S-boxes, Boolean Functions and Codes for the Resistance of Block Ciphers to Cryptographic Attacks, with or without Side Channels

2015 ◽  
pp. 151-171 ◽  
Author(s):  
Claude Carlet
Keyword(s):  
Boolean Functions ◽  
Block Ciphers ◽  
Side Channels ◽  
Cryptographic Attacks

scholarly journals Crypto-Archaeology: unearthing design methodology of DES s-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Design Methodology ◽  
Block Cipher ◽  
Block Ciphers ◽  
Public Domain ◽  
Differential Cryptanalysis ◽  
Linear Cryptanalysis ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

Crypto Archeology: Unearthing Design Methodologies of DES S-Boxes

2017 ◽  
Vol 2 (9) ◽  
pp. 30-34
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Functions ◽  
Design Methodology ◽  
Block Ciphers ◽  
Public Domain ◽  
Keen Interest ◽  
Design Methodologies ◽  
Substitution Boxes

US defense sponsored the DES program in 1971 and released it on 1977. It remained as a well-known and well-accepted de-facto standard of block ciphers until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each having four and are put in public domain without any mention of their design methodology. Due to this discovery of substitution Boxes, S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, a brief study on Crypto relevant properties of 4-bit Boolean Functions as well as 4-bit S-Boxes has been elaborated. The design Methodology of 32 4-bit DES S-Boxes have been of keen interest of this paper. The methodology of such 4-bit DES S-boxes that remained unturned due to the interference of NIST, have also been elaborated in this paper.

scholarly journals Applied study on cryptographic functions for algorithms used in communications security protocols

2020 ◽  
Vol XXIII (1) ◽  
pp. 243-247
Author(s):  
Florin Medeleanu
Keyword(s):  
Air Force ◽  
Boolean Functions ◽  
Building Blocks ◽  
Mathematical Tool ◽  
Linear Combinations ◽  
Applied Study ◽  
Important Field ◽  
Cryptographic Attacks ◽  
The Military ◽  
Linear Systems Of Equations

Communications security is one of the most important fields to take into account when designing a system that manages information, especially when implementing such a system for the military, no matter which branch, Navy, Air Force or Army. One important field when talking about information security in general is cryptology and within cryptology linear and nonlinear Boolean functions and maps are essential, important building blocks. They are used in the design of several block and stream ciphers. The study of cryptographic properties of these functions does not only help cryptanalysis but also plays an important role in the design of cryptographic algorithms that resist well against various cryptographic attacks. Linear and differential cryptanalysis of block ciphers is mainly based on determining and exploiting linear combinations of their components. The most useful mathematical tool for studying linearity of Boolean functions is the Walsh (or Hadamard) transform. This can be regarded as a size-2 discrete Fourier transform. Another method for determining linear combinations of cipher components is that of finding and solving linear systems of equations. This article reflects the authors’ effort to shed some light on this field.

New combination of simple additive and entropy weighting criteria for the selection of best substitution box

2021 ◽  
pp. 1-14
Author(s):  
Majid Khan ◽  
Haj Ismail ◽  
Iqra Ishaque ◽  
A, Iqtadar Hussain
Keyword(s):  
Block Ciphers ◽  
Encryption Algorithm ◽  
New Combination ◽  
Substitution Box ◽  
Fundamental Component ◽  
Substitution Boxes ◽  
Cryptographic Attacks ◽  
Ranking Technique ◽  
Selection Of

Substitution boxes (S-boxes) are among the most widely recognized and fundamental component of most modern block ciphers. This is on the grounds that they can give a cipher fortifying properties to oppose known and possible cryptanalytic assaults. We have suggested a novel tool to select nonlinear confusion component. This nonlinear confusion component added confusion capability which describes to make the connection among the key and the cipher as complex and engaging as possible. The confusion can be obtained by using substitution box (S-box) and complex scrambling algorithm that relies on key and the input (plaintext). Various statistical and cryptographic characteristics were introduced to measure the strength of substitution boxes (S-boxes). With the help of the present objective weight methods and ranking technique, we can select an ideal S-box among other constructed confusion component to make our encryption algorithm secure and robust against various cryptographic attacks.

scholarly journals On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Brajesh Kumar Singh
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Boolean Function ◽  
Lower Bounds ◽  
Boolean Functions ◽  
Coding Theory ◽  
Block Ciphers ◽  
Covering Radius ◽  
Third Order ◽  
Complicated Problem

The rth-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers. Because of the fact that its maximum equals the covering radius of the rth-order Reed-Muller code, it also plays an important role in coding theory. The computation of exact value or high lower bound on the rth-order nonlinearity of a Boolean function is very complicated problem, especially when r>1. This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form Tr1nλxd for all x∈𝔽2n, λ∈𝔽2n*, where a d=2i+2j+2k+1, where i, j, and   k are integers such that i>j>k≥1 and n>2i, and b d=23ℓ+22ℓ+2ℓ+1, where ℓ is a positive integer such that gcdℓ,𝓃=1 and n>6.

scholarly journals Crypto-Archaeology: unearthing design methodology of DES s-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Design Methodology ◽  
Block Cipher ◽  
Block Ciphers ◽  
Public Domain ◽  
Differential Cryptanalysis ◽  
Linear Cryptanalysis ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

Towards the optimal performance of integrating Warm and Delay against remote cache timing side channels on block ciphers

2019 ◽  
Vol 27 (5) ◽  
pp. 547-580
Author(s):  
Ziqiang Ma ◽  
Quanwei Cai ◽  
Jingqiang Lin ◽  
Bo Luo ◽  
Jiwu Jing
Keyword(s):  
Block Ciphers ◽  
Optimal Performance ◽  
Side Channels

Noise Sensitivity of Boolean Functions and Percolation

2015 ◽  
Author(s):  
Christophe Garban ◽  
Jeffrey E. Steif
Keyword(s):  
Boolean Functions ◽  
Noise Sensitivity
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