Perfectly Secure Shannon Cipher Construction Based on the Matrix Power Function

A Shannon cipher can be used as a building block for the block cipher construction if it is considered as one data block cipher. It has been proved that a Shannon cipher based on a matrix power function (MPF) is perfectly secure. This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. This property is important since finding the inverse of a one-way function is related to an N P -complete problem. The obtained results of perfect security on a theoretical level coincide with the N P -completeness notion due to the well known Yao theorem. The proposed cipher does not need multiple rounds for the encryption of one data block and hence can be effectively parallelized since operations with matrices allow this effective parallelization.

Information Theoretic Security for Shannon Cipher System under Side-Channel Attacks †

In this paper, we propose a new theoretical security model for Shannon cipher systems under side-channel attacks, where the adversary is not only allowed to collect ciphertexts by eavesdropping the public communication channel but is also allowed to collect the physical information leaked by the devices where the cipher system is implemented on, such as running time, power consumption, electromagnetic radiation, etc. Our model is very robust as it does not depend on the kind of physical information leaked by the devices. We also prove that in the case of one-time pad encryption, we can strengthen the secrecy/security of the cipher system by using an appropriate affine encoder. More precisely, we prove that for any distribution of the secret keys and any measurement device used for collecting the physical information, we can derive an achievable rate region for reliability and security such that if we compress the ciphertext using an affine encoder with a rate within the achievable rate region, then: (1) anyone with a secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate region. We derive our result by adapting the framework of the one helper source coding problem posed and investigated by Ahlswede and Körner (1975) and Wyner (1975). For reliability and security, we obtain our result by combining the result of Csizár (1982) on universal coding for a single source using linear codes and the exponential strong converse theorem of Oohama (2015) for the one helper source coding problem.