Near-zero Correlation Research Articles

Image Encryption Using High-Speed Scrambling and ‎Modular Arithmetic

With the enormous growth and advancement of the computer industry, it is critically necessary to transmit a large amount of encrypted multimedia data to prevent third parties from attacking one's privacy or misbehaving. This study proposes a new encryption strategy for preserving original images. It is highly effective and has been shown to be resilient against impulsive noise and loss of data. At first, some random data is entered within the perimeter of the image. Then, three rounds of high-speed scrambling and adaptive diffusion for pixels are carried out to mix the contiguous pixels at random and distribute the newly placed data throughout the image. The suggested encryption method can be used to encrypt original images in any form of representation directly. We offer a particular operation to carry out adaptive diffusion for pixel modulo arithmetic. The results of encryption are evaluated using the histogram, which shows a near-zero correlation with a Number of Pixel Change Rate (NPCR) of 099.624, a Unified Average Change Intensity (UACI) of 033.577, and an average entropy of 7.9993. The proposed method can accomplish much better speed and adapt better to impulse noise and loss of data interference than several conventional and cutting-edge encryption methods.

Correlation models for next-generation amplitude and cumulative intensity measures using artificial neural networks

Various next-generation intensity measures (IMs) have emerged in recent years. For instance, filtered incremental velocity, FIV3, was shown to be efficient in predicting the collapse of structures, or average spectral acceleration, Saavg, shown to be well-correlated with a wide range of response, from initiation of structural damage yielding to structural collapse. Different ground motion models (GMMs) are available to predict the probabilistic distribution of these IMs, given a set of seismological parameters. Nonetheless, a few key correlation models are still missing in the literature, which are elemental for a more holistic approach to ground motion record selection. These models are vital when performing seismic hazard analysis and ground motion record selection using state-of-the-art approaches like the conditional spectrum or generalized conditional intensity measure (GCIM) methods. This study uses a single machine-learning-based generalized ground motion model (GGMM) to estimate all the IMs. The model is based on the Next-Generation Attenuation (NGA)-West2 database and was utilized to quantify the correlations between the residuals. Correlations were calculated for intra- and inter-event residuals, but only those for total residuals are presented here, given their utility. Since the calculation of residuals comes from the same GMM and the same database of ground motions, this produces more consistent correlation coefficients between all IMs. To facilitate the usage of these correlation coefficients, predictive models of the empirical data were developed using machine-learning-based techniques, namely artificial neural networks (ANNs). It was found that FIV3 is strongly correlated with Sa(~1 s) and itself across all periods and has a weak negative correlation with duration at short periods and near-zero correlation for longer periods. Also, a stronger negative correlation between Sa and significant duration was found, compared with other prominent existing models. Direct correlation models between Sa and Saavg are also proposed.

A chaotic based image encryption scheme using elliptic curve cryptography and genetic algorithm

In the era of digital communication and data security, image encryption plays a crucial role in safeguarding sensitive information. Protecting sensitive visual data from unauthorized access drives the pursuit of advanced image encryption methods. This paper proposes a novel approach to enhance image encryption by combining the power of a chaotic map, elliptic curve cryptography, and genetic algorithm. The chaotic map, specifically Arnold’s cat map, is employed to introduce chaos and randomness into the encryption process. The proposed image encryption process involves applying Arnold’s cat map for shuffling the pixel positions, followed by elliptic curve cryptography for encrypting the pixel values using public and private keys. Additionally, a genetic algorithm is employed to optimize the key generation process, enhancing the security of the encryption scheme. The combined utilization of these techniques aims to achieve a high level of confidentiality and robustness in image encryption. The algorithm underwent thorough analysis. It achieved a maximum entropy score of 7.99, indicating a high level of randomness and unpredictability in the encrypted data. Additionally, it exhibited near-zero correlation, which suggests strong resistance against statistical attacks. Moreover, the cryptographic range of possible keys was found to be 2511\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{511}$$\\end{document}. This extensive key space makes the algorithm highly resilient against brute force attacks. It took only 0.5634 s to encrypt a moderately sized 512×512\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$512\ imes 512$$\\end{document} pixel image with an 8-bit image on a standard desktop computer with a 2.3 GHz processor and 16 GB of RAM. The experimental findings confirm that the proposed approach is highly effective and efficient in safeguarding sensitive image data from unauthorized access and potential attacks. This scheme has the benefit of allowing us to protect our private image data while it’s being transmitted.

