Scalable method of searching for full-period Nonlinear Feedback Shift Registers with GPGPU. New List of Maximum Period NLFSRs.

This paper addresses the problem of efficient searching for Nonlinear Feedback Shift Registers (NLFSRs) with a guaranteed full period. The maximum possible period for an $n$-bit NLFSR is $2^n-1$ (all-zero state is omitted). %but omitting all-0 state makes the period $2^n-1$ in their longest cycle of states. A multi-stages hybrid algorithm which utilizes Graphics Processor Units (GPU) power was developed for processing data-parallel throughput computation.Usage of abovementioned algorithm allows to give an extended list of n-bit NLFSR with maximum period for 7 cryptographically applicable types of feedback functions

Optimizations and Hardware Implementations for Composited de Bruijn Sequence Generators

A binary de Bruijn sequence with period 2^n is a sequence in which every length-n sub-sequence occurs exactly once. de Bruijn sequences have randomness properties that make them attractive for pseudorandom number generators. Unfortunately, it is very difficult to find de Bruijn sequence generators with large periods (e.g., 2^{64}) and most known de Bruijn sequence construction techniques are computationally quite expensive. In this thesis we present a set of optimizations that reduces the computational complexity of the de Bruijn sequence generators constructed by the composited construction technique, which is the most effective one we know. We call optimized composited de Bruijn sequence generators "OcDeb". An original (k, n)-composited de Bruijn sequence generator generates a sequence with period 2^{n+k} and uses O(k^2 + nk) bit operations. Our optimizations reduce this to O(klog (k) + log (n)) operations, allow retiming, and enable parallel implementations that produce multiple bits per clock cycle while reusing some combinational hardware. Our optimizations are formulated in lemmas and theorems with proofs. The benefits of OcDeb-k-n over (k, n)-composited de Bruijn sequence generators are demonstrate by comprehensive results in a 65nm CMOS ASIC library. For example, before place-and-route, an instance of OcDeb-32-32 has a period of 2^{64}, an area of 656 GE and a maximum performance of 1.67 Gbps, representing 1.7X and 29.4X improvement on area and performance respectively over the previous implementation method presented by Mandal and Gong; with parallelization, this instance can achieve 8.30 Gbps with an area of 1229 GE. An instance of OcDeb-512-32 has a period of 2^{544}, an area of 7949 GE, and a maximum performance of 1.43 Gbps

Design and Analysis of Cryptographic Pseudorandom Number/Sequence Generators with Applications in RFID

This thesis is concerned with the design and analysis of strong de Bruijn sequences and span n sequences, and nonlinear feedback shift register (NLFSR) based pseudorandom number generators for radio frequency identification (RFID) tags. We study the generation of span n sequences using structured searching in which an NLFSR with a class of feedback functions is employed to find span n sequences. Some properties of the recurrence relation for the structured search are discovered. We use five classes of functions in this structured search, and present the number of span n sequences for 6 <= n <= 20. The linear span of a new span n sequence lies between near-optimal and optimal. According to our empirical studies, a span n sequence can be found in the structured search with a better probability of success. Newly found span n sequences can be used in the composited construction and in designing lightweight pseudorandom number generators. We first refine the composited construction based on a span n sequence for generating long de Bruijn sequences. A de Bruijn sequence produced by the composited construction is referred to as a composited de Bruijn sequence. The linear complexity of a composited de Bruijn sequence is determined. We analyze the feedback function of the composited construction from an approximation point of view for producing strong de Bruijn sequences. The cycle structure of an approximated feedback function and the linear complexity of a sequence produced by an approximated feedback function are determined. A few examples of strong de Bruijn sequences with the implementation issues of the feedback functions of an (n+16)-stage NLFSR are presented. We propose a new lightweight pseudorandom number generator family, named Warbler family based on NLFSRs for smart devices. Warbler family is comprised of a combination of modified de Bruijn blocks (CMDB) and a nonlinear feedback Welch-Gong (WG) generator. We derive the randomness properties such as period and linear complexity of an output sequence produced by the Warbler family. Two instances, Warbler-I and Warbler-II, of the Warbler family are proposed for passive RFID tags. The CMDBs of both Warbler-I and Warbler-II contain span n sequences that are produced by the structured search. We analyze the security properties of Warbler-I and Warbler-II by considering the statistical tests and several cryptanalytic attacks. Hardware implementations of both instances in VHDL show that Warbler-I and Warbler-II require 46 slices and 58 slices, respectively. Warbler-I can be used to generate 16-bit random numbers in the tag identification protocol of the EPC Class 1 Generation 2 standard, and Warbler-II can be employed as a random number generator in the tag identification as well as an authentication protocol for RFID systems.1 yea

