An Algorithm for Improving Algebraic Degree of S-Box Based on Affine Equivalence Transformation

2017 ◽  
Vol 8 (1) ◽  
pp. 53-64
Author(s):  
Luong The Dung ◽  
Hoang Duc Tho
Keyword(s):  
Block Cipher ◽  
Algebraic Degree ◽  
Equivalence Transformation ◽  
Substitution Box ◽  
Differential Uniformity ◽  
Affine Equivalence ◽  
Nonlinear Part ◽  
Cube Attacks ◽  
Differential Attacks ◽  
Efficient Software

The Substitution box (S-box) plays an important role in a block cipher as it is the only nonlinear part of the cipher in most cases. To avoid various attacks on the ciphers and for efficient software implementation, S-boxes are required to satisfy a lot of properties, for instance being a permutation defined on the fields with even degrees, with a high algebraic degree, a low differential uniformity and a high nonlinearity, etc. However, it seems very difficult to find an S-box to satisfy all the criteria. The S-box of low algebraic degree is vulnerable to many attacks such as linear and differential cryptanalysis, for instance higher-order differential attacks, algebraic attacks or cube attacks. In this paper the authors propose an algorithm for improving algebraic degree of the S-box while not affecting its other important properties. The algorithm is based on affine equivalence transformation of the S-boxes.

scholarly journals Differentially low uniform permutations from known 4-uniform functions

2020 ◽  
Author(s):  
Marco Calderini
Keyword(s):  
Block Cipher ◽  
Differential Uniformity ◽  
Good Resistance ◽  
Gold Function ◽  
Differential Attacks

Abstract Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential uniformity. In particular, we give two constructions of differentially 6-uniform functions, modifying the Gold function and the Bracken–Leander function on a subfield.

scholarly journals More Low Differential Uniformity Permutations over F22k with k Odd

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yue Leng ◽  
Jinyang Chen ◽  
Tao Xie
Keyword(s):  
Block Ciphers ◽  
Algebraic Degree ◽  
Differential Uniformity ◽  
Numerical Examples ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Theoretical Results

Permutations with low differential uniformity, high algebraic degree, and high nonlinearity over F22k can be used as the substitution boxes for many block ciphers. In this paper, several classes of low differential uniformity permutations are constructed based on the method of choosing two permutations over F22k to get the desired permutations. The resulted low differential uniformity permutations have high algebraic degrees and nonlinearities simultaneously, which provide more choices for the substitution boxes. Moreover, some numerical examples are provided to show the efficacy of the theoretical results.

scholarly journals Cryptanalysis on SDDO-Based BM123-64 Designs Suitable for Various IoT Application Targets

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 353 ◽  
Author(s):  
Tran Phuc ◽  
Changhoon Lee
Keyword(s):  
Internet Of Things ◽  
High Speed ◽  
High Probability ◽  
Block Cipher ◽  
Algorithm Selection ◽  
Key Schedule ◽  
Boomerang Attack ◽  
Selection For ◽  
Differential Attacks

BM123-64 block cipher, which was proposed by Minh, N.H. and Bac, D.T. in 2014, was designed for high speed communication applications factors. It was constructed in hybrid controlled substitution–permutation network (CSPN) models with two types of basic controlled elements (CE) in distinctive designs. This cipher is based on switchable data-dependent operations (SDDO) and covers dependent-operations suitable for efficient primitive approaches for cipher constructions that can generate key schedule in a simple way. The BM123-64 cipher has advantages including high applicability, flexibility, and portability with different algorithm selection for various application targets with internet of things (IoT) as well as secure protection against common types of attacks, for instance, differential attacks and linear attacks. However, in this paper, we propose methods to possibly exploit the BM123-64 structure using related-key attacks. We have constructed a high probability related-key differential characteristics (DCs) on a full eight rounds of BM123-64 cipher. The related-key amplified boomerang attack is then proposed on all three different cases of operation-specific designs with effective results in complexity of data and time consumptions. This study can be considered as the first cryptographic results on BM123-64 cipher.

scholarly journals Complexity analysis and hardware implementation of extensible modulo addition for lightweight block cipher in Internet of Things (IOT)

2021 ◽  
Author(s):  
Sheraz Raza Siddique
Keyword(s):  
Internet Of Things ◽  
Hardware Implementation ◽  
Block Cipher ◽  
Complexity Analysis ◽  
National Security Agency ◽  
Round Function ◽  
Lightweight Block Cipher ◽  
Differential Attacks ◽  
The Internet Of Things ◽  
Feistel Structure

This project presents complexity analysis and hardware implementation of extensible modulo addition [15] encryption algorithm on a 32-bit lightweight FPGA based block cipher called INFLEX, which is designed for the internet of things (IoT) environment, supporting 64-bits key. It is designed for constrained hardware resources yet providing a highly secure scalable configuration for the variety of applications. This characteristic is obtained by the use of generalized Feistel structure combined with an improved block inflation feature. INFLEX follows a typical ARX (Add, Rotate, XOR) round function with a distinguished feature of block expansion and collapse as per user selected control string, which makes INFLEX act as a tweakable Cipher. We have shown comparison of INFLEX algorithm robustness and immunity against linear and differential attacks and demonstrated that it outperforms one of the benchmark block Ciphers Speck32/64 proposed by national security agency (NSA).

