New Construction of Blind Signatures From Braid Groups

A blind signature enables a user to obtain signatures on any message from an authority who cannot acquire any information on the message being signed. A blind ring signature scheme is designed as a ring signature scheme with the blindness property. The scheme allows any member of a group anonymously sign a message on behalf of the group. Also, the user with the message can blind it before transmitting to the group. At Asiacrypt 2010, Rückert constructed the first blind signature scheme using ideal lattices. Recently, Zhang, Jiang and Zheng, and Alkadri, Bansarkhani and Buchmann proposed two improved blind signature schemes based on the SIS problem and the Ring SIS problem in 2018 and 2020, respectively. At WISA 2019, motivated by these blind signature schemes, Le, Duong and Susilo constructed the first lattice-based blind ring signature scheme provably secure under the hardness assumption of the SIS problem in random oracle model. In this paper, we show that Rückert’s scheme, Alkadri-Bansarkhani-Buchmann scheme and Zhang-Jiang-Zheng scheme, and Le-Duong-Susilo scheme do not achieve blindness, i.e. the signer can link a valid message-signature pair after interacting with various users. We show that the cause of vulnerabilities of the blind schemes is that the blinding factors to hide real messages being signed are exposed by specific algebraic relations in the underlying rings. To hide the blinding factors, we use homomorphic encryption schemes. Finally, we propose a generic construction from a semantically secure homomorphic encryption scheme and a one-more unforgeable blind signature scheme that does not achieve blindness to a new blind signature scheme that achieves blindness as well as one-more unforgeability.

A blind ring signature scheme is a combination of a ring signature and a blind signature, which allows not only any member of a group of signers to sign on a message on behalf of the group without revealing its identity but also the user who possesses the message to blind it before sending to the group to be signed. Blind ring signature schemes are essential components in e-commercial, e-voting etc. In this paper, we propose the first blind ring signature scheme based on lattices. More precisely, our proposed scheme is proven to be secure in random oracle model under the hardness of the short integer solution (SIS) problem.

Blind signature offer the protection for sender's privacy and become an important primitive for electronic commerce. In this paper, we present a technique of matrix-vector-blinding for lattice-based blind signature. Building on this result, we propose two hierarchical ID-based blind signature schemes from with and without random oracle, which are secure against quantum attacks. We apply the latest technique of lattice basis delegation in fixed dimension from ABB10's[1] scheme to our constructions which contribute to shorter public key and signature. Both of our blind signature schemes are proven to hold the properties of perfect blindness and one-more unforgeableability. Our hierarchical ID-based blind signature schemes are communicationally efficient and needs only one round data exchanges between the signer and the user, and with a shorter public key and signature in comparison with similar schemes[2, 3]. We prove that our scheme is secure assuming that the short integer solution (SIS) problem is hard.

The development of quantum computation casts serious threats to the securities of most existing public-key cryptosystems. Braid-based cryptography is one of the alternatives that have potential advantages in resisting quantum attacks. In this paper, the state of the art of braid cryptography is surveyed, and then a new cryptographic problem—conjugate adjoining problem related to braid groups is proposed. Based on this problem, we design a new braid-based signature scheme. This scheme is efficient and provably secure in the random oracle model. Further, we present the comparison between braid-based signatures and RSA-based ones. The signing process of the braid-based schemes is more efficient than that of RSA-based ones, while the verifying process of the braid-based ones is observably slow. Hence, braid-based signatures are suitable for scenarios where the signing process has to be as quick as possible but delays are permitted in the verifying process, for example, in off-line e-cash systems. The key sizes in braid-based schemes are considerably large—about 2K bits in the case of secret keys and 12K bits in the case of public keys. However, braid operations are much simpler and more efficient than modular exponential operations. Therefore, braid-based schemes can be embedded into devices with low computational ability and large memory space. The capability of braid cryptosystems to resist currently known quantum attacks is also discussed from the perspective of hidden subgroup problems.

Quantum algorithms bring great challenges to classical public key cryptosystems, which makes cryptosystems based on non-commutative algebraic systems hop topic. The braid groups, which are non-commutative, have attracted much attention as a new platform for constructing quantum attack-resistant cryptosystems. A ring signature scheme is proposed based on the difficulty of the root extraction problem over braid groups, which can resist existential forgery against the adaptively chosen-message attack under the random oracle model.

An efficient provably secure identity-based blind signature (IBBS) scheme based on bilinear pairings is proposed. Assuming the intractability of the q-Strong Diffie-Hellman problem, our IBBS is unforgeable under adaptive chosen-message and ID attack. Because of avoiding using the inefficient MapToPoint function, our IBBS can offer advantages in runtime over the schemes available. Based on this ID-based blind signature scheme, we describe the first ID-based threshold blind signature (TBS) and show that it has security properties of unforgeability and robustness.

Blind signature allows a user to obtain a signature from an authority on any document, in such a way that the authority learns nothing about the message that is being signed. The blindness is an important property which distinguishes the blind signature from other signature schemes. Partially blind signature is an extension of blind signature that allows a signer to sign a partially blinded message that include pre-agreed information in the resulting signatures. Recently, Liao et al. proposed a pairing-based provable blind signature scheme without random oracles, and Hu et al. proposed an efficient ID-based partially blind signature scheme with security proof. But in this paper, we show that the two schemes do not satisfy the blindness and partially blindness, respectively. Liao et al.'s scheme is linkability and in Hu et al.'s scheme, a malicious user can replace pre-agreed common information with a special information

