Advance in Applied Cryptography Theory: Survey and Some New Results. Part 2. Keyless Cryptography

Actuality. The current paper is the second part of the paper “Advance in Applied Cryptography Theory: Survey and Some New Results. Part 1. Key Cryptography” published in the journal PTU, n.4, 2024. It is devoted to such specific area of applied cryptography as keyless one (KC\ Actuality of the current paper consists  in the fact that considered in it methods allow to provide a confidentiality of information transmission over public communication channels, either without any its encryption in advance, executing a natural properties of communication channels   or executing conventional key cryptography but with the keys which are elaborated before by means of KC.

The natural properties of communication channels can be the following: additive noise, multiray wave propagation, MIMO technology and existence of feedback channel.

Our paper starts with a consideration of Wyner’s concept of wire-tap channels and corresponding to it encoding and decoding methods providing very reliable information transmission over the main channels and negligible amount of information leaking over the wire-tap channels to eavesdroppers. Next it is investigated scenario   with a commutative encryption (CE) and corresponding protocol of message exchange over ordinary noiseless public channel that provides security of encrypted information but without any key exchange between users in advance. It is proved which of well known symmetric and asymmetric ciphers are commutative or non-commutative ones. Next model concerns a fading channels under the application of Dean-Goldsmith protocol in frames of MIMO technology. We are proving that this protocol is secure if, and only if, the number of eavesdropper antennas is less than the number of antennas at legitimate users. Next scenario executes  variable directional antennas (VDA) and it is proved for which conditions  on a locations of legitimate users and eavesdroppers  such approach occurs secure given the number of propagation rays is at least two..   We show in the next chapter that there is an attack compromising of recently proposed EVESkey cryptosystem and hence such one is not secure in spite of the statement of its authors.

Finally, we investigate several protocols intended for key sharing over noiseless constant public channels (like Internet) and established that they are mostly insecure because have all zero secret capacity. Only one protocol based on matrix channel exchange is able to provide security of key sharing but in terms of the required breaking complexity. Thus such approach can be used only for the case when legitimate users belong to low level of security requirements.

At the end of the paper we formulate several fundamental problems of applied cryptography which after of their solutions  could be very useful for practice.

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