An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of R\'edei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.Comment: 18 pages, 1 figur

Privacy-preserving information hiding and its applications

The phenomenal advances in cloud computing technology have raised concerns about data privacy. Aided by the modern cryptographic techniques such as homomorphic encryption, it has become possible to carry out computations in the encrypted domain and process data without compromising information privacy. In this thesis, we study various classes of privacy-preserving information hiding schemes and their real-world applications for cyber security, cloud computing, Internet of things, etc. Data breach is recognised as one of the most dreadful cyber security threats in which private data is copied, transmitted, viewed, stolen or used by unauthorised parties. Although encryption can obfuscate private information against unauthorised viewing, it may not stop data from illegitimate exportation. Privacy-preserving Information hiding can serve as a potential solution to this issue in such a manner that a permission code is embedded into the encrypted data and can be detected when transmissions occur. Digital watermarking is a technique that has been used for a wide range of intriguing applications such as data authentication and ownership identification. However, some of the algorithms are proprietary intellectual properties and thus the availability to the general public is rather limited. A possible solution is to outsource the task of watermarking to an authorised cloud service provider, that has legitimate right to execute the algorithms as well as high computational capacity. Privacypreserving Information hiding is well suited to this scenario since it is operated in the encrypted domain and hence prevents private data from being collected by the cloud. Internet of things is a promising technology to healthcare industry. A common framework consists of wearable equipments for monitoring the health status of an individual, a local gateway device for aggregating the data, and a cloud server for storing and analysing the data. However, there are risks that an adversary may attempt to eavesdrop the wireless communication, attack the gateway device or even access to the cloud server. Hence, it is desirable to produce and encrypt the data simultaneously and incorporate secret sharing schemes to realise access control. Privacy-preserving secret sharing is a novel research for fulfilling this function. In summary, this thesis presents novel schemes and algorithms, including: • two privacy-preserving reversible information hiding schemes based upon symmetric cryptography using arithmetic of quadratic residues and lexicographic permutations, respectively. • two privacy-preserving reversible information hiding schemes based upon asymmetric cryptography using multiplicative and additive privacy homomorphisms, respectively. • four predictive models for assisting the removal of distortions inflicted by information hiding based respectively upon projection theorem, image gradient, total variation denoising, and Bayesian inference. • three privacy-preserving secret sharing algorithms with different levels of generality

A measurement study of peer-to-peer bootstrapping and implementations of delay-based cryptography

