Interleaved Sequences of Geometric Sequences Binarized with Legendre Symbol of Two Types
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- TSUCHIYA Kazuyoshi
- Koden Electronics Co., Ltd.
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- NOGAMI Yasuyuki
- Graduate School of Natural Science and Technology, Okayama University
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- UEHARA Satoshi
- Faculty of Environmental Engineering, the University of Kitakyushu
抄録
<p>A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is a linear feedback shift register sequence with maximal period over a finite field. M-sequences have good statistical properties, however we must nonlinearize m-sequences for cryptographic purposes. A geometric sequence is a binary sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol. They showed the geometric sequences have good properties for the period, periodic autocorrelation and linear complexity. However, the geometric sequences do not have the balance property. In this paper, we introduce geometric sequences of two types and show some properties of interleaved sequences of the geometric sequences of two types. These interleaved sequences have the balance property and double the period of the geometric sequences by the interleaved structure. Moreover, we show correlation properties and linear complexity of the interleaved sequences. A key of our observation is that the second type geometric sequence is the complement of the left shift of the first type geometric sequence by half-period positions.</p>
収録刊行物
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- IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E100.A (12), 2720-2727, 2017
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詳細情報 詳細情報について
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- CRID
- 1390001206314908288
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- NII論文ID
- 130006236511
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- ISSN
- 17451337
- 09168508
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可