scholarly journals Provable Security Against a Differential Attack

1994 ◽  
Vol 23 (473) ◽  
Author(s):  
Kaisa Nyberg ◽  
Lars Ramkilde Knudsen
Keyword(s):  
Upper Bound ◽  
Provable Security ◽  
Block Cipher ◽  
Differential Cryptanalysis ◽  
Font Size ◽  
Differential Attack ◽  
Round Function ◽  
Differential Attacks

The purpose of this paper is to show that there exist DES-like iterated ciphers, which are provably resistant against differential attacks. The main result on the security of a DES-like cipher with independent round keys is Theorem 1, which gives an upper bound to the probability of <em>s</em>-round differentials, as defined in <em>Markov Ciphers and Differential Cryptanalysis </em> by X. Lai et al. and this upper bound depends only on the round function of the iterated cipher. Moreover, it is shown that there exist functions such that the probabilities of differentials are less than or equal to 2<sup><span style="font-size: x-small;">3-n</span></sup>, where <em>n</em> is the length of the plaintext block. We also show a prototype of an iterated block cipher, which is compatible with DES and has proven security against differential attacks.

scholarly journals Partial and Higher Order Differentials and Applications to the DES

1995 ◽  
Vol 2 (9) ◽  
Author(s):  
Lars Ramkilde Knudsen
Keyword(s):  
Block Cipher ◽  
Higher Order ◽  
Differential Attack ◽  
Running Time ◽  
Differential Attacks ◽  
Derivatives Of ◽  
Discrete Functions

In 1994 Lai considered higher order derivatives of discrete functions and<br />introduced the concept of higher order differentials. We introduce the concept<br />of partial differentials and present attacks on ciphers presumably secure<br />against differential attacks, but vulnerable to attacks using higher order and<br />partial differentials. Also we examine the DES for partial and higher order<br />differentials and give a differential attack using partial differentials on DES<br />reduced to 6 rounds using only 46 chosen plaintexts with an expected running time of about the time of 3,500 encryptions. Finally it is shown how to find a minimum nonlinear order of a block cipher using higher order differentials.

Lightweight VLSI Architectures for Image Encryption Applications

2022 ◽  
Vol 16 (1) ◽  
pp. 0-0
Keyword(s):  
Block Cipher ◽  
Wireless Sensor ◽  
Low Power Consumption ◽  
Substitution Box ◽  
Lightweight Cryptography ◽  
Vlsi Architectures ◽  
Look Up Table ◽  
Security Service ◽  
Constrained Environments ◽  
Symmetric Block

Lightweight cryptography offers significant security service in constrained environments such as wireless sensor networks and Internet of Things. The focus of this article is to construct lightweight SPN block cipher architectures with substitution box based on finite fields. The paper also details the FPGA implementation of the lightweight symmetric block cipher algorithm of SPN type with combinational S-box. Restructuring of traditional look-up-table Substitution Box (S-Box) sub-structure with a combinational logic S-box is attempted. Elementary architectures namely the basic round architecture and reduced datawidth architecture incorporating look-up-table and combinational S-Box substructure are compared in terms of area and throughput. Proposed restructure mechanism occupies less FPGA resources with no comprise in the latency and also demonstrates performance efficiency and low power consumption in Xilinx FPGAs. Robustness of the proposed method against various statistical attacks has been analyzed through comparison with other existing encryption mechanisms.

FlexAEAD v1.1 -A Lightweight AEAD Cipher with Integrated Authentication

2019 ◽  
Vol 6 (1) ◽  
pp. 15-24
Author(s):  
Eduardo Marsola do Nascimento ◽  
José Antonio Moreira Xexéo
Keyword(s):  
Block Cipher ◽  
Basic Algorithm ◽  
Resource Needs ◽  
Standardization Process ◽  
Computational Resources ◽  
Differential Attacks ◽  
Associated Data

This paperdescribes a symmetrical block cipher family – FlexAEAD v1.1. This is an updated version of the work presented as round 1 candidate on the contest for NIST lightweight crypto standardization process. It was engineered to be lightweight, consuming less computational resources than other ciphers and to work with different block and key sizes. Other important characteristic is to integrate the authentication on its basic algorithm. This approach is helps to reduce the resource needs. The algorithm capacity to resist against linear and different cryptanalysis attacks was evaluated. The FlexAEAD also supports the authentication of the Associated Data (AD). The version 1.1 makes the algorithm resistant to iterated differential attacks. It also resolves a padding attack on the AD that allowed messages to have the same tag if the last AD block was filled with zeros.

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