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International Convention on Information and Communication Technology, Electronics and Microelectronics

Optimization of the Key Sharing Protocol for Noiseless Public Channels without the Use of Cryptographic Assumptions

Коржик Валерий Иванович, Vladimir Starostin, М. М. Кабардов, Viktor Yakovlev, Aleksandr Gerasimovich, Aleksey Zhuvikin

Published Sep 27, 2021• 1 citation
Publisher

Abstract

Traditional physical-layer based secret key sharing scheme typically suggests some cryptographic assumption. In this paper we develop the key sharing protocol for noiseless public channels without any cryptographic assumptions that was proposed recently by the same group of authors. But in contrast to our previous investigations we introduce here more profound research of previous approach. First of all we replace four-step protocol presented before to two-step protocol without loss of key security. A comparison of protocol with and without additional sub key channel is given. Impossibility to use integers instead of matrices in execution of information exchange over the channel is demonstrated. Selecting of the main key sharing protocol parameters in order to minimize channel traffic, given the key bit reliability and information-theoretic security is provided. As a source of random date that are needed for a creation of matrices is tested a compact hardware device generating of truly random sequences. It follows from our investigations that the proposed key sharing protocol can be easily executed by individuals involved into ordinary Internet activity providing information theoretical security level even during post quantum period.

DOI
10.23919/mipro52101.2021.9596703

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Traditional physical-layer based secret key sharing scheme typically suggests some cryptographic assumption. In this paper we develop the key sharing protocol for noiseless public channels without any cryptographic assumptions that was proposed recently by the same group of authors. But in contrast to our previous investigations we introduce here more profound research of previous approach. First of all we replace four-step protocol presented before to two-step protocol without loss of key security. A comparison of protocol with and without additional sub key channel is given. Impossibility to use integers instead of matrices in execution of information exchange over the channel is demonstrated. Selecting of the main key sharing protocol parameters in order to minimize channel traffic, given the key bit reliability and information-theoretic security is provided. As a source of random date that are needed for a creation of matrices is tested a compact hardware device generating of truly random sequences. It follows from our investigations that the proposed key sharing protocol can be easily executed by individuals involved into ordinary Internet activity providing information theoretical security level even during post quantum period.
We propose a new key sharing protocol executed through any constant parameter noiseless public channel (as Internet itself) without any cryptographic assumptions and protocol restrictions on SNR in the eavesdropper channels.This protocol is based on extraction by legitimate users of eigenvalues from randomly generated matrices.A similar protocol was proposed recently by G. Qin and Z. Ding.But we prove that, in fact, this protocol is insecure and we modify it to be both reliable and secure using artificial noise and privacy amplification procedure.Results of simulation prove these statements.
In the current paper, some methods of information security protocols based on physical layer security are considered. It is proved that well known Shamir’s protocol can be applied to RSA cryptosystem but not to Rabin, Mac-Ellice and trellis based cryptosystems. The main stream of this paper is a description of key sharing protocol on constant public and noiseless channels (like Internet). It is shown that it is able to provide a high reliability and control of security in terms of Shannon’s information providing nothing-additional requirements to communication channels and without any cryptographic assumptions.
The term “keyless cryptography” as it is commonly adopted, applies to secure message transmission either directly without any key distribution in advance or as key sharing protocol between communicating users, based on physical layer security, before ordinary encryption/decryption procedures. In the current chapter the results are presented concerning to keyless cryptography that have been obtained by authors recently. Firstly Shamir’s protocol of secure communication is considered where commutative encryption procedure is executed. It has been found out which of the public key algorithms can be used with such protocol. Next item of consideration concerns Dean’s and Goldsmith’s cryptosystem based on multiple-input, multiple-output (MIMO) technology. It has been established under which conditions this cryptosystem is in fact secure. The third example under consideration is EVSkey scheme proposed recently by D. Qin and Z. Ding. It has been proven that such key distribution method is in fact insecure, in spite of the authors’ claims. Our main result is a description of a key sharing protocol executing over public noiseless channels (like internet) that provides a key sharing reliability and security without any cryptographic assumptions.
It has been proven that several recently published protocols for exchanging by keys over noiseless channels of the same authors as in the current paper, have real vulnerability to eavesdropping rooted in the attacker’s receiver optimization procedure. Moreover, we have proved that binary bits and real-valued numbers exchange protocols have zero secret capacity and are therefore unpromising in their applications. Protocols of exchanging by real-valued vectors and by matrices have nonzero secret capacity under the condition of hard decoding by eavesdroppers. The use of optimal soft decoding results in a compromise of such protocols. Thus, a problem is still open about an existence or non-existence for reliable key sharing protocols executed over noiseless public channels.
Although one-time pad encrypted files can be sent through Internet channels, the need for renewing shared secret keys have made this method unpractical. This work presents a scheme to turn practical the fast sharing of random keys over arbitrary Internet channels. Starting with a shared secret key sequence of length K_0 the users end up with a secure new sequence K >> K_0. Using these sequences for posteriori message encryption the legitimate users have absolute security control without the need for third parties. Additionally, the security level does not depend on the unproven difficulty of factoring numbers in primes. In the proposed scheme a fast optical random source generates random bits and noise for key renewals. The transmitted signals are recorded signals that carries both the random binary signals to be exchanged and physical noise that cannot be eliminated by the attacker. These signals allow amplification over the Internet network without degrading security. The proposed system is also secure against a-posteriori known-plaintext attack on the key. Information-theoretic analysis is presented and bounds for secure operation are quantitatively determined.
Due to the broadcast nature of wireless channels, wireless communication is vulnerable to eavesdropping, message modification, and node impersonation. Securing the wireless communication requires the shared secret keys between the communicating entities. Traditional security schemes rely on public key infrastructures and cryptographic algorithms to manage secret keys. Recently, many physical-layer-based methods have been proposed as alternative solutions for key generation in wireless networks. These methods exploit the inherent randomness of the wireless fading channel to generate secret keys while providing information-theoretical security without intensive cryptographic computations. This article provides an overview of the existing PHY-based key generation schemes exploiting the randomness of the wireless channels. Specifically, we first introduce the fundamental and general framework of the PHY-based key generation schemes and then categorize them into two classes: received-signal-strength-based and channel- phase-based protocols. Finally, we present a performance comparison of them in terms of key disagreement probability, key generation rate, key bit randomness, scalability, and implementation issues.