Balanced Encoding of Near-Zero Correlation for an AES Implementation

Balanced Encoding of Near-Zero Correlation for an AES Implementation

Duple Color Image Encryption System Based on 3-D Nonequilateral Arnold Transform for IIoT

The Industrial Internet of Things (IIoT) is to continuously integrate network communication, intelligent analysis and other technologies into every link of the industrial production process, thus greatly improving the manufacturing efficiency. While such systems greatly improve the productivity of the industry, they introduce major safety challenges during the design and operational phases. Therefore, it is necessary to encrypt and protect the information transmitted by the system during the design and runtime stages. This paper focuses on the transmission security of image data in every link of IIoT. Two color images that need to be transmitted can be encrypted into color ciphertext image by using 3D Non-equilateral Arnold Transform (3D-NEAT) and 3D Lorenz System (3D-LS). Different from the traditional algorithm which encrypts one plain image into one ciphertext image, our algorithm encrypts two color images into one color ciphertext image which will cause great confusion to the attacker whom illegally breaks the ciphertext image. First, the proposed method converts two color images with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N\times M$</tex-math></inline-formula> into a 3D bit-level matrix with size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N\times M\times 48$</tex-math></inline-formula> . Next, 3D-NEAT is applied to permutate the positions of the elements of the resulted 3D bit-level matrix. Then, the permutated 3D bit-level matrix is transformed into three 2D pixel-level images and then diffused by the random diffusion sequences which 3D-LS generates. Finally, the scrambling matrices generated by 3D-LS are used to scramble three diffused 2D pixel-level images and the output is considered as three color components of the encrypted image. The numerical experiments and security analysis show that the proposed image encryption scheme has strong resistance to several known attacks, and yields near-zero correlation and near-eight entropy for the RGB cipher image, and some performance is better than some of the recently proposed image encryption algorithms.

Structural sources of oil market volatility and correlation dynamics

This paper explores the structural driving sources of oil market volatility and correlation dynamics using our derived volatility impulse response and correlation decomposition functions. A focal point of this paper is to conduct hypothesis tests for the observed diverging dynamics of oil market volatilities (a steady decline in oil production volatility and a concurrent increase in oil price volatility). In order to circumvent the restriction of uncorrelated disturbances in traditional structural models with stochastic volatility, we specify a time-varying level-volatility transmission matrix that allows for time-varying correlations between level and volatility innovations. Our model generalization hence captures transmissions of unexpected changes in oil levels to oil volatilities, and proves more adequate than traditional models for estimating oil market dynamics. Our results reveal several new useful insights for policy-makers, firms and investors. First, we find that a decrease in oil price persistence is at the origin of the diverging pattern of oil volatilities. Second, decreased variability of flow supply shocks is responsible for about 32% of the reduction in oil production volatility, while increased variability of demand-side shocks explains almost 60% of the increase in oil price volatility. Lastly, we find a near-zero correlation between oil production and oil price since the mid-1980s – a result that supports the theoretical prediction that oil production is inelastic to oil price changes.

Separable reversible data hiding in an encrypted image using the adjacency pixel difference histogram

Information security is a practice of encrypting data in movement and on hold, improving discretion and integrity. One can protect, encrypt and decrypt critical data in several ways. One of them is reversible data hiding in an encrypted image. The technique enables the user to encrypt images that need authentication and restore them to their original form of images. This technique returns a lossless image as an output making it the most suiTable for medical images and the military. Histogram shifting of pixel difference is an effectual reversible data hiding method in information security. Each image's pixel is encrypted when a user wants to safely store a digital image in an open environment like a cloud. The authentication or any other relevant information related to that image is embedded in the pixel difference histogram. The proposed approach's advantage is that the grayscale image transfer is carried out exceedingly safely, with near-zero correlation and Entropy closer to 8. The Peak Signal Noise Ratio (PSNR) for a directly decrypted image with an embedding capacity of 0.0807 bpp is 50.84 dB. Moreover, the secret and cover images are retrieved without error.

