SECURE AND EFFICIENT DECENTRALIZED GROUP KEY ESTABLISHMENT REVISED ELGAMAL PROTOCOL FOR GROUP COMMUNICATION

in distributed system it is sometimes necessary for users to share the power to use a cryptosystem. The system secret is divided up into shares and securely stored by the entities forming the distributed cryptosystem. We propose a new Multi signature scheme without a trusted third party (TTP), based on a round optimal, publicly verifiable distributed key generation (DKG) protocol. In this propose system, we define a new propose ElGamal algorithm, in that ElGamal algorithm has two random numbers. The origina l ElGamal algorithm is that, it has only one random number. In order to improve its security, the proposed scheme adds one more random number. The security of the proposed signature scheme is the same with the ElGamal sig nature scheme which is based on the difficult computable nature of discrete logarithm over finite fields. In this paper, the algorithm is proposed to enhance the security and usage of more random number to make algorithm more complicate d, which can also make the link between the random number and the key more complicated. The scheme presented in this paper after analysis showed that the security level is kept high by using two random numbers and the time complex ity is reduced

Forward-Secure Multi-Signatures

Multi-signatures allow a group of signers to jointly sign a message in a compact and efficiently verifiable signature, ideally independent of the number of signers in the group. We present the first provably secure forward-secure multi-signature scheme by deriving a forward-secure signature scheme from the hierarchical identity-based encryption of Boneh, Boyen, and Goh (Eurocrypt 2005) and showing how the signatures in that scheme can be securely composed. Multi-signatures in our scheme contain just two group elements (one from each of the base groups) and require one exponentation and three pairing computations to verify

Cryptography in privacy-preserving applications.

Tsang Pak Kong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 95-107).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Privacy --- p.1Chapter 1.2 --- Cryptography --- p.5Chapter 1.2.1 --- History of Cryptography --- p.5Chapter 1.2.2 --- Cryptography Today --- p.6Chapter 1.2.3 --- Cryptography For Privacy --- p.7Chapter 1.3 --- Thesis Organization --- p.8Chapter 2 --- Background --- p.10Chapter 2.1 --- Notations --- p.10Chapter 2.2 --- Complexity Theory --- p.11Chapter 2.2.1 --- Order Notation --- p.11Chapter 2.2.2 --- Algorithms and Protocols --- p.11Chapter 2.2.3 --- Relations and Languages --- p.13Chapter 2.3 --- Algebra and Number Theory --- p.14Chapter 2.3.1 --- Groups --- p.14Chapter 2.3.2 --- Intractable Problems --- p.16Chapter 2.4 --- Cryptographic Primitives --- p.18Chapter 2.4.1 --- Public-Key Encryption --- p.18Chapter 2.4.2 --- Identification Protocols --- p.21Chapter 2.4.3 --- Digital Signatures --- p.22Chapter 2.4.4 --- Hash Functions --- p.24Chapter 2.4.5 --- Zero-Knowledge Proof of Knowledge --- p.26Chapter 2.4.6 --- Accumulators --- p.32Chapter 2.4.7 --- Public Key Infrastructure --- p.34Chapter 2.5 --- Zero Knowledge Proof of Knowledge Protocols in Groups of Unknown Order --- p.36Chapter 2.5.1 --- The Algebraic Setting --- p.36Chapter 2.5.2 --- Proving the Knowledge of Several Discrete Logarithms . --- p.37Chapter 2.5.3 --- Proving the Knowledge of a Representation --- p.38Chapter 2.5.4 --- Proving the Knowledge of d Out of n Equalities of Discrete Logarithms --- p.39Chapter 2.6 --- Conclusion --- p.42Chapter 3 --- Related Works --- p.43Chapter 3.1 --- Introduction --- p.43Chapter 3.2 --- Group-Oriented Signatures without Spontaneity and/or Anonymity --- p.44Chapter 3.3 --- SAG Signatures --- p.46Chapter 3.4 --- Conclusion --- p.49Chapter 4 --- Linkable Ring Signatures --- p.50Chapter 4.1 --- Introduction --- p.50Chapter 4.2 --- New Notions --- p.52Chapter 4.2.1 --- Accusatory Linking --- p.52Chapter 4.2.2 --- Non-slanderability --- p.53Chapter 4.2.3 --- Linkability in Threshold Ring Signatures --- p.54Chapter 4.2.4 --- Event-Oriented Linking --- p.55Chapter 4.3 --- Security Model --- p.56Chapter 4.3.1 --- Syntax --- p.56Chapter 4.3.2 --- Notions of Security --- p.58Chapter 4.4 --- Conclusion --- p.63Chapter 5 --- Short Linkable Ring Signatures --- p.64Chapter 5.1 --- Introduction --- p.64Chapter 5.2 --- The Construction --- p.65Chapter 5.3 --- Security Analysis --- p.68Chapter 5.3.1 --- Security Theorems --- p.68Chapter 5.3.2 --- Proofs --- p.68Chapter 5.4 --- Discussion --- p.70Chapter 5.5 --- Conclusion --- p.71Chapter 6 --- Separable Linkable Threshold Ring Signatures --- p.72Chapter 6.1 --- Introduction --- p.72Chapter 6.2 --- The Construction --- p.74Chapter 6.3 --- Security Analysis --- p.76Chapter 6.3.1 --- Security Theorems --- p.76Chapter 6.3.2 --- Proofs --- p.77Chapter 6.4 --- Discussion --- p.79Chapter 6.5 --- Conclusion --- p.80Chapter 7 --- Applications --- p.82Chapter 7.1 --- Offline Anonymous Electronic Cash --- p.83Chapter 7.1.1 --- Introduction --- p.83Chapter 7.1.2 --- Construction --- p.84Chapter 7.2 --- Electronic Voting --- p.85Chapter 7.2.1 --- Introduction --- p.85Chapter 7.2.2 --- Construction . --- p.87Chapter 7.2.3 --- Discussions --- p.88Chapter 7.3 --- Anonymous Attestation --- p.89Chapter 7.3.1 --- Introduction --- p.89Chapter 7.3.2 --- Construction --- p.90Chapter 7.4 --- Conclusion --- p.91Chapter 8 --- Conclusion --- p.92A Paper Derivation --- p.94Bibliography --- p.9

