Noisy Bits Research Articles

Hybrid Boolean Networks as Physically Unclonable Functions

We introduce a Physically Unclonable Function (PUF) based on an ultra-fast chaotic network known as a Hybrid Boolean Network (HBN) implemented on a field programmable gate array. The network, consisting of N coupled asynchronous logic gates displaying dynamics on the sub-nanosecond time scale, acts as a `digital fingerprint' by amplifying small manufacturing variations during a period of transient chaos. In contrast to other PUF designs, we use both N-bits per challenge and obtain N-bits per response by considering challenges to be initial states of the N-node network and responses to be states captured during the subsequent chaotic transient. We find that the presence of chaos amplifies the frozen-in randomness due to manufacturing differences and that the extractable entropy is approximately 50% of the maximum of N2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> bits. We obtain PUF uniqueness and reliability metrics μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inter</sub> = 0.40±0.01 and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intra</sub> = 0.05±0.00, respectively, for an N=256 network. These metrics correspond to an expected Hamming distance of 102.4 bits per response. Moreover, a simple cherry-picking scheme that discards noisy bits yields μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intra</sub> <; 0.01 while still retaining ~ 200 bits/response (corresponding to a Hamming distance of ~ 80 bits/response). In addition to characterizing the uniqueness and reliability, we demonstrate super-exponential scaling in the entropy up to N=512 and demonstrate that PUFmeter, a recent PUF analysis tool, is unable to model our PUF. Finally, we characterize the temperature variation of the HBN-PUF and propose future improvements.

Fast Frequency Sweep Analysis of Passive Miniature RF Circuits Based on Analytic Extension of Eigenvalues

The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with $4$-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the Successive Cancellation List (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by 0.15dB--0.3dB when we use CRC-aided SCL decoder with list size $32$ for both codes. The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar

Keep it Unsupervised: Horizontal Attacks Meet Deep Learning

To mitigate side-channel attacks, real-world implementations of public-key cryptosystems adopt state-of-the-art countermeasures based on randomization of the private or ephemeral keys. Usually, for each private key operation, a “scalar blinding” is performed using 32 or 64 randomly generated bits. Nevertheless, horizontal attacks based on a single trace still pose serious threats to protected ECC or RSA implementations. If the secrets learned through a single-trace attack contain too many wrong (or noisy) bits, the cryptanalysis methods for recovering remaining bits become impractical due to time and computational constraints. This paper proposes a deep learning-based framework to iteratively correct partially correct private keys resulting from a clustering-based horizontal attack. By testing the trained network on scalar multiplication (or exponentiation) traces, we demonstrate that a deep neural network can significantly reduce the number of wrong bits from randomized scalars (or exponents).When a simple horizontal attack can recover around 52% of attacked multiple private key bits, the proposed iterative framework improves the private key accuracy to above 90% on average and to 100% for at least one of the attacked keys. Our attack model remains fully unsupervised and excludes the need to know where the error or noisy bits are located in each separate randomized private key.

The Complexity of Bit Retrieval

Bit retrieval is the problem of reconstructing a periodic binary sequence from its periodic autocorrelation, with applications in cryptography and x-ray crystallography. After defining the problem, with and without noise, we describe and compare various algorithms for solving it. A geometrical constraint satisfaction algorithm, relaxed-reflect-reflect, is currently the best algorithm for noisy bit retrieval.

An efficient algorithm for the reconstruction of punctured convolutional codes

Puncturing is one of the methods of increasing the code rate, and the original code before puncturing is called the mother code. Any (N,K) convolutional code is obtainable by puncturing some (n,1) mother codes. The objective of a blind recognition of a channel code is to obtain its generator from the intercepted noisy bit stream. The process of the blind recognition of punctured convolutional codes consists of two parts: the reconstruction of the PGM of the (N,K) punctured convolutional code and the searching process of the mother code and its puncturing pattern. The process of finding the mother code is important for designing the optimum channel decoder. In this paper, a new searching algorithm with the computational complexity of O(K4) polynomial operations is proposed, compared to the existing searching algorithm by M. Cluzeau which requires O(K6) polynomial operations.

A robust algorithm for analysis of intercepted HF traffic under noisy environment

The aim of this paper is to introduce a novel algorithm for retrieval of information from noisy intercepted traffic. The design considerations for HF protocol along with its simulation are elaborated. The main contribution of our research work is proposal for novel method for recovery information from a partially decoded noisy bit stream for HF protocols. Statistical properties of language such as unigram, bigram, trigram frequency have been exploited for design of cost function. Also, histogram analysis along with mean and variance statistics of language are extracted and used for design of another cost function. In our proposed analysis algorithm these cost functions are used for automatic analysis of recorded baseband protocols. The algorithm for automatic estimation of non-standard parameters such as baud rate, data format is proposed. The results and analysis of proposed algorithms are discussed for simulated HF protocol recordings.