Grein. A New Non-Linear Cryptoprimitive

In this thesis, we will study a new stream cipher, Grein, and a new cryptoprimitive used in this cipher. The second chapter gives a brief introduction to cryptography in general. The third chapter looks at stream ciphers in general, and explains the advantages and disadvantages of stream ciphers compared to block ciphers. In the fourth chapter the most important building blocks used in stream ciphers are explained. The reader is excepted to know elementary abstract algebra, as much of the results in this chapter depend on it. In the fifth chapter, the stream cipher Grain is introduced. In chapter six, the new stream cipher, Grein, is introduced. Here, we look at the different components used in the cipher, and how they operate together. In chapter seven, we introduce an alteration to the Grein cryptosystem, which hopefully have some advantagesMaster i InformatikkMAMN-INFINF39

On cross joining de Bruijn sequences

We explain the origins of Boolean feedback functions of nonlinear feedback shift registers (NLFSRs) of fixed order n generating de Bruijn binary sequences. They all come into existence by cross joining operations starting from one maximum period feedback shift register, e.g., a linear one which always exists for any order n. The result obtained yields some constructions of NLFSRs generating maximum period $2^n-1$ binary sequences

New Family of Stream Ciphers as Physically Clone-Resistant VLSI-Structures

A new large class of $2^{100}$ possible stream ciphers as keystream generators KSGs, is presented. The sample cipher-structure-concept is based on randomly selecting a set of 16 maximum-period Nonlinear Feedback Shift Registers (NLFSRs). A non-linear combining function is merging the 16 selected sequences. All resulting stream ciphers with a total state-size of 223 bits are designed to result with the same security level and have a linear complexity exceeding $2^{81}$ and a period exceeding $2^{161}$. A Secret Unknown Cipher (SUC) is created randomly by selecting one cipher from that class of $2^{100}$ ciphers. SUC concept was presented recently as a physical security anchor to overcome the drawbacks of the traditional analog Physically Unclonable Functions (PUFs). Such unknown ciphers may be permanently self-created within System-on-Chip SoC non-volatile FPGA devices to serve as a digital clone-resistant structure. Moreover, a lightweight identification protocol is presented in open networks for physically identifying such SUC structures in FPGA-devices. The proposed new family may serve for lightweight realization of clone-resistant identities in future self-reconfiguring SoC non-volatile FPGAs. Such self-reconfiguring FPGAs are expected to be emerging in the near future smart VLSI systems. The security analysis and hardware complexities of the resulting clone-resistant structures are evaluated and shown to exhibit scalable security levels even for post-quantum cryptography.Comment: 24 pages, 7 Figures, 3 Table

Parallel generation of c[r]yptographically strong pseudo-random sequences

The operational disadvantages of perfectly secure cipher systems has led to the development of practically secure stream cipher systems. The security of such cipher systems depend on the strength of the keystream. In order to examine the strength of a sequence two different types of criteria are considered. Statistical tests, are designed to assess how a sequence with a particular property behaves randomly. Complexity measures, are applied to determine the complexity, or equivalently the unpredictability of a sequence. Sequences obtained by LFSR are considered as building blocks of pseudo-random (PR) sequence generators. Transformations on the decimal expansion of irrational numbers is an alternative method for generating PR sequences, which are studied and some encouraging results are reported