On New Stream Algorithms for Generation of Documents Dijests with High Avalanche Effect

• Date: 2019
• Main Authors: Устименко, Василь Олександрович, Пустовіт, Олександр Сергійович
• Format: Article
• Language: Ukrainian
• Published: Кам'янець-Подільський національний університет імені Івана Огієнка 2019
• Online Access: http://mcm-math.kpnu.edu.ua/article/view/174242
• Journal Title: Mathematical and computer modelling. Series: Physical and mathematical sciences

The family of key dependent algorithms for generating digests of electronic documents is proposed. Computer simulation allows to investigate high level of corresponding avalanche effect. Let K be a freely chosen finite commutative ring and m be a positive integer. Algorithm uses recently discovered homomorphic compression maps of free semigroup of potentially infinite texts written in the alphabet K onto finite group of cubic polynomial transformations of affine space Km.Cryptographic stability of proposed hash functions is connected with hard algebraic problems such as investigation of systems of algebraic equalities or decomposition of nonlinear map on free module into given generators.To make algorithm faster instead of cubical transformation  we take as digest its value  on some depending from  word w(p) additionally transformed by multiplication on pseudorandom matrix М. The algorithms are implemented in the cases of finite fields , commutative ring  and Boolean ring B(32) of order 232.Proposed algorithms can work with data in the form of texts, audio and video files, files with various extensions such as .avi, .tif, .pdf and etc. Algorithms can generate digests of already encrypted files, this option gives a possibility to check the integrity of files without their decryption. Suggested methods of digest generation have a stream nature, the speed for constant m is linearly dependent on variable n. Growth of n increases the cryptographic stability. The implementation in the form of block by block compression is possible but it has a lack of motivation because the size of the block restricts the number of variables in the system of nonlinear equations.The necessity of a further research and technological solutions on the constructions of key dependent hash functions is caused by cybersecurity calls, the increase of global information space, expectations of quantum computers appearance and development of bitcoins technology, which requires hashing of data of arbitrary size with its transformation into sequences of bits which form digests of the so called blockchains. Proposed algorithms of generation of sensitive for changes of documents digests will be used for cyberattacks detection and for the auditing of all files after registered intrusion