Abstract
Since 1975 many new cryptosystems have been based on elementary number theory, but until now it has not been recognised that they have been just as much grounded in the process of exponentiation. Lucas functions can be used to replace exponentiation to produce alternative cryptosystems that are not susceptible to attacks which rely on the fact that multiplication is closed under exponentiation, since Lucas functions do not exhibit this closure.
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Smith, P., Skinner, C. (1995). A public-key cryptosystem and a digital signature system based on the Lucas function analogue to discrete logarithms. In: Pieprzyk, J., Safavi-Naini, R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000447
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DOI: https://doi.org/10.1007/BFb0000447
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