Abstract
Applications of special representation of natural numbers as linear forms of the type x F t−1+y F 1, where F t−1 and F t are adjacent Fibonacci numbers, for constructing effective parallel algorithms of modular exponentiation and factorization are considered in this report. These operations over large numbers are ones of the main in design and analysis of well-known public-key cryptosystems like RSA-schemes. Proofs of two important theorems are shown also.
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Anisimov, A.V. (1995). Linear Fibonacci forms and parallel algorithms for high dimension arithmetic. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1995. Lecture Notes in Computer Science, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60222-4_93
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DOI: https://doi.org/10.1007/3-540-60222-4_93
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