Software and hardware implementation of the RSA public key cipher

Cryptographic systems and their use in communications are presented. The advantages obtained by the use of a public key cipher and the importance of this in a commercial environment are stressed. Two two main public key ciphers are considered. The RSA public key cipher is introduced and various methods for implementing this cipher on a standard, nondedicated, 8 bit microprocessor are investigated. The performance of the different algorithms are evaluated and compared. Various ways of increasing the performance are considered. The limitations imposed by the performance on the practical use of the cipher are discussed. The importance of the key to the security of the cipher is assessed. Different forms of attack are mentioned and a procedure for generating keys, which minimise the probability of a sucessful attack is presented. This procedure is implemented on a minicomputer. Use of the method on personal computers or microprocessors is examined. Methods for performing multiplication in hardware, with particular emphasis on the use of these methods in modular multiplication, are detailed. An algorithm for performing part of the encryption function in hardware and the hardware necessary for it is described. Different methods for implementing the hardware are discussed and one is choosen. A description of the hardware unit is given. The design and development of an application specific integrated circuit (ASIC) to perform key elements of the encryption function is described. The various stages of the design process are detailed. The results expected from this device and its integration into the overall encryption scheme are presented

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/

A survey of the mathematics of cryptology

Herein I cover the basics of cryptology and the mathematical techniques used in the field. Aside from an overview of cryptology the text provides an in-depth look at block cipher algorithms and the techniques of cryptanalysis applied to block ciphers. The text also includes details of knapsack cryptosystems and pseudo-random number generators

Cryptographic Pairings: Efficiency and DLP security

This thesis studies two important aspects of the use of pairings in cryptography, efficient algorithms and security. Pairings are very useful tools in cryptography, originally used for the cryptanalysis of elliptic curve cryptography, they are now used in key exchange protocols, signature schemes and Identity-based cryptography. This thesis comprises of two parts: Security and Efficient Algorithms. In Part I: Security, the security of pairing-based protocols is considered, with a thorough examination of the Discrete Logarithm Problem (DLP) as it occurs in PBC. Results on the relationship between the two instances of the DLP will be presented along with a discussion about the appropriate selection of parameters to ensure particular security level. In Part II: Efficient Algorithms, some of the computational issues which arise when using pairings in cryptography are addressed. Pairings can be computationally expensive, so the Pairing-Based Cryptography (PBC) research community is constantly striving to find computational improvements for all aspects of protocols using pairings. The improvements given in this section contribute towards more efficient methods for the computation of pairings, and increase the efficiency of operations necessary in some pairing-based protocol

Structure and Randomness of the Discrete Lambert Map

We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM). The mapping is closely related to the Discrete Log Problem, but has received far less attention since it is considered to be a more complicated map that is likely even harder to invert. However, this mapping is quite important because it underlies the security of the ElGamal Digital Signature Scheme. Using functional graphs induced by this mapping, we were able to find non-random properties that could potentially be used to exploit the ElGamal DSS

The zheng-seberry public key cryptosystem and signcryption

In 1993 Zheng-Seberry presented a public key cryptosystem that was considered efficient and secure in the sense of indistinguishability of encryptions (IND) against an adaptively chosen ciphertext adversary (CCA2). This thesis shows the Zheng-Seberry scheme is not secure as a CCA2 adversary can break the scheme in the sense of IND. In 1998 Cramer-Shoup presented a scheme that was secure against an IND-CCA2 adversary and whose proof relied only on standard assumptions. This thesis modifies this proof and applies it to a modified version of the El-Gamal scheme. This resulted in a provably secure scheme relying on the Random Oracle (RO) model, which is more efficient than the original Cramer-Shoup scheme. Although the RO model assumption is needed for security of this new El-Gamal variant, it only relies on it in a minimal way

Pairings in Cryptology: efficiency, security and applications

Abstract The study of pairings can be considered in so many di�erent ways that it may not be useless to state in a few words the plan which has been adopted, and the chief objects at which it has aimed. This is not an attempt to write the whole history of the pairings in cryptology, or to detail every discovery, but rather a general presentation motivated by the two main requirements in cryptology; e�ciency and security. Starting from the basic underlying mathematics, pairing maps are con- structed and a major security issue related to the question of the minimal embedding �eld [12]1 is resolved. This is followed by an exposition on how to compute e�ciently the �nal exponentiation occurring in the calculation of a pairing [124]2 and a thorough survey on the security of the discrete log- arithm problem from both theoretical and implementational perspectives. These two crucial cryptologic requirements being ful�lled an identity based encryption scheme taking advantage of pairings [24]3 is introduced. Then, perceiving the need to hash identities to points on a pairing-friendly elliptic curve in the more general context of identity based cryptography, a new technique to efficiently solve this practical issue is exhibited. Unveiling pairings in cryptology involves a good understanding of both mathematical and cryptologic principles. Therefore, although �rst pre- sented from an abstract mathematical viewpoint, pairings are then studied from a more practical perspective, slowly drifting away toward cryptologic applications

Fast Modular Reduction for Large-Integer Multiplication

The work contained in this thesis is a representation of the successful attempt to speed-up the modular reduction as an independent step of modular multiplication, which is the central operation in public-key cryptosystems. Based on the properties of Mersenne and Quasi-Mersenne primes, four distinct sets of moduli have been described, which are responsible for converting the single-precision multiplication prevalent in many of today\u27s techniques into an addition operation and a few simple shift operations. A novel algorithm has been proposed for modular folding. With the backing of the special moduli sets, the proposed algorithm is shown to outperform (speed-wise) the Modified Barrett algorithm by 80% for operands of length 700 bits, the least speed-up being around 70% for smaller operands, in the range of around 100 bits