Correlation-immune functions over finite fields

Mulan Liu; Peizhong Lu; Gary L. Mullen

doi:10.1109/18.669323

Correlation-immune functions over finite fields

Mulan Liu, Peizhong Lu, Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We give a series of constructions of correlation-immune function over finite fields. We prove that F₂ and F₃ are the only finite fields F_q with the property that every (n - 1)th correlation-immune function in n > 2 variables over F_q is linear. We also show that by choosing larger finite fields one can alleviate the tradeoff between the length of the linear equivalent and the order of correlation immunity. This is useful for the design of various cryptosystems.

Original language	English (US)
Pages (from-to)	1273-1276
Number of pages	4
Journal	IEEE Transactions on Information Theory
Volume	44
Issue number	3
DOIs	https://doi.org/10.1109/18.669323
State	Published - 1998

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/18.669323

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title = "Correlation-immune functions over finite fields",

abstract = "We give a series of constructions of correlation-immune function over finite fields. We prove that F2 and F3 are the only finite fields Fq with the property that every (n - 1)th correlation-immune function in n > 2 variables over Fq is linear. We also show that by choosing larger finite fields one can alleviate the tradeoff between the length of the linear equivalent and the order of correlation immunity. This is useful for the design of various cryptosystems.",

author = "Mulan Liu and Peizhong Lu and Mullen, {Gary L.}",

note = "Funding Information: Manuscript received July 24, 1996; revised October 23, 1997. The work of M. Liu was supported in part by the NNSF of China and the Wang Kuancheng Fund.",

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AU - Lu, Peizhong

AU - Mullen, Gary L.

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PY - 1998

Y1 - 1998

N2 - We give a series of constructions of correlation-immune function over finite fields. We prove that F2 and F3 are the only finite fields Fq with the property that every (n - 1)th correlation-immune function in n > 2 variables over Fq is linear. We also show that by choosing larger finite fields one can alleviate the tradeoff between the length of the linear equivalent and the order of correlation immunity. This is useful for the design of various cryptosystems.

AB - We give a series of constructions of correlation-immune function over finite fields. We prove that F2 and F3 are the only finite fields Fq with the property that every (n - 1)th correlation-immune function in n > 2 variables over Fq is linear. We also show that by choosing larger finite fields one can alleviate the tradeoff between the length of the linear equivalent and the order of correlation immunity. This is useful for the design of various cryptosystems.

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

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ER -

Correlation-immune functions over finite fields

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