When Lagged Fibonacci Generators jump
| Autor: | Moon K. Chetry, Vashek Matyas, Susil Kumar Bishoi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Fibonacci number business.industry Applied Mathematics Cryptography 010103 numerical & computational mathematics 0102 computer and information sciences 01 natural sciences Lagged Fibonacci generator Primitive polynomial 010201 computation theory & mathematics Jump Discrete Mathematics and Combinatorics State space Hardware_ARITHMETICANDLOGICSTRUCTURES 0101 mathematics business Stream cipher Computer Science::Cryptography and Security Mathematics Characteristic polynomial |
| Zdroj: | Discrete Applied Mathematics. 267:64-72 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2019.06.022 |
| 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. |
| Databáze: | OpenAIRE |
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