Abstract
In 1993 Lennon and Smith proposed to use Lucas functions instead of the exponentiation function as a one-way function in cryptographic mechanisms. Recently Smith and Skinner presented an ElGamal signature scheme based on Lucas functions.
In this paper we point out a serious weakness in this approach and present our version of an ElGamal signature scheme based on Lucas functions. Furthermore, we outline how to apply the ideas of the Meta-ElGamal signature scheme to Lucas functions. As a result we get various new signature schemes. In contradiction to a conjecture by Smith and Skinner the security of the schemes isn’t increased: It can be proved that a variant of the signature schemes based on Lucas functions can be universally forged if a related signature scheme in GF(p) can be universally forged. We further outline how the Meta signature scheme can be described in an elliptic curve environment and mention some other possible extensions.
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© 1995 IFIP International Federation for Information Processing
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Horster, P., Michels, M., Petersen, H. (1995). Digital signature schemes based on Lucas functions. In: Posch, R. (eds) Communications and Multimedia Security. IFIP Advances in Information and Communication Technology. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34943-5_15
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DOI: https://doi.org/10.1007/978-0-387-34943-5_15
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