The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function

Deng TANG; Rong LUO; Xiaoni DU

doi:10.1587/transfun.E99.A.2084

The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function

Deng TANG, Rong LUO, Xiaoni DU

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To resist algebraic and fast algebraic attacks, Boolean functions used in stream ciphers should have optimal algebraic immunity and good fast algebraic immunity. One challenge of cryptographic Boolean functions is to determine their ability to resist fast algebraic attacks, which can be measured by their fast algebraic immunities. In this letter, we determine the exact values of fast algebraic immunity of the majority function of 2^m and 2^m+1 variables. This is the first time that the exact values of the fast algebraic immunity of an infinite class of symmetric Boolean functions with optimal algebraic immunity are determined.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.11 pp.2084-2088

Publication Date: 2016/11/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.2084

Type of Manuscript: LETTER

Category: Cryptography and Information Security

Authors

Deng TANG
  Southwest Jiaotong University
Rong LUO
  Southwest Jiaotong University
Xiaoni DU
  Northwest Normal University

Keyword

stream cipher, Boolean function, algebraic attack, fast algebraic immunity

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Deng TANG, Rong LUO, Xiaoni DU, "The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 11, pp. 2084-2088, November 2016, doi: 10.1587/transfun.E99.A.2084.
Abstract: To resist algebraic and fast algebraic attacks, Boolean functions used in stream ciphers should have optimal algebraic immunity and good fast algebraic immunity. One challenge of cryptographic Boolean functions is to determine their ability to resist fast algebraic attacks, which can be measured by their fast algebraic immunities. In this letter, we determine the exact values of fast algebraic immunity of the majority function of 2^m and 2^m+1 variables. This is the first time that the exact values of the fast algebraic immunity of an infinite class of symmetric Boolean functions with optimal algebraic immunity are determined.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.2084/_p

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@ARTICLE{e99-a_11_2084,
author={Deng TANG, Rong LUO, Xiaoni DU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function},
year={2016},
volume={E99-A},
number={11},
pages={2084-2088},
abstract={To resist algebraic and fast algebraic attacks, Boolean functions used in stream ciphers should have optimal algebraic immunity and good fast algebraic immunity. One challenge of cryptographic Boolean functions is to determine their ability to resist fast algebraic attacks, which can be measured by their fast algebraic immunities. In this letter, we determine the exact values of fast algebraic immunity of the majority function of 2^m and 2^m+1 variables. This is the first time that the exact values of the fast algebraic immunity of an infinite class of symmetric Boolean functions with optimal algebraic immunity are determined.},
keywords={},
doi={10.1587/transfun.E99.A.2084},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2084
EP - 2088
AU - Deng TANG
AU - Rong LUO
AU - Xiaoni DU
PY - 2016
DO - 10.1587/transfun.E99.A.2084
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2016
AB - To resist algebraic and fast algebraic attacks, Boolean functions used in stream ciphers should have optimal algebraic immunity and good fast algebraic immunity. One challenge of cryptographic Boolean functions is to determine their ability to resist fast algebraic attacks, which can be measured by their fast algebraic immunities. In this letter, we determine the exact values of fast algebraic immunity of the majority function of 2^m and 2^m+1 variables. This is the first time that the exact values of the fast algebraic immunity of an infinite class of symmetric Boolean functions with optimal algebraic immunity are determined.
ER -