Algebraic techniques on searching linear diffusion layers in block cipher

2016 ◽  
Vol 9 (17) ◽  
pp. 4285-4294 ◽  
Author(s):  
Wenying Zhang ◽  
Wenyu Zhang
Keyword(s):  
Block Cipher ◽  
Linear Diffusion ◽  
Diffusion Layers

scholarly journals Design of Lightweight Linear Diffusion Layers from Near-MDS Matrices

2017 ◽  
pp. 129-155 ◽  
Author(s):  
Chaoyun Li ◽  
Qingju Wang
Keyword(s):  
Finite Fields ◽  
Lower Bounds ◽  
Hadamard Matrices ◽  
Circulant Matrices ◽  
Linear Cryptanalysis ◽  
Implementation Cost ◽  
Linear Diffusion ◽  
Diffusion Layers ◽  
Nonlinear Layer ◽  
Trade Offs

Near-MDS matrices provide better trade-offs between security and efficiency compared to constructions based on MDS matrices, which are favored for hardwareoriented designs. We present new designs of lightweight linear diffusion layers by constructing lightweight near-MDS matrices. Firstly generic n×n near-MDS circulant matrices are found for 5 ≤ n ≤9. Secondly, the implementation cost of instantiations of the generic near-MDS matrices is examined. Surprisingly, for n = 7, 8, it turns out that some proposed near-MDS circulant matrices of order n have the lowest XOR count among all near-MDS matrices of the same order. Further, for n = 5, 6, we present near-MDS matrices of order n having the lowest XOR count as well. The proposed matrices, together with previous construction of order less than five, lead to solutions of n×n near-MDS matrices with the lowest XOR count over finite fields F2m for 2 ≤ n ≤ 8 and 4 ≤ m ≤ 2048. Moreover, we present some involutory near-MDS matrices of order 8 constructed from Hadamard matrices. Lastly, the security of the proposed linear layers is studied by calculating lower bounds on the number of active S-boxes. It is shown that our linear layers with a well-chosen nonlinear layer can provide sufficient security against differential and linear cryptanalysis.

Several Properties of Binary Diffusion Layers for Block Cipher

2012 ◽  
Vol 23 (9) ◽  
pp. 2430-2437 ◽  
Author(s):  
Ting CUI ◽  
He-Shan CHEN ◽  
Chen-Hui JIN
Keyword(s):  
Block Cipher ◽  
Binary Diffusion ◽  
Diffusion Layers

Randomized nonlinear software-oriented MDS diffusion layers

2019 ◽  
Vol 11 (2) ◽  
pp. 123-131
Author(s):  
Mohammad Reza Mirzaee Shamsabad ◽  
Seyed Mojtaba Dehnavi ◽  
Akbar Mahmoodi Rishakani
Keyword(s):  
Algebraic Structures ◽  
Linear Diffusion ◽  
Diffusion Layers ◽  
Symmetric Ciphers ◽  
Critical Components ◽  
Theoretical Results

Abstract MDS diffusion layers are critical components in the design of symmetric ciphers. In this paper, after introducing some new algebraic structures, we provide new MDS matrices over special types of R-modules. With the help of the proposed methodology, we have more flexibility in designing software-oriented diffusion layers. Most notably, we construct randomized and/or nonlinear MDS diffusion layers, based upon the presented theoretical results, and discuss the resistance of the presented diffusion layers against various kinds of cryptanalysis, compared with classical linear diffusion layers.

A Method to Bound the Number of Active S-Boxes for a Kind of AES-Like Structure

2019 ◽  
Vol 62 (8) ◽  
pp. 1121-1131
Author(s):  
Qian Wang ◽  
Chenhui Jin
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Hash Function ◽  
High Performance ◽  
Block Cipher ◽  
Hash Functions ◽  
Theoretical Method ◽  
Building Blocks ◽  
Branch Number ◽  
Diffusion Layers

AbstractDue to the strong security and high performance of the AES block cipher, many hash functions take AES-like structures as building blocks. To evaluate the security of these AES-like structures against differential cryptanalysis, giving the lower bounds on the number of active S-boxes in a differential trail, is an important perspective. However, the original ‘wide-trail strategy’ for AES becomes less effective to get tight bounds for these AES-like structures, because of the different state dimensions (M×M2, instead of M×M) and different round functions from AES. In this paper, we focus on a kind of AES-like structure with state dimensions M×M2, diffusion-optimal permutations and MixColumns transformations using MDS matrices. Inspired by the ‘wide-trail strategy’, we propose a theoretical method to count active S-boxes, by which we prove that there are at least rBd(Bd−1) active S-boxes in any 2r(r≥3) rounds of such an AES-like structure, where Bd is the differential branch number of the MixColumns transformation and equals to M+1. What’s more, this lower bound can be achieved by some diffusion layers. As examples, we apply our method to the LANE hash function and 3D block cipher, optimal lower bounds are both got.

scholarly journals Beyond-Birthday-Bound Security for 4-round Linear Substitution-Permutation Networks

2020 ◽  
pp. 305-326
Author(s):  
Yuan Gao ◽  
Chun Guo ◽  
Meiqin Wang ◽  
Weijia Wang ◽  
Jiejing Wen
Keyword(s):  
Real World ◽  
Provable Security ◽  
Linear Diffusion ◽  
Popular Approach ◽  
Diffusion Layers ◽  
Linear Substitution ◽  
Non Linear ◽  
Beyond Birthday Bound ◽  
Permutation Networks

