A Survey on Exotic Signatures for Post-quantum Blockchain: Challenges and Research Directions

Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this article, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and that are crucial cryptographic tools used in the blockchain ecosystem for (1) account management, (2) consensus efficiency, (3) empowering scriptless blockchain, and (4) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind, and ring signatures. Herein the term "exotic"refers to signatures with properties that are not just beyond the norm for signatures, e.g., unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats

A Survey on Exotic Signatures for Post-Quantum Blockchain: Challenges & Research Directions

Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this paper, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and which are crucial cryptographic tools used in the blockchain ecosystem for (i) account management, (ii) consensus efficiency, (iii) empowering scriptless blockchain, and (iv) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind and ring signatures. Herein the term exotic refers to signatures with properties which are not just beyond the norm for signatures e.g. unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats

A Lattice-based Provably Secure Multisignature Scheme in Quantum Random Oracle Model

The multisignature schemes are attracted to utilize in some cryptographic applications such as the blockchain. Though the lattice-based constructions of multisignature schemes exist as quantum-secure multisignature, a multisignature scheme whose security is proven in the quantum random oracle model (QROM), rather than the classical random oracle model (CROM), is not known. In this paper, we propose a first lattice-based multisignature scheme whose security is proven in QROM. Although our proposed scheme is based on the Dilithium-QROM signature, whose security is proven in QROM, their proof technique cannot be directly applied to the multisignature setting. The difficulty of proving the security in QROM is how to program the random oracle in the security proof. To solve the problems in the security proof, we develop several proof techniques in QROM. First, we employ the searching query technique by Targi and Unruh to convert the Dilithium-QROM into the multisignature setting. For the second, we develop a new programming technique in QROM since the conventional programming techniques seem not to work in the multisignature setting of QROM. We combine the programming technique by Unruh with the one by Liu and Zhandry. The new technique enables us to program the random oracle in QROM and construct the signing oracle in the security proof

Untraceable Blind Multisignature

Multisignature is a variant of digital signature which enables a document to be signed by multiple signers simultaneously in a collaboration. It ensures the fairness property of the signer. Blind signature is another variant of digital signature in which a message is signed without disclosing its content. Blindness is an important property of blind signature in which, the message and the signature are unlinkable after signature is attached to the message.In this Thesis, we designed a Blind Multisignature protocol with security features of blind signatures and multisignature. The security of the scheme lies in hard computational assumptions such as Integer Factorization problem (IFP), computational Diffie-Hellman problem (CDHP) and discrete logarithmic problem (DLP). The correctness of the scheme is tested mathematically and the scheme is also implemented in Java platform. The computational cost of the proposed scheme is low and the signature length (in byte) is nominal with the message size. The time of computation of each phase is computed and found to be low as compared to competent schemes. The security analysis of the scheme is done rigorously and the security features such as untraceability, blindness and unforgeability of the proposed scheme has been analysed and found secure under the attack. The scheme has properties of both blind signature and multi-signature. This scheme can be applied to real life applications such as electronic cash and electronic voting

Group Signatures: Unconditional Security for Members

First a detailed definition of group signatures, originally suggested by Chaum and van {Heijst}, is given. Such signatures allow members of a group to sign messages anonymously on behalf of the group subject to the constraint that, in case of disputes later on, a designated authority can identify the signer. It is shown that if such schemes are to provide information theoretic anonymity, then the length of the secret information of the members and the authority increases with the number of members and the number of signatures each member is allowed to make. A dynamic scheme meeting these lower bounds is described. Unlike previous suggestions it protects each member unconditionally against framing, i.e.\ being held responsible for a signature made by someone else

How to Prove Statements Obliviously?

Cryptographic applications often require proving statements about hidden secrets satisfying certain circuit relations. Moreover, these proofs must often be generated obliviously, i.e., without knowledge of the secret. This work presents a new technique called --- FRI on hidden values --- for efficiently proving such statements. This technique enables a polynomial commitment scheme for values hidden inside linearly homomorphic primitives, such as linearly homomorphic encryption, linearly homomorphic commitment, group exponentiation, fully homomorphic encryption, etc. Building on this technique, we obtain the following results. 1. An efficient SNARK for proving the honest evaluation of FHE ciphertexts. This allows for an efficiently verifiable private delegation of computation, where the client only needs to perform logarithmic many FHE computations to verify the correctness of the computation. 2. An efficient approach for privately delegating the computation of zkSNARKs to a single untrusted server, without making any non-black-box use of cryptography. All prior works require multiple servers and the assumption that some subset of the servers are honest. 3. A weighted threshold signature scheme that does not require any setup. In particular, parties may sample their own keys independently, and no distributed key generation (DKG) protocol is needed. Furthermore, the efficiency of our scheme is completely independent of the weights. Prior to this work, there were no known black-box feasibility results for any of these applications. We also investigate the use of this approach in the context of public proof aggregation. These are only a few representative applications that we explore in this paper. We expect our techniques to be widely applicable in many other scenarios

Keeping Authorities "Honest or Bust" with Decentralized Witness Cosigning

The secret keys of critical network authorities - such as time, name, certificate, and software update services - represent high-value targets for hackers, criminals, and spy agencies wishing to use these keys secretly to compromise other hosts. To protect authorities and their clients proactively from undetected exploits and misuse, we introduce CoSi, a scalable witness cosigning protocol ensuring that every authoritative statement is validated and publicly logged by a diverse group of witnesses before any client will accept it. A statement S collectively signed by W witnesses assures clients that S has been seen, and not immediately found erroneous, by those W observers. Even if S is compromised in a fashion not readily detectable by the witnesses, CoSi still guarantees S's exposure to public scrutiny, forcing secrecy-minded attackers to risk that the compromise will soon be detected by one of the W witnesses. Because clients can verify collective signatures efficiently without communication, CoSi protects clients' privacy, and offers the first transparency mechanism effective against persistent man-in-the-middle attackers who control a victim's Internet access, the authority's secret key, and several witnesses' secret keys. CoSi builds on existing cryptographic multisignature methods, scaling them to support thousands of witnesses via signature aggregation over efficient communication trees. A working prototype demonstrates CoSi in the context of timestamping and logging authorities, enabling groups of over 8,000 distributed witnesses to cosign authoritative statements in under two seconds.Comment: 20 pages, 7 figure