The Bitcoin gold correlation puzzle

Bitcoin is regularly referred to as new gold, digital gold or gold 2.0. If Bitcoin is indeed gold-like the correlation of Bitcoin and gold returns should be positive. We estimate the correlation of the two assets across time, across different return frequencies and across quantiles and find a near-zero correlation inconsistent with the claimed similarity. We offer two explanations for this puzzle: either the similarity is only a narrative and not accepted by investors or there are other forces at play that depress the true correlation. Such forces could be a substitution effect, investors sell gold and buy Bitcoin, and a catching up effect, investors buy Bitcoin to catch up with the market weight of gold.

Uncover the cover to recover the hidden secret - A separable reversible data hiding framework

The volatile development in the multimedia cognitive content is changing the global set-up towards a cloud-based architecture which is helped us with a massive amount of computer storage and the highest computational platform. Cost-saving and elasticity of services will be provided by progressive cloud computing technology for users. With the advancement in multimedia technology, the data owners outsource their private multimedia data on the hybrid cloud. Meantime the cloud servers also carry out some highly computationally expensive tasks. Nevertheless, there is an opportunity for security infracts possible in the public cloud environment. It makes an alarm for a cloud environment in security aspects. Before outsourcing multimedia data, an encryption technique is needed for safeguarding against several attacks. But performing the same is a significant challenge. A new research area was recently awakened on privacy-preserving Reversible Data Hiding (RDH) especially for multimedia data over the outsourced environment. A novel RDH for an encrypted image was proposed in this paper by using the (Most Significant Bit) MSB difference of the pixel value. By using this method, any third-party people can embed the ciphertext in the cipher image without the knowledge of the cover and secret. A person with decryption keys can get back the secret and the cover without any loss. The proposed work achieves the embedding capacity up to 1 bpp (bits per pixel) with the encryption quality of near-zero correlation and uniform histogram. The decrypted image is also retrieved with infinite Peak Signal to Noise Ratio (PSNR), unit Structural Similarity Index Metric (SSIM) and zero Bit Error Rate (BER).

Optimal concurrency on FPGA for lightweight medical image encryption

Digitized forms of images do widely used for medical diagnostics. To maintain the privacy of an individual in e-health care applications, securing the medical image becomes essential. Hence exclusive encryption algorithms have been developed to protect the confidentiality of medical images. As an alternative to software implementations, the realization of image encryption architectures on hardware platforms such as FPGA offers significant benefit with its reconfigurable feature. This paper presents a lightweight image encryption scheme for medical image security feasible to realize as concurrent architectural blocks on reconfigurable hardware like FPGA to achieve higher throughput. In the proposed encryption scheme, Lorentz attractor’s chaotic keys perform the diffusion process. Simultaneously, the pseudo-random memory addresses obtained from a Linear Feedback Shift Register (LFSR) circuit accomplishes the confusion process. The proposed algorithm implemented on Intel Cyclone IV FPGA (EP4CE115F29C7) analyzed the optimal number of concurrent blocks to achieve a tradeoff among throughput and resource utilization. Security analyses such as information entropy, histogram, correlation, and PSNR confirms the algorithm’s encryption quality. The strength of diffusion keys was ensured by randomness verification through the standard test suite from the National Institute of Standards and Technology (NIST). The proposed scheme has a larger keyspace of 2384 that guarantees good confusion through near-zero correlation, and successful diffusion with a PSNR of &lt;5 dB towards the statistical attacks. Based on the hardware analysis, the optimal number of concurrent architectural blocks (2 N) on the chosen FPGA to achieve higher throughput (639.37 Mbps), low power dissipation (138.85 mW), minimal resource utilization (1268 Logic Elements) and better encryption quality for the proposed algorithm is recommended as 4 (with N = 2).

