The Chinese Remainder Theorem

The oldest remainder problems in the world date back to 3rd century China. The Chinese Remainder Theorem was used as the basis in calendar computations, construction, commerce and astronomy problems. Today, the theorem has advanced uses in many branches of mathematics and extensive applications in computing, coding and cryptography. The Chinese Remainder Theorem is an excellent example of how mathematics that emerged in the 3rd century AC has developed and remains relevant in today’s world. This paper will explore the historical development of the Chinese Remainder Theorem along with central properties of linear congruences. In addition to providing a historical overview of the Chinese Remainder Theorem, this paper will examine several modern applications of the Chinese Remainder Theorem

Compartmented Threshold RSA Based on the Chinese Remainder Theorem

In this paper we combine the compartmented secret sharing schemes based on the Chinese remainder theorem with the RSA scheme in order to obtain, as a novelty, a dedicated solution for compartmented threshold decryption or compartmented threshold digital signature generation. AMS Subject Classification: 94A60, 94A62, 11A07 Keywords and phrases: threshold cryptography, secret sharing, Chinese remainder theore

A privacy preserving framework for cyber-physical systems and its integration in real world applications

A cyber-physical system (CPS) comprises of a network of processing and communication capable sensors and actuators that are pervasively embedded in the physical world. These intelligent computing elements achieve the tight combination and coordination between the logic processing and physical resources. It is envisioned that CPS will have great economic and societal impact, and alter the qualify of life like what Internet has done. This dissertation focuses on the privacy issues in current and future CPS applications. as thousands of the intelligent devices are deeply embedded in human societies, the system operations may potentially disclose the sensitive information if no privacy preserving mechanism is designed. This dissertation identifies data privacy and location privacy as the representatives to investigate the privacy problems in CPS. The data content privacy infringement occurs if the adversary can determine or partially determine the meaning of the transmitted data or the data stored in the storage. The location privacy, on the other hand, is the secrecy that a certain sensed object is associated to a specific location, the disclosure of which may endanger the sensed object. The location privacy may be compromised by the adversary through hop-by-hop traceback along the reverse direction of the message routing path. This dissertation proposes a public key based access control scheme to protect the data content privacy. Recent advances in efficient public key schemes, such as ECC, have already shown the feasibility to use public key schemes on low power devices including sensor motes. In this dissertation, an efficient public key security primitives, WM-ECC, has been implemented for TelosB and MICAz, the two major hardware platform in current sensor networks. WM-ECC achieves the best performance among the academic implementations. Based on WM-ECC, this dissertation has designed various security schemes, including pairwise key establishment, user access control and false data filtering mechanism, to protect the data content privacy. The experiments presented in this dissertation have shown that the proposed schemes are practical for real world applications. to protect the location privacy, this dissertation has considered two adversary models. For the first model in which an adversary has limited radio detection capability, the privacy-aware routing schemes are designed to slow down the adversary\u27s traceback progress. Through theoretical analysis, this dissertation shows how to maximize the adversary\u27s traceback time given a power consumption budget for message routing. Based on the theoretical results, this dissertation also proposes a simple and practical weighted random stride (WRS) routing scheme. The second model assumes a more powerful adversary that is able to monitor all radio communications in the network. This dissertation proposes a random schedule scheme in which each node transmits at a certain time slot in a period so that the adversary would not be able to profile the difference in communication patterns among all the nodes. Finally, this dissertation integrates the proposed privacy preserving framework into Snoogle, a sensor nodes based search engine for the physical world. Snoogle allows people to search for the physical objects in their vicinity. The previously proposed privacy preserving schemes are applied in the application to achieve the flexible and resilient privacy preserving capabilities. In addition to security and privacy, Snoogle also incorporates a number of energy saving and communication compression techniques that are carefully designed for systems composed of low-cost, low-power embedded devices. The evaluation study comprises of the real world experiments on a prototype Snoogle system and the scalability simulations

Sharing DSS by the Chinese Remainder Theorem

In this paper, we propose a new threshold scheme for the Digital Signature Standard (DSS) using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth-Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on the CRT

Constructing Ideal Secret Sharing Schemes based on Chinese Remainder Theorem

Since $(t,n)$-threshold secret sharing (SS) was initially proposed by Shamir and Blakley separately in 1979, it has been widely used in many aspects. Later on, Asmuth and Bloom presented a $(t,n)$-threshold SS scheme based on the Chinese Remainder Theorem(CRT) for integers in 1983. However, compared with the most popular Shamir\u27s $(t,n)$-threshold SS scheme, existing CRT based schemes have a lower information rate, moreover, they are harder to construct. To overcome these shortcomings of the CRT based scheme, 1) we first propose a generalized $(t,n)$-threshold SS scheme based on the CRT for the polynomial ring over a finite field. We show that our scheme is ideal, i.e., it is perfect in security and has the information rate 1. By comparison, we show that our scheme has a better information rate and is easier to construct compared with existing threshold SS schemes based on the CRT for integers. 2) We show that Shamir\u27s scheme, which is based on the Lagrange interpolation polynomial, is a special case of our scheme. Therefore, we establish the connection among threshold schemes based on the Lagrange interpolation, schemes based on the CRT for integers and our scheme. 3) As a natural extension of our threshold scheme, we present a weighted threshold SS scheme based on the CRT for polynomial rings, which inherits the above advantages of our threshold scheme over existing weighted schemes based on the CRT for integers

