoretic cryptography is discussed based on conditional Rényi entropies. Our discussion focuses not only on cryptography but also on the definitions of conditional Rényi entropies and the related information theoretic inequalities. First, we revisit conditional Rényi entropies, and clarify what kind of properties are required and actually satisfied. Then, we propose security criteria based on Rényi entropies, which suggests us deep relations between (conditional) Rényi entropies and error probabilities by using several guessing strategies. Based on these results, unified proof of impossibility, namely, the lower bounds of key sizes is derived based on conditional Rényi entropies. Our model and lower bounds include the Shannon’s perfect secrecy, and the minentropy based encryption presented by Dodis, and Alimomeni and Safavi-Naini. Finally, new optimal symmetric key cryptography and almost optimal secret sharing schemes are proposed which achieve our lower bounds.
Abstract: Cryptography is the science of keeping private information from unauthorized access of ensuring data integrity and authentication, and it is the strongest tool for controlling against much kind of security threats. Role of cryptography appears in many secured area like government agencies, large banks, telecommunications companies and other corporations who handle sensitive or military data. Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. This paper consists of the main aspects of quantum cryptography and it investigates the information about where and all quantum cryptography takes place. Keywords- cryptography; photons; quantum key distribution; Protocols; I.
The security of classical cryptography based on computational complexity assumptions has been severely challenged with the rapid development of quantum computers and quantum algorithms. Quantum cryptography, which offers unconditional security based on some principles of quantum mechanics, has become a significant branch and hotspot in the field of modern cryptography research. In this paper, we review the research and development of several important and well-studied branches of quantum cryptography in terms of theory and experiment, including quantum key distribution, quantum secret sharing, quantum secure direct communication, quantum signature, and quantum private query. We also briefly review the research and development of some other branches which are currently in the stage of theoretical research but receive widespread concern from academia, including quantum private comparison, quantum anonymous voting, quantum secure multi-party summation, quantum sealed-bid auction, quantum public key cryptosystem, quantum key agreement, quantum dialogue, and quantum identity authentication. In addition, we discuss some open issues and future research directions for the branches referred to above.
Introduction/purpose: The problem of efficient distribution of cryptographic keys in communication systems has existed since its first days and is especially emphasized by the emergence of mass communication systems. Defining and implementing efficient protocols for symmetric cryptographic keys establishment in such circumstances is of great importance in raising information security in cyberspace. Methods: Using the methods of Information Theory and Secure Multiparty Computation, protocols for direct establishment of cryptographic keys between communication parties have been defined. Results: The paper defines two new approaches to the problem of establishing cryptographic keys. The novelty in the protocol defined in the security model based on information theory is based on the source of common randomness, which in this case is the EEG signal of each subject participating in the communication system. Experimental results show that the amount of information leaking to the attacker is close to zero. A novelty in the second case, which provides security with keys at the level of computer security by applying Secure Multiparty Computation, is in the new application field, namely generation and distribution of symmetric cryptographic keys. It is characteristic of both approaches that within the framework of formal theories, it is possible to draw conclusions about their security characteristics in a formal way. Conclusions: The paper describes two new approaches for establishing cryptographic keys in symmetric cryptographic systems with experimental results. The significance of the proposed solutions lies in the fact that they enable the establishment of secure communication between communication parties from end to end, avoiding the influence of a trusted third party. In that way, the achieved communication level security significantly increases in relation to classical cryptographic systems.