Gender, Selection into Employment, and the Wage Impact of Immigration

Immigrant supply shocks are typically expected to reduce the wage of comparable workers. Natives may respond to the lower wage by moving to markets that were not directly targeted by immigrants and where presumably the wage did not drop. This paper argues that the wage change observed in the targeted market depends not only on the size of the native response, but also on which natives choose to respond. A non-random response alters the composition of the sample of native workers, mechanically changing the average native wage in affected markets and biasing the estimated wage impact of immigration. We document the importance of this selection bias in the French labor market, where women accounted for a rapidly increasing share of the foreign-born workforce since 1976. The raw correlations suggest that the immigrant supply shock did not change the wage of French women, but led to a sizable decline in their employment rate. In contrast, immigration had little impact on the employment rate of men, but led to a sizable drop in the male wage. We show that the near-zero correlation between immigration and female wages arises partly because the native women who left the labor force had relatively low wages. Adjusting for the selection bias results in a similar wage elasticity for both French men and women (between -0.8 and -1.0).

Gender, Selection into Employment, and the Wage Impact of Immigration

Immigrant supply shocks are typically expected to reduce the wage of comparable workers. Natives may respond to the lower wage by moving to markets that were not directly targeted by immigrants and where presumably the wage did not drop. This paper argues that the wage change observed in the targeted market depends not only on the size of the native response, but also on which natives choose to respond. A non-random response alters the composition of the sample of native workers, mechanically changing the average native wage in affected markets and biasing the estimated wage impact of immigration. We document the importance of this selection bias in the French labor market, where women accounted for a rapidly increasing share of the foreign-born workforce since 1976. The raw correlations suggest that the immigrant supply shock did not change the wage of French women, but led to a sizable decline in their employment rate. In contrast, immigration had little impact on the employment rate of men, but led to a sizable drop in the male wage. We show that the near-zero correlation between immigration and female wages arises partly because the native women who left the labor force had relatively low wages. Adjusting for the selection bias results in a similar wage elasticity for both French men and women (between -0.8 and -1.0).

Women on boards and corporate social irresponsibility: evidence from a Granger style reverse causality minimisation procedure

We hypothesise bi-directional causality between gender diversity on boards and corporate social irresponsibility (CSI). Firms exposed to CSI incidents are likely to increase their board gender diversity for reputational purposes. Simultaneously, gender diversity adds skills and networks to boards which supports their monitoring function and should reduce CSI incidents. Econometrically, this relationship is plagued with reverse causality. Consequently, we propose a Granger-style reverse causality minimisation procedure. Our procedure involves three steps. Firstly, we regress board diversity (BD) on lagged CSI to separate diversity into two components, one driven by CSI (BDDCS) and another unrelated to CSI (BDUCS), with the latter being the sum of the intercept and the disturbance term. Secondly, we confirm that BDUCS experiences a near-zero correlation to CSI and that a Granger causality F-test for CSI affecting BDUCS is clearly insignificant. Thirdly, we regress CSI on lagged BDUCS, lagged CSI and its interaction term. Applying our procedure to 2,880 US firms between 2007 and 2016, we find that boards with higher diversity, for reasons other than CSI, were significantly better than their lower diversity counterparts in reducing CSI incidents once encountering them. This effect is economically stronger for diversity unrelated to CSI than for overall diversity.

Validation of the Korean version of the Moral Judgment Scale: A process dissociation approach to moral dilemmas

Conway and Gawronski proposed a scale that independently measures utilitarian and deontological inclinations underlying moral judgments, based on an individual's endorsement of acceptable or unacceptable responses to 10 congruent and 10 incongruent moral dilemmas. This study aimed to develop and standardize the Korean version of this scale and examine the psychometric characteristics of various indexes extracted from it. The English version was translated and back-translated by two independent bilinguals. Inconsistencies between the backward translated version and the original version were resolved by consultation with an independent psychologist. Using an online survey, Korean adults aged 18 years or older were asked to read 20 dilemmas in the Korean version and indicate whether the action undertaken in each dilemma was acceptable, the probability that they would undertake the action themselves, and their level of tension and happiness. A total of 469 adults participated. Participants additionally answered questions that assessed utilitarianism and their level of antisocial personality disorder. Analysis showed that it was appropriate to use 20 dilemmas (10 incongruent and 10 congruent) in Korean adults but psychometric characteristics were different from those of the original English version. The correlation of probability that utilitarianism would drive responses (KU) and the probability that deontology would drive the responses (KD) was -.23 (p < .001). KU showed a significant correlation with utilitarianism (.18, p < .001) and a near-zero correlation with antisocial personality disorder. KD showed a correlation of -.27 (p < .001) with utilitarianism and a correlation of -.13 (p < .01) with antisocial personality disorder. A previous study that proposed that utilitarian and deontological inclinations are independent in moral judgment found a near-zero correlation between U and D, which was different from the result of the present study. Additionally, the limitations and implications of this study are discussed.