A Secret Image Sharing Based on Logistic-Chebyshev Chaotic Map and Chinese Remainder Theorem

Visual secret sharing (VSS) was introduced in order to solve information security issues. It is a modern cryptographic technique. It involves breaking up a secret image into $n$ secured components known as shares. The secret image is recovered with utmost secrecy when all of these shares are lined up and piled together. A (3, 3)-secret image sharing scheme (SIS) is provided in this paper by fusing the Chinese Remainder Theorem (CRT) and the Logistic-Chebyshev map (LC). Sharing a confidential image created with CRT has various benefits, including lossless recovery, the lack of further encryption, and minimal recovery calculation overhead. Firstly, we build a chaotic sequence using an LC map. The secret value pixel for the secret image is permuted in order to fend off differential attackers. To encrypt the scrambled image, we apply our CRT technique to create three shares. Finally, the security analysis of our (3, 3)-SIS scheme is demonstrated and confirmed by some simulation results

Software and Critical Technology Protection Against Side Channel Analysis Through Dynamic Hardware Obfuscation

Side Channel Analysis (SCA) is a method by which an adversary can gather information about a processor by examining the activity being done on a microchip though the environment surrounding the chip. Side Channel Analysis attacks use SCA to attack a microcontroller when it is processing cryptographic code, and can allow an attacker to gain secret information, like a crypto-algorithm\u27s key. The purpose of this thesis is to test proposed dynamic hardware methods to increase the hardware security of a microprocessor such that the software code being run on the microprocessor can be made more secure without having to change the code. This thesis uses the Java Optimized Processor (JOP) to identify and _x SCA vulnerabilities to give a processor running RSA or AES code more protection against SCA attacks

A high-speed integrated circuit with applications to RSA Cryptography

Merged with duplicate record 10026.1/833 on 01.02.2017 by CS (TIS)The rapid growth in the use of computers and networks in government, commercial and private communications systems has led to an increasing need for these systems to be secure against unauthorised access and eavesdropping. To this end, modern computer security systems employ public-key ciphers, of which probably the most well known is the RSA ciphersystem, to provide both secrecy and authentication facilities. The basic RSA cryptographic operation is a modular exponentiation where the modulus and exponent are integers typically greater than 500 bits long. Therefore, to obtain reasonable encryption rates using the RSA cipher requires that it be implemented in hardware. This thesis presents the design of a high-performance VLSI device, called the WHiSpER chip, that can perform the modular exponentiations required by the RSA cryptosystem for moduli and exponents up to 506 bits long. The design has an expected throughput in excess of 64kbit/s making it attractive for use both as a general RSA processor within the security function provider of a security system, and for direct use on moderate-speed public communication networks such as ISDN. The thesis investigates the low-level techniques used for implementing high-speed arithmetic hardware in general, and reviews the methods used by designers of existing modular multiplication/exponentiation circuits with respect to circuit speed and efficiency. A new modular multiplication algorithm, MMDDAMMM, based on Montgomery arithmetic, together with an efficient multiplier architecture, are proposed that remove the speed bottleneck of previous designs. Finally, the implementation of the new algorithm and architecture within the WHiSpER chip is detailed, along with a discussion of the application of the chip to ciphering and key generation

The role of market-based incentives in promoting low carbon development in developing countries

Includes bibliographical references.The economic advancement that society has experienced in the past two centuries is largely based on a carbon intensive development model. This is now causing a vexing problem because the exploitation of fossil fuels is a leading cause of global climate change. As developing countries advance energy-intensive developmental agendas, a more sustainable approach is necessary to facilitate growth without the accompanying negative environmental externalities inherent to the business as usual approach. The purpose of this thesis is to explore the relationship between market-based incentives (MBIs) for reducing greenhouse gas emissions and the underlying host country context. The main research question is: How does host country context affect MBIs in developing countries? The theoretical framework is drawn from the literature on market based environmental policy, and links to the literature on governance in areas of limited statehood. The thesis links five distinct empirical papers to present a cohesive body of research. The experience of the internationally mandated Clean Development Mechanism (CDM) is explored via qualitative comparison between China and South Africa, and between Zambia and South Africa. A quantitative analysis of utilisation and underlying host country indicators is also presented to further understand the antecedents of CDM uptake at the national level. Furthermore, South Africa's nationally mandated promotion of renewable energy is explored. This includes a comparison with Germany to highlight how key considerations of renewable energy promotion vary between a developed and developing country. The research finds MBIs in developing countries, both internationally and nationally mandated, to be highly dependent on the overall host country context. The key aspects identified include 1) host country prioritisation of low carbon development; 2) supporting structures and policies that generate awareness, build capabilities and encourage private sector participation; and 3) access to finance, with a specific focus on cost of capital. The findings support the market-based environmental policy literature that suggests an effective regulatory framework by the state is a necessary condition for MBIs in developing countries. However it also shows that the regulatory framework alone is not a sufficient condition for successful implementation of MBIs in the developing world. Consequently, the overall host country context determines private sector interest in and the success of MBIs in developing countries