Two results on spontaneous anonymous group signatures.

Chan Kwok Leong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 72-78).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Preliminaries --- p.4Chapter 2.1 --- Notation --- p.4Chapter 2.2 --- Cryptographic Primitives --- p.5Chapter 2.2.1 --- Symmetric Key Cryptography --- p.5Chapter 2.2.2 --- Asymmetric Key Cryptosystem --- p.6Chapter 2.2.3 --- Secure Hash Function --- p.7Chapter 2.2.4 --- Digital Signature --- p.8Chapter 2.2.5 --- Digital Certificate and Public Key Infrastructure --- p.8Chapter 2.3 --- Provable Security and Security Model --- p.9Chapter 2.3.1 --- Mathematics Background --- p.9Chapter 2.3.2 --- One-Way Function --- p.10Chapter 2.3.3 --- Candidate One-way Functions --- p.12Chapter 2.4 --- Proof Systems --- p.15Chapter 2.4.1 --- Zero-knowledge Protocol --- p.15Chapter 2.4.2 --- Proof-of-Knowledge Protocol --- p.17Chapter 2.4.3 --- Honest-Verifier Zero-Knowledge (HVZK) Proof of Knowl- edge Protocols (PoKs) --- p.18Chapter 2.5 --- Security Model --- p.19Chapter 2.5.1 --- Random Oracle Model --- p.19Chapter 2.5.2 --- Generic group model (GGM) --- p.20Chapter 3 --- Signature Scheme --- p.21Chapter 3.1 --- Introduction --- p.21Chapter 3.2 --- Security Notation for Digital Signature --- p.23Chapter 3.3 --- Security Proof for Digital Signature --- p.24Chapter 3.3.1 --- Random Oracle Model for Signature Scheme --- p.24Chapter 3.3.2 --- Adaptive Chosen Message Attack --- p.24Chapter 3.4 --- Schnorr Identification and Schnorr Signature --- p.25Chapter 3.4.1 --- Schnorr's ROS assumption --- p.26Chapter 3.5 --- Blind Signature --- p.27Chapter 4 --- Spontaneous Anonymous Group (SAG) Signature --- p.30Chapter 4.1 --- Introduction --- p.30Chapter 4.2 --- Background --- p.30Chapter 4.2.1 --- Group Signature --- p.30Chapter 4.2.2 --- Threshold Signature --- p.31Chapter 4.3 --- SAG signatures --- p.33Chapter 4.4 --- Formal Definitions and Constructions --- p.35Chapter 4.4.1 --- Ring-type construction --- p.36Chapter 4.4.2 --- CDS-type construction --- p.36Chapter 4.5 --- Discussion --- p.37Chapter 5 --- Blind Spontaneous Anonymous Signature --- p.39Chapter 5.1 --- Introduction --- p.39Chapter 5.2 --- Definition --- p.40Chapter 5.2.1 --- Security Model --- p.41Chapter 5.2.2 --- Definitions of security notions --- p.41Chapter 5.3 --- Constructing blind SAG signatures --- p.43Chapter 5.3.1 --- Blind SAG signature: CDS-type [1] --- p.43Chapter 5.3.2 --- "Blind SAG signature: ring-type [2, 3]" --- p.44Chapter 5.4 --- Security Analysis --- p.44Chapter 5.4.1 --- Multi-key parallel one-more unforgeability of blind signature --- p.45Chapter 5.4.2 --- Security of our blind SAG signatures --- p.47Chapter 5.5 --- Discussion --- p.49Chapter 6 --- Linkable Spontaneous Anonymous Group Signature --- p.51Chapter 6.1 --- introduction --- p.51Chapter 6.2 --- Related work --- p.51Chapter 6.3 --- Basic Building Blocks --- p.52Chapter 6.3.1 --- Proving the Knowledge of Several Discrete Logarithms --- p.53Chapter 6.3.2 --- Proving the Knowledge of d Out of n Equalities of Discrete Logarithms --- p.55Chapter 6.4 --- Security Model --- p.57Chapter 6.4.1 --- Syntax --- p.57Chapter 6.4.2 --- Notions of Security --- p.59Chapter 6.5 --- Our Construction --- p.63Chapter 6.5.1 --- An Linkable Threshold SAG Signature Scheme --- p.63Chapter 6.5.2 --- Security --- p.65Chapter 6.5.3 --- Discussions --- p.67Chapter 7 --- Conclusion --- p.70Bibliography --- p.7

