Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem

A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the {\it anchor sequence}. Based on this idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we discuss how the proposed schemes can be used for multilevel threshold function sharing by employing it in a threshold RSA cryptosystem as an example

Visual secret sharing and related Works -A Review

The accelerated development of network technology and internet applications has increased the significance of protecting digital data and images from unauthorized access and manipulation. The secret image-sharing network (SIS) is a crucial technique used to protect private digital photos from illegal editing and copying. SIS can be classified into two types: single-secret sharing (SSS) and multi-secret sharing (MSS). In SSS, a single secret image is divided into multiple shares, while in MSS, multiple secret images are divided into multiple shares. Both SSS and MSS ensure that the original secret images cannot be reconstructed without the correct combination of shares. Therefore, several secret image-sharing methods have been developed depending on these two methods for example visual cryptography, steganography, discrete wavelet transform, watermarking, and threshold. All of these techniques are capable of randomly dividing the secret image into a large number of shares, each of which cannot provide any information to the intrusion team.  This study examined various visual secret-sharing schemes as unique examples of participant secret-sharing methods. Several structures that generalize and enhance VSS were also discussed in this study on covert image-sharing protocols and also this research also gives a comparative analysis of several methods based on various attributes in order to better concentrate on the future directions of the secret image. Generally speaking, the image quality generated employing developed methodologies is preferable to the image quality achieved through using the traditional visual secret-sharing methodology

Asymptotically Ideal CRT-based Secret Sharing Schemes for Multilevel and Compartmented Access Structures

Multilevel and compartmented access structures are two important classes of access structures where participants are grouped into levels/compartments with different degrees of trust and privileges. The construction of secret sharing schemes for such access structures has been in the attention of researchers for a long time. Two main approaches have been taken so far: one of them is based on polynomial interpolation and the other one is based on the Chinese Remainder Theorem (CRT). In this paper we propose the first asymptotically ideal CRT-based secret sharing schemes for (disjunctive, conjunctive) multilevel and compartmented access structures. Our approach is compositional and it is based on a variant of the Asmuth-Bloom secret sharing scheme where some participants may have public shares. Based on this, we show that the proposed secret sharing schemes for multilevel and compartmented access structures are asymptotically ideal if and only if they are based on 1-compact sequences of co-primes

Secure key design approaches using entropy harvesting in wireless sensor network: A survey

Physical layer based security design in wireless sensor networks have gained much importance since the past decade. The various constraints associated with such networks coupled with other factors such as their deployment mainly in remote areas, nature of communication etc. are responsible for development of research works where the focus is secured key generation, extraction, and sharing. Keeping the importance of such works in mind, this survey is undertaken that provides a vivid description of the different mechanisms adopted for securely generating the key as well its randomness extraction and also sharing. This survey work not only concentrates on the more common methods, like received signal strength based but also goes on to describe other uncommon strategies such as accelerometer based. We first discuss the three fundamental steps viz. randomness extraction, key generation and sharing and their importance in physical layer based security design. We then review existing secure key generation, extraction, and sharing mechanisms and also discuss their pros and cons. In addition, we present a comprehensive comparative study of the recent advancements in secure key generation, sharing, and randomness extraction approaches on the basis of adversary, secret bit generation rate, energy efficiency etc. Finally, the survey wraps up with some promising future research directions in this area

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

Society-oriented cryptographic techniques for information protection

Groups play an important role in our modern world. They are more reliable and more trustworthy than individuals. This is the reason why, in an organisation, crucial decisions are left to a group of people rather than to an individual. Cryptography supports group activity by offering a wide range of cryptographic operations which can only be successfully executed if a well-defined group of people agrees to co-operate. This thesis looks at two fundamental cryptographic tools that are useful for the management of secret information. The first part looks in detail at secret sharing schemes. The second part focuses on society-oriented cryptographic systems, which are the application of secret sharing schemes in cryptography. The outline of thesis is as follows

Privacy preserving algorithms for newly emergent computing environments

Privacy preserving data usage ensures appropriate usage of data without compromising sensitive information. Data privacy is a primary requirement since customers' data is an asset to any organization and it contains customers' private information. Data seclusion cannot be a solution to keep data private. Data sharing as well as keeping data private is important for different purposes, e.g., company welfare, research, business etc. A broad range of industries where data privacy is mandatory includes healthcare, aviation industry, education system, federal law enforcement, etc.In this thesis dissertation we focus on data privacy schemes in emerging fields of computer science, namely, health informatics, data mining, distributed cloud, biometrics, and mobile payments. Linking and mining medical records across different medical service providers are important to the enhancement of health care quality. Under HIPAA regulation keeping medical records private is important. In real-world health care databases, records may well contain errors. Linking the error-prone data and preserving data privacy at the same time is very difficult. We introduce a privacy preserving Error-Tolerant Linking Algorithm to enable medical records linkage for error-prone medical records. Mining frequent sequential patterns such as, patient path, treatment pattern, etc., across multiple medical sites helps to improve health care quality and research. We propose a privacy preserving sequential pattern mining scheme across multiple medical sites. In a distributed cloud environment resources are provided by users who are geographically distributed over a large area. Since resources are provided by regular users, data privacy and security are main concerns. We propose a privacy preserving data storage mechanism among different users in a distributed cloud. Managing secret key for encryption is difficult in a distributed cloud. To protect secret key in a distributed cloud we propose a multilevel threshold secret sharing mechanism. Biometric authentication ensures user identity by means of user's biometric traits. Any individual's biometrics should be protected since biometrics are unique and can be stolen or misused by an adversary. We present a secure and privacy preserving biometric authentication scheme using watermarking technique. Mobile payments have become popular with the extensive use of mobile devices. Mobile applications for payments needs to be very secure to perform transactions and at the same time needs to be efficient. We design and develop a mobile application for secure mobile payments. To secure mobile payments we focus on user's biometric authentication as well as secure bank transaction. We propose a novel privacy preserving biometric authentication algorithm for secure mobile payments