Constructing de Bruijn Sequences Based on a New Necessary Condition

2020 ◽  
Vol 31 (03) ◽  
pp. 301-312
Author(s):  
Zhongxiao Wang ◽  
Xiangyu Wang ◽  
Tian Tian
Keyword(s):  
Necessary Condition ◽  
State Graph ◽  
Nonlinear Feedback ◽  
Conjugate State ◽  
De Bruijn Sequences ◽  
State Formula ◽  
Nonlinear Feedback Shift Register ◽  
Feedback Shift Register ◽  
De Bruijn ◽  
Special Cycle

In this paper, we propose a new necessary condition for feedback functions of de Bruijn sequences and discuss its application in constructing de Bruijn sequences. It is shown that a large number of de Bruijn sequences could be easily constructed by precomputing an [Formula: see text]-stage nonlinear feedback shift register (NFSR) with a special cycle structure—that is, if a state [Formula: see text] is on a cycle generated by this NFSR, then all the states with the same Hamming weight as [Formula: see text] are also on this cycle. Moreover, if there are [Formula: see text] different cycles in the state graph of the precomputed NFSR, then we can construct [Formula: see text] de Bruijn sequences by the different choices of conjugate state pairs, where [Formula: see text].

On Equivalence of Cascade Connections of Two Nonlinear Feedback Shift Registers

2019 ◽  
Vol 62 (12) ◽  
pp. 1793-1804
Author(s):  
Jianghua Zhong ◽  
Dongdai Lin
Keyword(s):  
Stream Ciphers ◽  
Nonlinear Feedback ◽  
Stage Number ◽  
State Diagrams ◽  
Hardware Implementations ◽  
Cascade Connection ◽  
N Stage ◽  
Nonlinear Feedback Shift Register ◽  
Nonlinear Feedback Shift Registers ◽  
Feedback Shift Register

Abstract Grain is a hardware-oriented finalist in the eSTREAM Stream Cipher Project. As a particular Galois nonlinear feedback shift register (NFSR), cascade connection of two NFSRs has been used as the main building block in the Grain family of stream ciphers. Two NFSRs are said to be equivalent if their sets of output sequences are equal. Finding properties of equivalent cascade connections of two NFSRs is useful to the design of the Grain family of stream ciphers. This paper first gives some properties of feedback functions between equivalent cascade connections of two NFSRs. It then shows that a cascade connection of two NFSRs and its equivalent Galois NFSR have isomorphic state diagrams if they have the same stage number. Finally, the paper reveals that for any given cascade connection of an $m$-stage NFSR1 into an $n$-stage NFSR2, there is only another one equivalent cascade connection of an $m$-stage NFSR3 into an $n$-stage NFSR4; moreover, the feedback functions of NFSR1 and NFSR3 are dual complementary, and the feedback functions of NFSR2 and NFSR4 are complementary. As an application of this property, the paper shows that the existing Grain family of stream ciphers have used the ones with lower cost of hardware implementations between their own two equivalent cascade connections, confirming their good design criteria.

scholarly journals Improved Conditional Differential Analysis on NLFSR-Based Block Cipher KATAN32 with MILP

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhaohui Xing ◽  
Wenying Zhang ◽  
Guoyong Han
Keyword(s):  
Mixed Integer Linear Programming ◽  
Time Complexity ◽  
Block Cipher ◽  
Mixed Integer ◽  
Differential Analysis ◽  
Nonlinear Feedback ◽  
Key Recovery ◽  
Nonlinear Feedback Shift Register ◽  
Feedback Shift Register ◽  
Key Recovery Attacks

In this paper, a new method for constructing a Mixed Integer Linear Programming (MILP) model on conditional differential cryptanalysis of the nonlinear feedback shift register- (NLFSR-) based block ciphers is proposed, and an approach to detecting the bit with a strongly biased difference is provided. The model is successfully applied to the block cipher KATAN32 in the single-key scenario, resulting in practical key-recovery attacks covering more rounds than the previous. In particular, we present two distinguishers for 79 and 81 out of 254 rounds of KATAN32. Based on the 81-round distinguisher, we recover 11 equivalent key bits of 98-round KATAN32 and 13 equivalent key bits of 99-round KATAN32. The time complexity is less than 2 31 encryptions of 98-round KATAN32 and less than 2 33 encryptions of 99-round KATAN32, respectively. Thus far, our results are the best known practical key-recovery attacks for the round-reduced variants of KATAN32 regarding the number of rounds and the time complexity. All the results are verified experimentally.

Novel way to research nonlinear feedback shift register

2014 ◽  
Vol 57 (9) ◽  
pp. 1-14 ◽  
Author(s):  
DaWei Zhao ◽  
HaiPeng Peng ◽  
LiXiang Li ◽  
SiLi Hui ◽  
YiXian Yang
Keyword(s):  
Shift Register ◽  
Nonlinear Feedback ◽  
Nonlinear Feedback Shift Register ◽  
Feedback Shift Register

Generation of special form shift registers using a dedicated software platform

2019 ◽  
Vol 7 (25) (1-2) ◽  
pp. 25-34
Author(s):  
Paweł Augustynowicz
Keyword(s):  
Special Form ◽  
Heterogeneous Environments ◽  
Nonlinear Feedback ◽  
Unified Framework ◽  
The Core ◽  
Unified Algorithm ◽  
Nonlinear Feedback Shift Register ◽  
Nonlinear Feedback Shift Registers ◽  
Feedback Shift Register ◽  
Feedback Shift Registers

This article describes crucial functionalities of a Unified Framework for Nonlinear Feedback Shift Register Generation (UFfNG). The core of UFfNG framework is a unified algorithm for Nonlinear Feedback Shift Registers (NLFSR) enumeration which can be effectively implemented in heterogeneous environments including CPUs, GPUs and FPGAs. For the sake of completeness, implementation and efficiency results for each platform are discussed and presented.

Sign in / Sign up

Export Citation Format

Share Document