Abstract
This paper proposes a new public key encryption scheme. It is based on the difficulty of deducing x and y from A and B = x·A ·y in a specific monoid (m,·) which is noncommutative. So we select and do research work on the certain monoid which is formed by all the n×n matrices over finite field F 2 under multiplication. By the cryptographic properties of an “ergodic matrix”, we propose a hard problem based on the ergodic matrices over F 2, and use it construct a public key encryption scheme.
This work supported by the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No. 20050183032, and the Jilin Province Education Office Science Foundation Project of China under Grant No.2004150 and No. 2005180.
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Shi-Hui, P., Yong-Zhe, Z., Hong-Wei, Z. (2007). Construct Public Key Encryption Scheme Using Ergodic Matrices over GF(2). In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_16
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DOI: https://doi.org/10.1007/978-3-540-72504-6_16
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