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Conference of Open Innovations Association (FRUCT)

Vulnerability of the Key Sharing Protocol Executing over the Noiseless Public Channels with Feedback

Коржик Валерий Иванович, Viktor Yakovlev, Vladimir Starostin, Alexey Lapshin, Aleksei Zhuvikin

Published Apr 24, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.23919/fruct61870.2024.10516344

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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.
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.
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.
In this paper, the problem of key generation over an unauthenticated public channel in a network setup is considered. The considered model consists of four terminals: two legitimate terminals who need to share a key, a helper and an active adversary. The legitimate terminals and the helper are allowed to exchange messages over a public noiseless channel, to which the adversary has full access and may modify messages exchanged through this public channel. We investigate two types of keys: secret key (secure from the adversary only) and private key (secure from both the helper and the adversary). We characterize the relationship between the key rates in our model and the existing models with a passive adversary. We characterize conditions under which the generated key rates in this model are non-zero, and further provide an authentication scheme to show that key capacities, if are non-zero, are the same as those for the scenario with a passive adversary.
The method of secret key sharing between units that did not possess any secret keys in advance is considered.It is assumed that between these units there are duplex wireless MIMO fading channels.In a recent paper published by D. Qin and Z. Dingh a new key sharing protocol has been proposed between legitimate users based on eigenvalues which are invariant under permutation of two matrices in their product.We extend this statement to a characteristic polynomial and by the way to matrix trace.Methods of key bits extraction are optimized both theoretically and experimentally.On the contrary to a statement of D. Qin and Z. Ding we prove that their key sharing protocol occurs insecure if eavesdroppers have the same channels as legitimate users.In order to provide reliability and security of the shared keys both error correction codes and privacy amplification methods can be used.
Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network? In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding. If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself! We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.