A robust algorithm for analysis of intercepted HF traffic under noisy environment

The aim of this paper is to introduce a novel algorithm for retrieval of information from noisy intercepted traffic. The design considerations for HF protocol along with its simulation are elaborated. The main contribution of our research work is proposal for novel method for recovery information from a partially decoded noisy bit stream for HF protocols. Statistical properties of language such as unigram, bigram, trigram frequency have been exploited for design of cost function. Also, histogram analysis along with mean and variance statistics of language are extracted and used for design of another cost function. In our proposed analysis algorithm these cost functions are used for automatic analysis of recorded baseband protocols. The algorithm for automatic estimation of non-standard parameters such as baud rate, data format is proposed. The results and analysis of proposed algorithms are discussed for simulated HF protocol recordings.

Shape adaptive, robust iris feature extraction from noisy iris images

In the current iris recognition systems, noise removing step is only used to detect noisy parts of the iris region and features extracted from there will be excluded in matching step. Whereas depending on the filter structure used in feature extraction, the noisy parts may influence relevant features. To the best of our knowledge, the effect of noise factors on feature extraction has not been considered in the previous works. This paper investigates the effect of shape adaptive wavelet transform and shape adaptive Gabor-wavelet for feature extraction on the iris recognition performance. In addition, an effective noise-removing approach is proposed in this paper. The contribution is to detect eyelashes and reflections by calculating appropriate thresholds by a procedure called statistical decision making. The eyelids are segmented by parabolic Hough transform in normalized iris image to decrease computational burden through omitting rotation term. The iris is localized by an accurate and fast algorithm based on coarse-to-fine strategy. The principle of mask code generation is to assign the noisy bits in an iris code in order to exclude them in matching step is presented in details. An experimental result shows that by using the shape adaptive Gabor-wavelet technique there is an improvement on the accuracy of recognition rate.

A new accurate noise-removing approach for non-cooperative iris recognition

The applications of biometric technology for automated personal identification become ubiquitous. Iris recognition is well known for high accuracy and reliability among the biometric traits. This paper presents an efficient noise-removing approach for non-cooperative iris recognition systems. Proposed method removed the noise factors including eyelids, eyelashes, reflections, out of framework, pupil and sclera. The novelty is to detect eyelashes and reflections through finding appropriate thresholds using a procedure called statistical decision making. The eyelids are detected using parabolic Hough transform in normalized iris image to increase computational speed. In addition, a coarse-to-fine strategy for accurate and fast iris localization is proposed. The Gabor-wavelet and a novel encoding strategy proposed in our previous work are also used here to generate the iris codes. We elaborate the principle of mask code generation to assign noisy bits in an iris code to exclude them in matching step. Experimental results on CASIA-IrisV3-Interval database show superiority of the proposed scheme among other state-of-the-art methods available in the literature.

On Extracting Common Random Bits From Correlated Sources

Suppose Alice and Bob receive strings of unbiased independent but noisy bits from some random source. They wish to use their respective strings to extract a common sequence of random bits with high probability but without communicating. How many such bits can they extract? The trivial strategy of outputting the first <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex> </formula> bits yields an agreement probability of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(1-\varepsilon)^{k}&lt;2^{-1.44k\varepsilon}$</tex></formula> , where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\varepsilon$</tex> </formula> is the amount of noise. We show that no strategy can achieve agreement probability better than <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$2^{-k\varepsilon/(1-\varepsilon)}$</tex> </formula> .

A new image compression method using noise bit removal

For communication and storage efficiency, image data should be substantially compressed. The compression ratio is limited by noise, which degrades the correlation between pixels. Due to the statistical nature of X-rays and the electromagnetic field, medical images are contaminated with random noise. Because of this effect, considerable effort has been devoted to remove noise from medical images. In this study, we use standard deviation to evaluate the noise level and subsequently estimate the number of noisy bits for each pixel. By discarding these noisy bits, the compression ratio can be improved. This method was verified using a synthetic digital image and tested in various radiological image modalities. This technique can increase the ratio up to 3.9 for MRI from 2.5 without significantly affecting the image quality. This process will have a great impact on storage reduction, transmission rate and the speed of image display and manipulation.