scholarly journals Retraction Note to: On the Minimum the Sum-of-Squares Indicator of a Balanced Boolean Function

2020 ◽  
pp. C1-C1
Author(s):  
Yu Zhou ◽  
Zepeng Zhuo
Keyword(s):  
Boolean Function ◽  
Sum Of Squares

scholarly journals On the confusion coefficient of Boolean functions

2021 ◽  
Vol 16 (1) ◽  
pp. 1-13
Author(s):  
Yu Zhou ◽  
Jianyong Hu ◽  
Xudong Miao ◽  
Yu Han ◽  
Fuzhong Zhang
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Power Analysis ◽  
Signal To Noise Ratio ◽  
Sum Of Squares ◽  
Hamming Weight ◽  
Signal To Noise ◽  
Trade Offs ◽  
Cryptographic Algorithms ◽  
Transparency Order

Abstract The notion of the confusion coefficient is a property that attempts to characterize confusion property of cryptographic algorithms against differential power analysis. In this article, we establish a relationship between the confusion coefficient and the autocorrelation function for any Boolean function and give a tight upper bound and a tight lower bound on the confusion coefficient for any (balanced) Boolean function. We also deduce some deep relationships between the sum-of-squares of the confusion coefficient and other cryptographic indicators (the sum-of-squares indicator, hamming weight, algebraic immunity and correlation immunity), respectively. Moreover, we obtain some trade-offs among the sum-of-squares of the confusion coefficient, the signal-to-noise ratio and the redefined transparency order for a Boolean function.

ONE SUFFICIENT AND NECESSARY CONDITION ON BALANCED BOOLEAN FUNCTIONS WITH σf = 22n + 2n+3(n ≥ 3)

2014 ◽  
Vol 25 (03) ◽  
pp. 343-353 ◽  
Author(s):  
YU ZHOU ◽  
LIN WANG ◽  
WEIQIONG WANG ◽  
XINFENG DONG ◽  
XIAONI DU
Keyword(s):  
Lower Bound ◽  
Boolean Function ◽  
Lower Bounds ◽  
Boolean Functions ◽  
Sum Of Squares ◽  
Necessary Condition ◽  
Resilient Function ◽  
The Absolute ◽  
Global Avalanche Characteristics ◽  
Sufficient And Necessary Condition

The Global Avalanche Characteristics (including the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Son et al. (1998) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function. In this paper, we give a sufficient and necessary condition on a balanced Boolean function reaching the lower bound on the sum-of-squares indicator. We also analyze whether these balanced Boolean functions exist, and if they reach the lower bounds on the sum-of-squares indicator or not. Our result implies that there does not exist a balanced Boolean function with n-variable for odd n(n ≥ 5). We conclude that there does not exist a m(m ≥ 1)-resilient function reaching the lower bound on the sum-of-squares indicator with n-variable for n ≥ 7.

scholarly journals Measuring the Sum-of-Squares Indicator of Boolean Functions in Encryption Algorithm for Internet of Things

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Yu Zhou ◽  
Yongzhuang Wei ◽  
Fengrong Zhang
Keyword(s):  
Internet Of Things ◽  
Boolean Function ◽  
Boolean Functions ◽  
Search Algorithm ◽  
Sum Of Squares ◽  
Encryption Algorithm ◽  
Correlation Distribution ◽  
Cryptographic Algorithm ◽  
Global Avalanche Characteristics ◽  
The Internet Of Things

Encryption algorithm has an important application in ensuring the security of the Internet of Things. Boolean function is the basic component of symmetric encryption algorithm, and its many cryptographic properties are important indicators to measure the security of cryptographic algorithm. This paper focuses on the sum-of-squares indicator of Boolean function; an upper bound and a lower bound of the sum-of-squares on Boolean functions are obtained by the decomposition Boolean functions; some properties and a search algorithm of Boolean functions with the same autocorrelation (or cross-correlation) distribution are given. Finally, a construction method to obtain a balanced Boolean function with small sum-of-squares indicator is derived by decomposition Boolean functions. Compared with the known balanced Boolean functions, the constructed functions have the higher nonlinearity and the better global avalanche characteristics property.

scholarly journals On Negabent Functions and Nega-Hadamard Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Zepeng Zhuo ◽  
Jinfeng Chong
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Sum Of Squares ◽  
Hadamard Transform ◽  
Autocorrelation Coefficient ◽  
Equivalent Statement ◽  
Hadamard Transforms

The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called negabent function. In this paper, the special Boolean functions by concatenation are presented. We investigate their nega-Hadamard transforms, nega-autocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement onf1∥f2which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed asf(Ax⊕a)⊕b·x⊕cis discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained.

PEMODELAN MATEMATIS ADSORPSI CO2 DENGAN STRONG BASE ANION EXCHANGE RESIN SEBAGAI ADSORBEN UNTUK PURIFIKASI BIOGAS

2015 ◽  
Vol 5 (1) ◽  
pp. 11
Author(s):  
Anies Mutiari ◽  
Wiratni Wiratni ◽  
Aswati Mindaryani
Keyword(s):  
Anion Exchange ◽  
Pilot Plant ◽  
Exchange Resin ◽  
Anion Exchange Resin ◽  
Scale Up ◽  
Sum Of Squares ◽  
Strong Base ◽  
Model Transfer ◽  
Plant Parameter

Pemurnian biogas telah banyak dilakukan untuk menghilangkan kadar CO2  dan meningkatkan kandungan CH4  yang terkandung di dalamnya. Kandungan CH4 yang tinggi akan memberikan unjuk kerja yang lebih baik. Model  matematis proses adsorpsi CO2 disusun berdasarkan teori lapisan film antar fasa, dimana pada proses yang ditinjau terdapat tiga fase yaitu gas, cair dan padat. Model matematis dari data eksperimental   kecepatan dan kesetimbangan proses adsorpsi CO2 melalui mekanisme pertukaran ion di suatu kolom adsorpsi telah dibuat. Model ini dibuat untuk mencari konstanta yang dapat dipergunakan pada proses scale up data laboratorium ke skala pilot plant. Parameter proses kecepatan yang dicari nilainya adalah koefisien transfer massa massa volumetris CO2 pada fase cair (kLa), koefisien transfer massa volumetris CO2 pada fasegas (kGa) dan tetapan laju reaksi (k1 dan k2). Pada hasil penelitian ini ditunjukkan bahwa nilai parameter yang diperoleh sesuai hasil fitting data dengan model matematis yang digunakan, yaitu model transfer massa pada lapisan film antar fase secara seri: adalah kGa, kla, k1 dan k2  dengan nilai Sum of Squares Error (SSE) rata-rata 0,0431. Perbandingan nilai kGa hasil simulasi dan teoritisnya memberikan kesalahan rata-rata 18,79%. Perbandingan nilai kLa hasil simulasi dan teoritis memberikan kesalahan rata-rata 7,92%.Kata kunci: model matematis, adsorpsi CO2, pemurnian biogas

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