Inclusion Relations of Boolean Functions Satisfying PC(<I>l</I>) of Order <I>k</I>

Tetsu IWATA; Kaoru KUROSAWA

Inclusion Relations of Boolean Functions Satisfying PC(l) of Order k

Tetsu IWATA, Kaoru KUROSAWA

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In cryptography, we want a Boolean function which satisfies PC(l) of order k for many (l,k). Let PC_n(l,k) be a set of Boolean functions with n input bits satisfying PC(l) of order k. From a view point of construction, it is desirable that there exists (l₀,k₀) such that PC_n(l₀, k₀) PC_n(l_i,k_i) for many i 1. In this paper, we show a negative result for this problem. We prove that PC_n(l₁,k₁) PC_n(l₂,k₂) for a large class of l₁, k₁, l₂ and k₂.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.1 pp.47-53

Publication Date: 2003/01/01

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Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

Category: Symmetric Ciphers and Hash Functions

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Tetsu IWATA, Kaoru KUROSAWA, "Inclusion Relations of Boolean Functions Satisfying PC(l) of Order k" in IEICE TRANSACTIONS on Fundamentals, vol. E86-A, no. 1, pp. 47-53, January 2003, doi: .
Abstract: In cryptography, we want a Boolean function which satisfies PC(l) of order k for many (l,k). Let PC_n(l,k) be a set of Boolean functions with n input bits satisfying PC(l) of order k. From a view point of construction, it is desirable that there exists (l₀,k₀) such that PC_n(l₀, k₀) PC_n(l_i,k_i) for many i 1. In this paper, we show a negative result for this problem. We prove that PC_n(l₁,k₁) PC_n(l₂,k₂) for a large class of l₁, k₁, l₂ and k₂.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e86-a_1_47/_p

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@ARTICLE{e86-a_1_47,
author={Tetsu IWATA, Kaoru KUROSAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Inclusion Relations of Boolean Functions Satisfying PC(l) of Order k},
year={2003},
volume={E86-A},
number={1},
pages={47-53},
abstract={In cryptography, we want a Boolean function which satisfies PC(l) of order k for many (l,k). Let PC_n(l,k) be a set of Boolean functions with n input bits satisfying PC(l) of order k. From a view point of construction, it is desirable that there exists (l₀,k₀) such that PC_n(l₀, k₀) PC_n(l_i,k_i) for many i 1. In this paper, we show a negative result for this problem. We prove that PC_n(l₁,k₁) PC_n(l₂,k₂) for a large class of l₁, k₁, l₂ and k₂.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - Inclusion Relations of Boolean Functions Satisfying PC(l) of Order k
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 47
EP - 53
AU - Tetsu IWATA
AU - Kaoru KUROSAWA
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2003
AB - In cryptography, we want a Boolean function which satisfies PC(l) of order k for many (l,k). Let PC_n(l,k) be a set of Boolean functions with n input bits satisfying PC(l) of order k. From a view point of construction, it is desirable that there exists (l₀,k₀) such that PC_n(l₀, k₀) PC_n(l_i,k_i) for many i 1. In this paper, we show a negative result for this problem. We prove that PC_n(l₁,k₁) PC_n(l₂,k₂) for a large class of l₁, k₁, l₂ and k₂.
ER -