Advanced framework for highly secure and cloud‐based storage of colour images

The evergrowing virtualised information technology infrastructure is powered by cloud-centric technology around the world. Cloud-based multimedia storage has become an essential aspect for users and business behemoths. However, as per a survey of Norton, around 3800 breaches have been publicly disclosed with 4.1 billion numbers of records exposed in 2019, which is a 54% rise when compared to 2018. So the data security is a widely quoted barrier for cloud storage. Ciphering the confidential images before transmission and subsequent storage in cloud database needs critical attention for techno-specific applications. In image encryption, chaos-based keys can do better confusion, but the diffusion process using XOR is vulnerable to chosen plain text attack. The proposed colour image encryption scheme innately uses Deoxyribo Nucleic Acid coding that blends well with chaotic cryptosystem for an efficient statistical shift. The ciphered images are stored in authenticated and authorised cloud storage facilities. The experimentation is carried out with the help of Amazon Web Services storage instances. The proposed image encryption scheme offers a strong resistance towards the brute force, occlusion, statistical and differential attacks and yields near-zero correlation and good entropy.

The Internal/External Frame of Reference of Mathematics, English, and Russian Self-Concepts

The internal/external (I/E) frame of reference entails high, positive association of mathematics and verbal achievements with matching academic self-concepts but negative or near-zero correlation with their nonmatching self-concepts. This study aimed to extend the traditional I/E model by contrasting the mathematics domain with two foreign languages (English and Russian). A total of 540 Azeri eighth-grade students participated in this study. Confirmatory factor analysis revealed distinct domain-specific self-concepts for two foreign languages and mathematics, indicating a negative or near-zero nonsignificant correlations between academic self-concepts and nonmatching achievement domains but high positive, significant correlation between academic self-concepts and matching achievement domains. This study revealed distinct domain-specific self-concepts for two foreign languages, indicating a negative or near-zero nonsignificant correlations between verbal self-concepts and nonmatching verbal achievement domains. It was difficult to form a single verbal domain. The findings could be used to inform the design of interventions to improve learners’ academic self-concept and achievement.

Independently together: subthalamic theta and beta opposite roles in predicting Parkinson's tremor.

Tremor is a core feature of Parkinson’s disease and the most easily recognized Parkinsonian sign. Nonetheless, its pathophysiology remains poorly understood. Here, we show that multispectral spiking activity in the posterior-dorso-lateral oscillatory (motor) region of the subthalamic nucleus distinguishes resting tremor from the other Parkinsonian motor signs and strongly correlates with its severity. We evaluated microelectrode-spiking activity from the subthalamic dorsolateral oscillatory region of 70 Parkinson’s disease patients who underwent deep brain stimulation surgery (114 subthalamic nuclei, 166 electrode trajectories). We then investigated the relationship between patients’ clinical Unified Parkinson’s Disease Rating Scale score and their peak theta (4–7 Hz) and beta (13–30 Hz) powers. We found a positive correlation between resting tremor and theta activity (r = 0.41, P < 0.01) and a non-significant negative correlation with beta activity (r = −0.2, P = 0.5). Hypothesizing that the two neuronal frequencies mask each other’s relationship with resting tremor, we created a non-linear model of their proportional spectral powers and investigated its relationship with resting tremor. As hypothesized, patients’ proportional scores correlated better than either theta or beta alone (r = 0.54, P < 0.001). However, theta and beta oscillations were frequently temporally correlated (38/70 patients manifested significant positive temporal correlations and 1/70 exhibited significant negative correlation between the two frequency bands). When comparing theta and beta temporal relationship (r θ β) to patients’ resting tremor scores, we found a significant negative correlation between the two (r = −0.38, P < 0.01). Patients manifesting a positive correlation between the two bands (i.e. theta and beta were likely to appear simultaneously) were found to have lower resting tremor scores than those with near-zero correlation values (i.e. theta and beta were likely to appear separately). We therefore created a new model incorporating patients’ proportional theta–beta power and r θ βscores to obtain an improved neural correlate of resting tremor (r = 0.62, P < 0.001). We then used the Akaike and Bayesian information criteria for model selection and found the multispectral model, incorporating theta–beta proportional power and their correlation, to be the best fitting model, with 0.96 and 0.89 probabilities, respectively. Here we found that as theta increases, beta decreases and the two appear separately—resting tremor is worsened. Our results therefore show that theta and beta convey information about resting tremor in opposite ways. Furthermore, the finding that theta and beta coactivity is negatively correlated with resting tremor suggests that theta–beta non-linear scale may be a valuable biomarker for Parkinson’s resting tremor in future adaptive deep brain stimulation techniques.

