Advance in Keyless Cryptography

*Valery Korzhik, Vladimir Starostin, Victor Yakovlev, Muaed Kabardov, Andrej Krasov and Sergey Adadurov*

## **Abstract**

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.

**Keywords:** keyless cryptography, protocols, public cryptosystems, MIMO technology, cryptographic assumptions

## **1. Introduction**

The term keyless cryptography dates back many years ago. See for example the paper [1]. One author of this chapter used also before this term many times, for example in the papers [2–4]. This term is commonly used in two senses: either in the scenarios where information transmission security is provided by special channel properties without execution of key sharing protocol in advance, or in the second scenarios where specific channel properties are used on the stage of secret key sharing between users, whereas later are executed ordinary key-based cryptography. An approach to a providing of security at the cost of channel properties was termed as physical layer security [5]. As a rule, it means that communication channel plays the role of some randomizer due to their specific stochastic properties. However, sometimes such randomization is provided by the use of artificial noises by the communicating users.

A natural question arises—why it is not sufficiently to execute algorithms of the so-called *public key cryptosystems* (PKC), invented by W. Diffie and M. Hellman and developed later by many cryptographers: A. Shamir, Rabin, El Gamal, McEliece, J. Massey, and others (see [6, 7])? The point is that PKC have some drawbacks that limit their practical use. The main of these are:


One more way out to provide secure key sharing is an implementation of quantum cryptography [10]. But unfortunately such approach requires the use of very specific quantum devices.

The objections mentioned above give the reason to turn to keyless cryptography which is what we do in this chapter. In Section 2 we investigate Shamir's protocol for secure communication over public channels but without any key sharing in advance. This protocol corresponds to the first scenario. Section 3 presents Dean and Goldsmith cryptosystem that performs channel transmission like a randomizer in the first scenario. We turn out under which restrictions on the channel such protocol is in fact secure. In Section 4 the second scenario (with key sharing) is considered and it is shown that on the contrary to author's claims [11], such *key sharing protocol* (KSP) is in fact insecure. Section 5 corresponds also to the second scenarios. We present a new KSP and prove that such protocol for appropriated chosen parameters provides reliable shared keys which are secure in terms of Shannon information without any cryptographic assumptions. Section 6 summarized all previous results and presents our opinion regarding to possible future investigations.