Proof-of-Stake Sidechains

Sidechains have long been heralded as the key enabler of blockchain scalability and interoperability. However, no modeling of the concept or a provably secure construction has so far been attempted. We provide the first formal definition of what a sidechain system is and how assets can be moved between sidechains securely. We put forth a security definition that augments the known transaction ledger properties of persistence and liveness to hold across multiple ledgers and enhance them with a new ``firewall\u27\u27 security property which safeguards each blockchain from its sidechains, limiting the impact of an otherwise catastrophic sidechain failure. We then provide a sidechain construction that is suitable for proof-of-stake (PoS) sidechain systems. As an exemplary concrete instantiation we present our construction for an epoch-based PoS system consistent with Ouroboros (Crypto~2017), the PoS blockchain protocol used in Cardano which is one of the largest pure PoS systems by market capitalisation, and we also comment how the construction can be adapted for other protocols such as Ouroboros Praos (Eurocrypt~2018), Ouroboros Genesis (CCS~2018), Snow White and Algorand. An important feature of our construction is {\em merged-staking} that prevents ``goldfinger\u27\u27 attacks against a sidechain that is only carrying a small amount of stake. An important technique for pegging chains that we use in our construction is cross-chain certification which is facilitated by a novel cryptographic primitive we introduce called ad-hoc threshold multisignatures (ATMS) which may be of independent interest. We show how ATMS can be securely instantiated by regular and aggregate digital signatures as well as succinct arguments of knowledge such as STARKs and bulletproofs with varying degrees of storage efficiency

Challenges and Implications of Verifiable Builds for Security-Critical Open-Source Software

The majority of computer users download software from the Internet and run it directly on their machine. They expect applications to work as advertised, and implicitly trust them not to perform any malicious activities. For security-sensitive applications though, users need the assurance that what they downloaded is what has been officially released by the developers, and that it comes directly from audited sources to avoid surreptitious backdoors. However, the compilation process from source code to binary files, and more generally, the toolchain used in software packaging, has not been designed with verifiability in mind. Rather, the output of compilers is often dependent on parameters that can be strongly tied to the building environment, and may not be easily repeatable anywhere else. In this paper, we first manually replicate a close match to the official binaries of sixteen most recent versions of TrueCrypt for Windows up to v7.1a, a widely known open-source encryption tool, and explain the remaining differences that can solely be attributed to non-determinism in the build process. This experiment provides the missing guarantee on the official binaries, and makes audits on TrueCrypt's source code more meaningful. Also, it gives insights about what constitutes sources of non-determinism in a compilation process, which may help create future verifiable build processes. We also summarize challenges faced by Bitcoin, Tor, Debian and other Linux distributions in designing automated methods, such as deterministic and reproducible builds, for the verification of their official packages. Finally, we discuss a few suggestions for achieving deterministic builds

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