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Journal of Computer Security

A unified model for unconditionally secure key distribution

Stelvio Cimato, Antonella Cresti, Paolo D’Arco

Published Feb 1, 2006• 12 citations
Publisher

Abstract

A key distribution scheme is a method by means of which a trusted party distributes pieces of information among a set of users in such a way that each group of them can compute a common key for secure communication. In this paper we present a model for unconditionally secure key distribution schemes, i.e., schemes whose security is independent of the power of the adversary. We prove lower bounds on the amount of information the trusted party has to generate and each user has to keep secret in such schemes, and we show that some previous unconditionally secure models for key distribution fall in our model. As a consequence, the lower bounds given in the literature for these models can be seen as corollaries of our results. Hence, the main contribution of the paper consists in pointing out a sort of common structure underlying some apparently different key distribution techniques.

DOI
10.3233/jcs-2006-14102

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A key distribution scheme is a method by means of which a trusted party distributes pieces of information among a set of users in such a way that each group of them can compute a common key for secure communication. In this paper we present a model for unconditionally secure key distribution schemes, i.e., schemes whose security is independent of the power of the adversary. We prove lower bounds on the amount of information the trusted party has to generate and each user has to keep secret in such schemes, and we show that some previous unconditionally secure models for key distribution fall in our model. As a consequence, the lower bounds given in the literature for these models can be seen as corollaries of our results. Hence, the main contribution of the paper consists in pointing out a sort of common structure underlying some apparently different key distribution techniques.
A non-interactive conference key distribution scheme (NICKDS) is a system that allows selected sets of users to securely share a common key without interacting with each other. In this paper, we consider unconditionally secure setting where the is no limit on adversary's computation power. Unconditionally secure NICKDS has been considered with security against an adversary who can corrupt up to w users. We strengthen the security model of the system by allowing the adversary to also obtain conference keys of conferences whose members are honest, and use a game bases approach to define security. We give two other ways of defining security, using probability distance and mutual information and show the relationship between the three definitions of security.
Key distribution plays a fundamental role in cryptography. Currently, the quantum scheme stands as the only known method for achieving unconditionally secure key distribution. This method has been demonstrated over distances of 508 and 1002 kilometers in the measurement-device-independent and twin-field configurations, respectively. However, quantum key distribution faces transmission distance issues and numerous side channel attacks since the basic physical picture requires the use of quantum channels between users. Even when quantum repeater and quantum constellation are used, commercializing quantum cryptography on a large scale remains unattainable due to the considerable expense and significant technical hurdles associated with establishing a global quantum network and facilitating mobile quantum communication. Here, by discovering the provable quantum one-way function, we propose another key distribution scheme with unconditional security, named probability key distribution, that promises users between any two distances to generate a fixed and high secret key rate. There are no quantum channels for exchanging quantum signals between two legitimate users. Non-local entangled states can be generated, identified and measured in the equivalent virtual protocol and can be used to extract secret keys. We anticipate that this discovery presents a paradigm shift in achieving unconditionally secure cryptography, thereby facilitating its widespread application on a global scale.
Abstract. We consider secret key agreement by multiple parties observ-ing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, with-out making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of “how far ” is the joint distribution of the initial observations of the parties and the eaves-dropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper’s side information. The closeness of the two distribu-tions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypoth-esis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers
Unconditionally secure physical key distribution schemes are very slow, and it is practically impossible to use a one-time-pad based cipher to guarantee unconditional security for the encryption of data because using the key bits more than once gives out statistical information, for example via the known-plain-text-attack or by utilizing known components of the protocol and language statistics. Here, we outline a protocol that reduces this speed problem and allows almost-one-time-pad based communication with an unconditionally secure physical key of finite length. The physical, unconditionally secure key is not used for data encryption but is employed in order to generate and share a new software-based key without any known-plain-text component. The software-only-based key distribution is then changed from computationally secure to unconditionally secure, because the communicated key-exchange data (algorithm parameters, one-way functions of random numbers, etc.) are encrypted in an unconditionally secure way with a one-time-pad. For practical applications, this combined physical/software key distribution based communication looks favorable compared to the software-only and physical-only key distribution based communication whenever the speed of the physical key distribution is much lower than that of the software-based key distribution. A mathematical security proof of this new scheme remains an open problem.
We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models the parties wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. In the channel model, the first party can choose a sequence of inputs to a discrete memoryless channel, which has outputs at the other parties and at the eavesdropper. After each channel use, the parties can engage in arbitrarily many rounds of interactive authenticated communication over a public channel. At the end, each party should be able to generate the key. In the source model, the parties wishing to generate a secret key (as well as the eavesdropper) receive a certain number of independent identically distributed copies of jointly distributed random variables after which the parties are allowed interactive authenticated public communication, at the end of which each party should be able to generate the key. We derive new lower and upper bounds on the secret key rate under the source model and the channel model, and introduce a technique for proving that a given expression bounds the secrecy rate from above in the channel model. Our lower bounds strictly improve what is essentially the best known lower bound in both the source model and the channel model. Our upper bound in the channel model strictly improves the current state of art upper bound. We do not know whether our new upper bound in the source model represents an strict improvement but it includes the current best known bound as a special case.