Abstract
We are interested in monoids and its applications. If every element x in a monoid has a quasi-inverse y in the sense of von Neumann, that satisfies x ·y ·x = x and y ·x ·y = y, the monoid is regular. Our purpose is to use regular monoids to build two abstract algebraic public key cryptosystems: key exchange protocol and public key encryption with keyword search scheme. In addition to illustrating how the two cryptosystems work, we provide instances of these abstract algebraic models and analyse them in terms of cryptanalysis security.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Diffie, W.: The First Ten of Public Key Cryptography. Proceedings of the IEEE 76(5), 560–577 (1988)
Rivest, R.L., Shamir, A., Adleman, L.M.: Cryptographic Communications System and Method. U.S. Patent #4,405,829 (1983)
Steinberg, B.: A Theory of Transformation Monoids: Combinatorics and Representation Theory. The Electronic Journal of Combinatorics 17 #R164 (2010)
Waters, B., Balfanz, D., Durfee, G., Smetters, D.: Building an Encrypted and Searchable Audit Log. In: The 11th Annual Network and Distributed System Security Symposium, NDSS 2004, San Diego, California (2004)
Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public Key Encryption with Keyword Search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004)
Campell, S.L., Meyer, C.D.: Generalized Inverse of Linear Transformations. Dover Publications, New York (1979)
Menezes, A.J., Oorschot, P.C.V., Vanstone, S.A.: Handbook of Applied Cryptography, p. 33. CRC Press (1997)
ANSI X9.30 (PART 2), American National Standard for Financial Services - Public key cryptography using irreversible algorithms for the financial services industry - Part 2: The secure hash algorithm (SHA), ASC X9 Secretariat - American Bankers Association (1993)
Rivest, R.: The MD5 Message-Digest Algorithm. RFC 1321 (1992)
Gorenstein, D.: The Classification of Finite Simple Groups Vol. 1. Groups of Noncharacteristic 2 Type. The University Series in Mathematics. Plenum Press (1983) ISBN 978-0-306-41305-6, MR 746470
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, T.D., Dang, V.H. (2013). Quasi-inverse Based Cryptography. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39649-6_45
Download citation
DOI: https://doi.org/10.1007/978-3-642-39649-6_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39648-9
Online ISBN: 978-3-642-39649-6
eBook Packages: Computer ScienceComputer Science (R0)