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When Lagged Fibonacci Generators jump

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CHETRY Moon K. BISHOI Susil Kumar MATYÁŠ Václav

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Discrete Applied Mathematics
Fakulta / Pracoviště MU

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Citace
www http://dx.doi.org/10.1016/j.dam.2019.06.022
Doi http://dx.doi.org/10.1016/j.dam.2019.06.022
Klíčová slova Stream cipher; Primitive polynomial; LFSR; LFG; Jump index
Popis Jansen introduced a primitive called jumped Linear Feedback Shift Register (LFSR) for building LFSRs that can be clocked a large number of times with a single simple operation. This is useful in the construction of stream ciphers based on clock-controlled LFSRs. A concept of Lagged Fibonacci Generator (LFG) is also used as an important building block of key-stream generators in stream cipher cryptography. In this paper, we use the jumping concept of Jansen in case of LFG. We show that unlike LFSRs, LFGs need not jump always in the state space itself, even though the characteristic polynomial is primitive. Instead, it may have a hyper space jump depending on the characteristic primitive polynomial. We give a necessary and sufficient condition for an LFG to jump within the state space itself and when it exists, it is same as the degree of the characteristic polynomial.