A Cipher Based on Prefix Codes.

Otokar Grošek,Peter Horák,Viliam Hromada

doi:10.3390/s21186236

Abstract

A prefix code, a P-code, is a code where no codeword is a prefix of another codeword. In this paper, a symmetric cipher based on prefix codes is proposed. The simplicity of the design makes this cipher usable for Internet of Things applications. Our goal is to investigate the security of this cipher. A detailed analysis of the fundamental properties of P-codes shows that the keyspace of the cipher is too large to mount a brute-force attack. Specifically, in this regard we will find bounds on the number of minimal P-codes containing a binary word given in advance. Furthermore, the statistical attack is difficult to mount on such cryptosystem due to the attacker’s lack of information about the actual words used in the substitution mapping. The results of a statistical analysis of possible keys are also presented. It turns out that the distribution of the number of minimal P-codes over all binary words of a fixed length is Gaussian.

Highlights

A prefix code, a P-code, is a code where no codeword is a prefix of another codeword [1]
|w| > 1, we have found a dictionary with codewords of different lengths, i.e., a dictionary not included in the previous case
We implemented Algorithm 1 in programming language C++ and used it to calculate the cardinalities of sets V x for all possible binary strings x of lengths ν = 1, 2, . . . , 26

Summary

Introduction

A prefix code, a P-code, is a code where no codeword is a prefix of another codeword [1]. The oldest known example of a P-code is the Argenti code [2] (16th century). P-codes were used by Peter the Great, where the plaintext was the Cyrillic alphabet [2]. The Soviet cipher known as VIC [3], used P-codes as one of the rounds during the encryption. In the mid of the 20th century, the properties of P-codes were studied by the leading scholars in the area, including Shannon, Fano, Huffman, etc. One area of cryptography which employs prefix codes is the DNA cryptography [4], in which many cryptosystems utilize binary prefix codes as the plaintext space [5,6,7,8]

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Conclusion