This thesis researches two distinct areas of study in both peer-to-peer networking formodern cryptocurrencies and implementations of delay-based cryptography.The first part of the thesis researches elements of peer-to-peer network mechanisms,with a specific focus on the dependencies on centralised infrastructure required for theinitial participation in such networks.Cryptocurrencies rely on decentralised peer-to-peer networks, yet the method bywhich new peers initially join these networks, known as bootstrapping, presents a significantchallenge. Our original research consists of a measurement study of 74 cryptocurrencies.Our study reveals a prevalent reliance on centralised infrastructure which leadsto censorship-prone bootstrapping techniques leaving networks vulnerable to censorshipand manipulation.In response, we explore alternative bootstrapping methods seeking solutions lesssusceptible to censorship. However, our research demonstrates operational challengesand limitations which hinder their effectiveness, highlighting the complexity of achievingcensorship-resistance in practice.Furthermore, our global measurement study uncovers the details of cryptocurrencypeer-to-peer networks, revealing instances outages and intentional protocol manipulationimpacting bootstrapping operations. Through a volunteer network of probes deployedacross 42 countries, we analyse network topology, exposing centralisation tendencies andunintentional peer exposure.Our research also highlights the pervasive inheritance of legacy bootstrapping methods,perpetuating security vulnerabilities and censorship risks within cryptocurrencysystems. These findings illuminate broader concerns surrounding decentralisation andcensorship-resistance in distributed systems.In conclusion, our study offers valuable insights into cryptocurrency bootstrappingtechniques and their susceptibility to censorship, paving the way for future research andinterventions to enhance the resilience and autonomy of peer-to-peer networks.In the second part of the thesis, attention shifts towards delay-based cryptography,where the focus lies on the creation and practical implementations of timed-release encryptionschemes. Drawing from the historical delay-based cryptographic protocols, thisthesis presents two original research contributions.The first is the creation of a new timed-release encryption scheme with a propertytermed implicit authentication. The second contribution is the development of a practicalconstruction called TIDE (TIme Delayed Encryption) tailored for use in sealed-bidauctions.Timed-Release Encryption with Implicit Authentication (TRE-IA) is a cryptographicprimitive which presents a new property named implicit authentication (IA). This propertyensures that only authorised parties, such as whistleblowers, can generate meaningfulciphertexts. By incorporating IA techniques into the encryption process, TRE-IAaugments a new feature in standard timed-release encryption schemes by ensuring thatonly the party with the encryption key can create meaningful ciphertexts. This propertyensures the authenticity of the party behind the sensitive data disclosure. Specifically, IAenables the encryption process to authenticate the identity of the whistleblower throughthe ciphertext. This property prevents malicious parties from generating ciphertextsthat do not originate from legitimate sources. This ensures the integrity and authenticityof the encrypted data, safeguarding against potential leaks of information not vettedby the party performing the encryption.TIDE introduces a new method for timed-release encryption in the context of sealedbidauctions by creatively using classic number-theoretic techniques. By integratingRSA-OEAP public-key encryption and the Rivest Shamir Wagner time-lock assumptionwith classic number theory principles, TIDE offers a solution that is both conceptuallystraightforward and efficient to implement.Our contributions in TIDE address the complexities and performance challengesinherent in current instantiations of timed-release encryption schemes. Our researchoutput creates a practical timed-release encryption implementation on consumer-gradehardware which can facilitate real-world applications such as sealed-bid auctions withclear steps for implementation.Finally, our thesis concludes with a review of the prospects of delay-based cryptographywhere we consider potential applications such as leveraging TIDE for a publicrandomness beacon.<br/

Bounded-Collusion IBE from Key Homomorphism

In this work, we show how to construct IBE schemes that are secure against a bounded number of collusions, starting with underlying PKE schemes which possess linear homomorphisms over their keys. In particular, this enables us to exhibit a new (bounded-collusion) IBE construction based on the quadratic residuosity assumption, without any need to assume the existence of random oracles. The new IBE’s public parameters are of size O(tλlogI) where I is the total number of identities which can be supported by the system, t is the number of collusions which the system is secure against, and λ is a security parameter. While the number of collusions is bounded, we note that an exponential number of total identities can be supported. More generally, we give a transformation that takes any PKE satisfying Linear Key Homomorphism, Identity Map Compatibility, and the Linear Hash Proof Property and translates it into an IBE secure against bounded collusions. We demonstrate that these properties are more general than our quadratic residuosity-based scheme by showing how a simple PKE based on the DDH assumption also satisfies these properties.National Science Foundation (U.S.) (NSF CCF-0729011)National Science Foundation (U.S.) (NSF CCF-1018064)United States. Defense Advanced Research Projects Agency (DARPA FA8750-11-2-0225

A Framework for Uncertain Cloud Data Security and Recovery Based on Hybrid Multi-User Medical Decision Learning Patterns

Machine learning has been supporting real-time cloud based medical computing systems. However, most of the computing servers are independent of data security and recovery scheme in multiple virtual machines due to high computing cost and time. Also, this cloud based medical applications require static security parameters for cloud data security. Cloud based medical applications require multiple servers to store medical records or machine learning patterns for decision making. Due to high Uncertain computational memory and time, these cloud systems require an efficient data security framework to provide strong data access control among the multiple users. In this work, a hybrid cloud data security framework is developed to improve the data security on the large machine learning patterns in real-time cloud computing environment. This work is implemented in two phases’ i.e. data replication phase and multi-user data access security phase. Initially, machine decision patterns are replicated among the multiple servers for Uncertain data recovering phase. In the multi-access cloud data security framework, a hybrid multi-access key based data encryption and decryption model is implemented on the large machine learning medical patterns for data recovery and security process. Experimental results proved that the present two-phase data recovering, and security framework has better computational efficiency than the conventional approaches on large medical decision patterns