Maciej Sawka and Marcin Niemiec

Published in

Energies 2022, 15(19), 6864


cybersecurity; cryptography; block ciphers; symmetric key; iterated ciphers; smart grids

Open Access



Many systems in use today require strong cryptographic primitives to ensure confidentiality and integrity of data. This is especially true for energy systems, such as smart grids, as their proper operation is crucial for the existence of a functioning society. Because of this, we observe new developments in the field of cryptography every year. Among the developed primitives, one of the most important and widely used are iterated block ciphers. From AES (Advanced Encryption Standard) to LEA (Lightweight Encryption Algorithm), these ciphers are omnipresent in our world. While security of the encryption process of these ciphers is often meticulously tested and verified, an important part of them is neglected—the key expansion. Many modern ciphers use key expansion algorithms which produce reversible sub-key sequences. This means that, if the attacker finds out a large-enough part of this sequence, he/she will be able to either calculate the rest of the sequence, or even the original key. This could completely compromise the cipher. This is especially concerning due to research done into side-channel attacks, which attempt to leak secret information from memory. In this paper, we propose a novel scheme which can be used to create key expansion algorithms for modern ciphers. We define two important properties that a sequence produced by such algorithm should have and ensure that our construction fulfills them, based on the research on hashing functions. In order to explain the scheme, we describe an example algorithm constructed this way, as well as a cipher called IJON which utilizes it. In addition to this, we provide results of statistical tests which show the unpredictability of the sub-key sequence produced this way. The tests were performed using a test suite standardized by NIST (National Institute for Standards and Technology). The methodology of our tests is also explained. Finally, the reference implementation of the IJON cipher is published, ready to be used in software. Based on the results of tests, we conclude that, while more research and more testing of the algorithm is advised, the proposed key expansion scheme provides a very good generation of unpredictable bits and could possibly be used in practice.