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Journal of Computer Security

A unified model for unconditionally secure key distribution

CimatoStelvio, CrestiAntonella, D'ArcoPaolo

Published Jan 1, 2006• 1 citation
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 sec...
DOI
10.5555/1239376.1239378

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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.
We focus on unconditionally secure conference key distribution. Many onetime keys shared by users are needed for perfect secure communication. Our approach is to use a twoparty key agreement system as an underlying cryptographic primitive and extend it to a conference system which is as secure as the twopart system. With the spanning tree in this paper, the conference key distribution system can be executed in parallel to the largest extent and it is efficient for dynmaic changing group.
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.
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.
Classical cryptography is based on the computational difficulty to compute the secret key using the current computing systems. Depending only on the difficulty of computational complexity does not provide enough security because finding a fast method to calculate the secret key will compromise the security of the systems. Quantum computing uses the law of physics for communication allowing new concepts to be applied in computing specially in cryptography and key distribution by applying quantum theorems and principles. In this paper, we are introducing a new model for quantum key distribution between three parties or more where there is a trusted center providing the clients the necessary secret information to securely communicate with each other.
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.