Blind signatures allow a signer to issue signatures on messages chosen by the signature recipient. The main property is that the recipient’s message is hidden from the signer. There are many applications, including Chaum’s e-cash system and Privacy Pass, where no special distribution of the signed message is required, and the message can be random. Interestingly, existing notions do not consider this practical use case separately. In this paper, we show that constraining the recipient’s choice over the message distribution spawns a surprising new primitive that improves the well-established state-of-the-art. We formalize this concept by introducing the notion of non-interactive blind signatures ( $$\textsf{NIBS}$$ ). Informally, the signer can create a presignature with a specific recipient in mind, identifiable via a public key. The recipient can use her secret key to finalize it and receive a blind signature on a random message determined by the finalization process. The key idea is that online interaction between the signer and recipient is unnecessary. We show an efficient instantiation of $$\textsf{NIBS}$$ in the random oracle model from signatures on equivalence classes. The exciting part is that, in this case, for the recipient’s public key, we can use preexisting keys for Schnorr, ECDSA signatures, El-Gamal encryption scheme or even the Diffie-Hellman key exchange. Reusing preexisting public keys allows us to distribute anonymous tokens similarly to cryptocurrency airdropping. Additional contributions include tagged non-interactive blind signatures ( $$\textsf{TNIBS}$$ ) and their efficient instantiation. A generic construction in the random oracle or common reference string model based on verifiable random functions, standard signatures, and non-interactive proof systems.

Electronic voting is an alternative mechanism of ballot based voting which empowers voters to cast their secret and secure vote electronically over a public channel. Many onward-thinking countries are adopting the electronic voting system to upgrade their election process. E-voting system is more complicated to construct. Thus it expects more security as compared to the postal voting system. The objective of the paper is twofold. Firstly, we proposed an efficient blind signature scheme using the identity-based cryptosystem in the random oracle model. The proposed scheme uses the combination of Boldyreva’s blind signature scheme and Choon-Cheon’s Identity-based signature. Additionally, we reduce its security to the Gap Diffie-Hellman Complexity (GDH). Under the adaptive chosen message and ID attacks it is secure against existential forgery attack. We show our proposed system performed better as compared to existing systems. Secondly, we construct an E-voting system based on our ID-based blind signature and Boneh’s short signature scheme (EVS-ID-BS) that fulfills the E-voting security requirements. To the best of our knowledge, EVS-ID-BS is the first practical implementation of E-voting system based on ID-BS Scheme which is constructed in the random oracle model. Proposed EVS-ID-BS scheme provides batch verifiability for a significantly large number of voters, needs less bandwidth cost and require less interaction with election authority.

Restrictive blind signatures allow a recipient to receive a blind signature on a message unknown to the signer but the choice of the message is restricted and must conform to certain rules. Partially blind signatures allow a signer to explicitly include necessary information (expiration date, collateral conditions, or whatever) in the resulting signatures under some agreement with the receiver. Restrictive partially blind signatures incorporate the advantages of these two blind signatures. In this paper we first propose a new restrictive partially blind signature scheme from bilinear pairings. Since the proposed scheme does not use Chaum-Pedersen's knowledge proof protocol, it is much more efficient than the original restrictive partially blind signature scheme. We then present a formal proof of security in the random oracle model. Moreover, we use the proposed signature scheme to build an untraceable off-line electronic cash system followed Brand's construction.

In this paper, we propose a practical ID-based (partially)blind signature scheme. Our scheme combines the already existing notions of blind signatures and identity-based cryptography.The signatures are shown secure in the random oracle model. We show how to use our ID-based PBSs to construct an electronic cash (e-cash) system in which multiple banks can securely distribute untraceable e-cash.

Liao et al. proposed first blind signature schemes without random oracles from pairings and provided security proofs in CIS'05. However, we show that their blind scheme is neither blind, nor unforgeable, anyone not to query the signing oracle can forge signature of any message.

SummaryStrong Designated Verifier Signature (SDVS) provides authentication for the signer and the verifier such that the signer is assured that what s/he has signed, is only verified by the designated verifier. Currently, the security of most of the SDVS schemes is based on hard problems in the number theory. As it is proved that all kinds of cryptosystems which are based on the number theory will not tolerate quantum attacks, here, an SDVS scheme based on hard problems in coding theory is presented. We have proved that the suggested scheme is unforgeable under a chosen message attack in Random Oracle Model. Copyright © 2016 John Wiley & Sons, Ltd.

We analyze several alternatives of blind digital signatures, for an electronic electoral system in a distributed architecture environment, in view of the persistence of blind signature problems in electoral processes. The objective is to recognize and propose an alternative of a blind signature scheme to improve privacy, confidentiality for the voter and in this way reduce any type of vulnerability with respect to the information of the same. The deductive method is used to summarize the information of the scientific articles studied. It results in a blind signature prototype based on algorithms to mitigate the vulnerabilities of voter information. It is concluded that, in order to guarantee privacy and confidentiality, several blind signature schemes must be implemented together to obtain the benefits of each of them, thus reducing the risks to which the voter's information is exposed in this process.

Kakvi and Kiltz (EUROCRYPT'12) proposed the first tight security reduction for RSA full domain hash signature scheme (RSA-FDH) with public exponent e < N1/4 in the random oracle (RO) model, and they left an open problem which called for a tightly secure RSA-FDH for N1/4 < e < N. In this paper, we consider the improved RSA (iRSA) trapdoor functions, introduced by Cao (Science in China'01), are functions that the security can be strictly proved to be equivalent to the factoring. We show that iRSA-FDH has a tight security reduction for e < N. Technically we construct iRSA lossy trapdoor functions, and then we apply the lossiness of the iRSA trapdoor functions to obtain tight security reductions for iRSA-FDH in the RO model. Finally, we propose a tightly secure blind signature scheme based on our iRSA lossy trapdoor functions in the RO model.