arXiv:1410.1120 · IEEE Transactions on Information Theory

Security Formalizations and Their Relationships for Encryption and Key Agreement in Information-Theoretic Cryptography

Mitsugu Iwamoto, Kazuo Ohta, Junji Shikata

Published Aug 28, 2017• 29 citations

Abstract

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.

DOI: 10.1109/tit.2017.2744650

Related papers

Formalization of information-theoretic security for key agreement, revisited

Junji Shikata

In this paper, we investigate relationships between the following formalizations of information-theoretic security for key agreement protocols which may have agreement-errors: formalizations extended (or relaxed) from Shannon's perfect secrecy by using mutual information and statistical distance; and the ones of composable security by Maurer et al. and Canetti. Then, we explicitly show that those are essentially equivalent. We also derive lower bounds on the adversary's (or distinguisher's) advantage and the size of a correlated randomness resource required under all of the above formalizations at once through our relationships. In addition, we observe impossibility results which easily follow from the lower bounds.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20137 citations

Information Theoretic Security for Encryption Based on Conditional Renyi Entropies.

Mitsugu Iwamoto, Junji Shikata

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.

Jan 1, 20130 citations

Information-theoretically secure key-insulated key-agreement

Takenobu Seito, Junji Shikata

In this paper, we study key-agreement which realizes the protection against key-exposure problems in the information-theoretic security setting. And we newly define a model and security notions for information-theoretically secure key-insulated key-agreement (KI-KA for short). In addition, we show tight lower bounds of sizes of entities' secret-keys required for KI-KA. We also propose constructions of KI-KA which are provably secure and optimal. Furthermore, we provide some applications of KI-KA.

IEEE Information Theory Workshop (ITW)Oct 1, 20113 citations

Trends and Development of Information-Theoretic Cryptography

Junji Shikata

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.

IEICE Transactions on Fundamentals of Electronics Communications and Computer SciencesJan 1, 20150 citations

Contributions to Information Theoretically Secure Communication

Setareh Sharifian

Secure communication ensures the integrity and confidentiality of communication between connected devices. An information-theoretic approach to secure communication gives the strongest confidentiality guarantee by assuming that the attacker has unlimited computing power. The earliest formal model and definition of information-theoretic secure communication is by Shannon, who employed a secret key shared between communicating parties to provide confidentiality. An alternative elegant information-theoretic approach to secure communication views the natural characteristics of the environment (i.e., channel’s noise) as a resource to build security functionalities. This approach was first proposed by Wyner, and the corresponding secure communication model is called the wiretap channel model. These two approaches introduce two primary resources for providing information-theoretic secure communication: the shared secret key and physical properties of the communication medium. In this thesis, we study how to employ the above two resources for secure message transmission. We study this by using channel’s noise in the wiretap channel model. In this model, a sender is connected to the receiver and the adversary through two noisy channels. We propose a new wiretap encoding scheme with strong secrecy that provides perfect secrecy and reliability, asymptotically. The construction treats the noise in the adversary’s channel as a source of randomness that is extracted and used to hide the message from the adversary. We realize the wiretap channel model using cooperative jamming to evaluate the performance of wiretap codes in practice. We consider a model called keyed wiretap channel that unifies Wyner’s model with Shannon’s model of perfect secrecy for information systems, and propose a keyed encoding schemes with strong secrecy and other properties that are attractive in practice. We also study two-party information-theoretic secret key agreement when the two parties have access to samples of a common source of randomness and use a single message transmission to arrive at a shared random key. We propose a secret key agreement protocol in this setting, prove its security, and show its superior performance compared to other known protocols with the same properties. Finally, we propose an information-theoretic secret key agreement over a virtual wiretap channel created by cooperative jamming.

May 15, 20200 citations

Cryptography with imperfect randomness

Leonid Reyzin, Bhavana Kanukurthi

Cryptographic protocols, though used in a wide range of everyday tasks, are typically built for certain unrealistic ideal conditions in which the user is assumed to work. For example, one such condition that is implicitly assumed is that the user has perfect randomness that she can use as her cryptographic secret key. Another commonly made assumption is that the user runs her cryptographic tasks (such as encryption) on a device that is perfectly secure; that is, its internals are not tampered with or even observed by an adversary. In this thesis, we focus on designing cryptographic techniques that are secure under less-than-ideal conditions. In order to remove the assumption that users share perfectly random secret keys, we study the problem of privacy amplification: key agreement between two parties who both know a weak secret w, such as a password. The goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string R that is fully secret from the adversary. R may then be used as a key for running symmetric cryptographic protocols (such as encryption or authentication). Because we make no computational assumptions, the entropy in R can come only from w. Thus such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. In this thesis, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up to constant factors. We also extend our results to the case where the users share correlated secrets w and w' . This setting occurs, for example, when the secrets are biometric readings taken at different points of time and is more generally known as information-reconciliation.

Jan 1, 20110 citations