Propensity to decide on involuntary hospitalisation in primary medical care: Dispositional or situational determinants?

BackgroundThe incidence of involuntary hospitalisations varies widely among and within countries. One factor that could account for these variations is the local profile of medical doctors deciding on involuntary admissions. The first goal of this study was to test whether to decide on an involuntary hospitalisation was an individual or a situational disposition. The second goal was to explore doctors' characteristics associated with the use of coercion in specific situations. MethodMedical doctors of four French-speaking Swiss cantons with the competence, according to cantonal laws, to decide on an involuntary hospitalisation were invited to take part in an online survey. Respondents were asked whether they would decide on an involuntary hospitalisation or not in seven clinical vignettes. Propensity to decide on involuntary hospitalisation was estimated with a two-parameter logistic item response model and latent class analysis. Univariate logistic regression models were used to test whether individual factors were associated with the use of coercion in each situation. Results192 medical doctors completed the online questionnaire. There was near-zero correlation between vignettes: an involuntary hospitalisation decided on by a doctor in one situation was not related to the use of coercion in another. No subgroup was more prone to generally resort to coercion. However, some individual characteristics were related to the use of coercion in specific situations. ConclusionsMedical doctors' propensity to use coercion for mental health problems was better accounted for by situational rather than dispositional factors. Thus, the use of coercion should be examined as a multidimensional concept.

FPGA based generic RO TRNG architecture for image confusion

True Random Number Generator (TRNG) has become a central element of today’s secure communication. TRNGs developed through FPGA implementation have a significant role in a number of applications in multimedia communication. Ring Oscillator (RO) has been adopted extensively for developing device-independent TRNG structures. The proposed design is a generic TRNG architecture based on an arrangement of ROs with post-processing. This TRNG was initially tested on Altera Cyclone II FPGA which consumed only 64 inverters to produce good randomness. Also, the device-independent capability of this design has been verified by implementing it on other two FPGA families Xilinx Artix – 7 and Microsemi Smart Fusion2. True randomness was also verified by conducting restart experiment, and the statistical properties of TRNG were evaluated through entropy analysis and NIST SP 800–22 tests. The proposed TRNG yields 26.640650 Mbps as throughput with a sampling clock of 27 MHz. Going beyond the regular key generation utility, the evolving random bits of TRNG were packed suitably to perform confusion of grayscale images producing a near-zero correlation of pixels, thereby extending the application of TRNG to image encryption.

Does Bitcoin add value to global industry portfolios?

Bitcoin has been increasingly viewed as a new form of investment, yet its role as an asset in a diversified industry portfolio is not well understood. In this paper, we explore the dynamic interdependence between Bitcoin and the ten global industry sectors classified by the Global Industry Classification Standard. We find, in accordance with previous literature, that Bitcoin is relatively isolated from traditional industries. While the near-zero correlation with traditional financial assets offers some diversification benefits to investors, these benefits are counterbalanced by the volatility of the asset. Bitcoin’s optimal presence in a minimum variance portfolio is only about 1 percent – a weight that is robust to various methods for estimating the return covariance matrix. Bitcoin’s optimal weight in portfolios maximizing Sharpe and Sortino ratios are on the magnitude of 10 to 20 percent. Hence, the value of Bitcoin as an asset in a diversified portfolio critically depends on investors’ views about the future of Blockchain technology.