Recent works of Cogliati et al. (CRYPTO 2018) have initiated provable treatments of Substitution-Permutation Networks (SPNs), one of the most popular approach to construct modern blockciphers. Such theoretical SPN models may employ non-linear diffusion layers, which enables beyond-birthday-bound provable security. Though, for the model of real world blockciphers, i.e., SPN models with linear diffusion layers, existing provable results are capped at birthday security up to 2n/2 adversarial queries, where n is the size of the idealized S-boxes.In this paper, we overcome this birthday barrier and prove that a 4-round SPN with linear diffusion layers and independent round keys is secure up to 22n/3 queries. For this, we identify conditions on the linear layers that are sufficient for such security, which, unsurprisingly, turns out to be slightly stronger than Cogliati et al.’s conditions for birthday security. These provides additional theoretic supports for real world SPN blockciphers.

scholarly journals Compact Implementation of ARIA on 16-Bit MSP430 and 32-Bit ARM Cortex-M3 Microcontrollers

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 908
Author(s):  
Hwajeong Seo ◽  
Hyunjun Kim ◽  
Kyoungbae Jang ◽  
Hyeokdong Kwon ◽  
Minjoo Sim ◽  
...  
Keyword(s):  
Block Cipher ◽  
Memory Access ◽  
Security Level ◽  
The Novel ◽  
Pipeline Architecture ◽  
Diffusion Layers ◽  
Mode Of Operation ◽  
Memory Accesses ◽  
And Diffusion ◽  
Code Book

In this paper, we propose the first ARIA block cipher on both MSP430 and Advanced RISC Machines (ARM) microcontrollers. To achieve the optimized ARIA implementation on target embedded processors, core operations of ARIA, such as substitute and diffusion layers, are carefully re-designed for both MSP430 (Texas Instruments, Dallas, TX, USA) and ARM Cortex-M3 microcontrollers (STMicroelectronics, Geneva, Switzerland). In particular, two bytes of input data in ARIA block cipher are concatenated to re-construct the 16-bit wise word. The 16-bit word-wise operation is executed at once with the 16-bit instruction to improve the performance for the 16-bit MSP430 microcontroller. This approach also optimizes the number of required registers, memory accesses, and operations to half numbers rather than 8-bit word wise implementations. For the ARM Cortex-M3 microcontroller, the 8×32 look-up table based ARIA block cipher implementation is further optimized with the novel memory access. The memory access is finely scheduled to fully utilize the 3-stage pipeline architecture of ARM Cortex-M3 microcontrollers. Furthermore, the counter (CTR) mode of operation is more optimized through pre-computation techniques than the electronic code book (ECB) mode of operation. Finally, proposed ARIA implementations on both low-end target microcontrollers (MSP430 and ARM Cortex-M3) achieved (209 and 96 for 128-bit security level, respectively), (241 and 111 for 192-bit security level, respectively), and (274 and 126 for 256-bit security level, respectively). Compared with previous works, the running timing on low-end target microcontrollers (MSP430 and ARM Cortex-M3) is improved by (92.20% and 10.09% for 128-bit security level, respectively), (92.26% and 10.87% for 192-bit security level, respectively), and (92.28% and 10.62% for 256-bit security level, respectively). The proposed ARIA–CTR implementation improved the performance by 6.6% and 4.0% compared to the proposed ARIA–ECB implementations for MSP430 and ARM Cortex-M3 microcontrollers, respectively.

scholarly journals Lightweight and Side-channel Secure 4 × 4 S-Boxes from Cellular Automata Rules

2018 ◽  
pp. 311-334
Author(s):  
Ashrujit Ghoshal ◽  
Rajat Sadhukhan ◽  
Sikhar Patranabis ◽  
Nilanjan Datta ◽  
Stjepan Picek ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Low Cost ◽  
Building Blocks ◽  
Block Ciphers ◽  
Side Channel ◽  
Design Strategies ◽  
Cryptographic Primitives ◽  
Linear Diffusion ◽  
Low Area ◽  
Diffusion Layers

This work focuses on side-channel resilient design strategies for symmetrickey cryptographic primitives targeting lightweight applications. In light of NIST’s lightweight cryptography project, design choices for block ciphers must consider not only security against traditional cryptanalysis, but also side-channel security, while adhering to low area and power requirements. In this paper, we explore design strategies for substitution-permutation network (SPN)-based block ciphers that make them amenable to low-cost threshold implementations (TI) - a provably secure strategy against side-channel attacks. The core building blocks for our strategy are cryptographically optimal 4×4 S-Boxes, implemented via repeated iterations of simple cellular automata (CA) rules. We present highly optimized TI circuits for such S-Boxes, that consume nearly 40% less area and power as compared to popular lightweight S-Boxes such as PRESENT and GIFT. We validate our claims via implementation results on ASIC using 180nm technology. We also present a comparison of TI circuits for two popular lightweight linear diffusion layer choices - bit permutations and MixColumns using almost-maximum-distance-separable (almost-MDS) matrices. We finally illustrate design paradigms that combine the aforementioned TI circuits for S-Boxes and diffusion layers to obtain fully side-channel secure SPN block cipher implementations with low area and power requirements.

A novel cryptosystem based on abstract automata and Latin cubes

2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth
Keyword(s):  
Block Cipher ◽  
Finite Automata ◽  
Theoretical Background ◽  
Point Of View ◽  
Theoretical Point ◽  
Transition Matrices ◽  
Encryption And Decryption ◽  
Secret Keys ◽  
Automata Network ◽  
Fully Functioning

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.

A Chaos-Based Approach for Correcting the Security Level of a Block Cipher Algorithm

2016 ◽  
Vol 11 (2) ◽  
pp. 92
Author(s):  
Fatma Zayen Sbiaa ◽  
Medien Zeghid ◽  
Sonia Kotel ◽  
Rached Tourki ◽  
Mohsen Machhout ◽  
...  
Keyword(s):  
Block Cipher ◽  
Security Level
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