Fair E-Payment Protocol Based on Simple Partially Blind Signature Scheme

This paper presents a simple partially blind signature scheme with low computation. By converse using the partially blind signature scheme, we build a simple fair e-payment protocol. In the protocol, two participants achieve the goals of exchanging their digital signatures from each other in a simple way. An ado vantage of this scheme is that this approach does not require the intervention of the third party in any case. The low-computation property makes our scheme very attractive for mobile client and smart-card implementation in many e-commerce applications.

Provably Secure Convertible Directed Partially Blind Signatures

Combining the concept of partially blind signature with the concept of directed signature, we introduce a new concept of convertible directed partially blind signature （CDPBS）, in which only the signer and the user can verify, confirm and disavow the validity of given signatures and convert given signatures into universally verifiable ones, to meet the need of signing personally or commercially sensitive messages. We give a formal definition of CDPBS and propose a concrete provably secure CDPBS scheme. The proposed scheme is efficient and secure, in which its unforgeability is the same as that of the Schnorr＇s signature scheme and its untransferability relies on the hardness of the decisional Diffie-Hellman problem. Furthermore, by letting the user＇s private key be a common constant, the proposed scheme can be used as a normal partially blind signature scheme.

Untraceable partially blind signature based on DLOG problem

This paper proposes a new untraceable Partially Blind Signature scheme which is a cross between the traditional signature scheme and the blind signature scheme. In this proposed scheme, the message M that the signer signed can be divided into two parts. The first part can be known to the signer (like that in the traditional signature scheme) while the other part cannot be known to the signer (like that in the blind signature scheme). After having signed M, the signer cannot determine if he has made the signature of M except through the part that he knows. We draw ideas from Brands' 'Restricted Blind Signature' to solve the Untraceable Partially Blind Signature problem. Our scheme is a probabilistic signature scheme and the security of our Untraceable Partially Blind Signature scheme relies on the difficulty of computing discrete logarithm.

A new lattice-based partially blind signature with more complete proof

Partially blind signatures are introduced on the basis of blind signatures,which not only retain the advantages of blind signatures,but also solve the contradiction between anonymity and controllability in blind signatures.With the development of quantum computing technology,it becomes more urgent to construct secure partially blind signature schemes in quantum environments.In this paper,we present a new partially blind signature scheme and prove the security under the Ring-SIS assumption in the random oracle model.To avoid the restart problem of signature schemes caused by rejection sampling,a large number of random numbers are sampled in advance,so that they only need to be re-selected at the current stage without terminating the whole signature process when the conditions are not met.In addition,the hash tree technology is used to reduce communication costs and improve interactive performance.In order to avoid the errors in the security proof of the previous scheme,our proof builds upon and extends the modular framework for blind signatures of Hauck et al.and the correctness,partial blindness,and one-more unforgeability of the scheme are proved in detail according to the properties of the linear hash function.

Forgeability of Wang-Tang-Li's ID-Based Restrictive Partially Blind Signature Scheme

Restrictive partially blind signature （RPBS） plays an important role in designing secure electronic cash system Very recently, Wang, Tang and Li proposed a neW ID-based restrictive partially blind signature （ID-RPBS） and gave the security proof. In this paper, we present a cryptanalysis of the scheme and show that the signature scheme does not satisfy the property of unforgeability as claimed. More precisely, a user can forge a valid message-signature pair （ID, msg, info＇, σ＇） instead of the original one （ID, msg, info, σ）, where info is the original common agreed information and info＇≠info. Therefore, it will be much dangerous if Wang-Tang-Li＇s ID-RPBS scheme is applied to the off-line electronic cash system. For example, a bank is supposed to issue an electronic coin （or bill） of $100 to a user, while the user can change the denomination of the coin （bill） to any value, say $100 000 000, at his will.

A Fair Off-Line Electronic Cash Scheme Based on Restrictive Partially Blind Signature

A fair off-line electronic cash scheme was presented based on a provable secure restrictive par-tially blind signature. The scheme is more efficient than those of previous works as the expiry date and de-nomination information are embedded in the electronic cash, which alleviates the storage pressure for the bank to check double spending, and the bank need not use different public keys for different coin values, shops and users need not carry a list of bank抯 public keys to verify in their electronic wallet. The modular exponentiations are reduced for both the user and the bank by letting the trustee publish the public values with different structure as those of previous electronic cash schemes. The scheme security is based on the random oracle model and the decision Diffie-Hellman assumption. The scheme can be easily extended to multi-trustees and multi-banks using threshold cryptography.

A Fair E-Cash Scheme Based on Elliptic Curve Cryptography

A new fair off-line electronic cash scheme on elliptic curve cryptography was presented. The new scheme is more efficient than those by extending fair off-line electronic cash scheme from finite field into elliptic curve cryptography and introducing a new elliptic curve discrete logarithm assumption. The expiry date and denomination are embedded into the blindly signed coin by integrating partially blind signature with restrictive blind signature. A bank need not use different public keys for different coin values, shops and users need not carry a list of bank’s public keys to verify in their electronic wallet. At the same time, the bank just needs to keep undue electronic coins for double spending check in his database, thus bank’s database can be dramatically reduced.

Anonymity control in electronic check systems

Electronic check systems, as one of electronic payment systems, are more desirable than other electronic cash systems. In the system, only a single cheek is used to pay any price that is not more than the face value. The main problem in check systems is to design an efficient refund mechanism that makes refired cheeks undistinguished from initial checks during payment and deposit. The problem of anonymity control also called fairmess is also an important issue in check systelns. All check systems yet are unconditional anonymity that opens the door to misuse for crime such as laundering and blackmailing. In this paper, the notion of anonylnity revocation is introduced to electronic check system for the fitst thne, and a model of fair electronic check system is proposed. An effieient fair online electronic check system with reusable refund is presented. In the system, a passive trustee is elnployed to revoke the anonymity of unhonest users. Moreover, the system solves the reusability problem of refunds thanks to the RSA-based partially signature. The system is efficient and meets all basic security requirements.

ID-Based Fair Off-Line Electronic Cash System with Multiple Banks

ID-based public key cryptography （ID-PKC） has many advantages over certificate-based public key cryptography （CA-PKC）, and has drawn researchers＇ extensive attention in recent years. However, the existing electronic cash schemes are constructed under CA-PKC, and there seems no electronic cash scheme under ID-PKC up to now to the best of our knowledge. It is important to study how to construct electronic cash schemes based on ID-PKC from views on both practical perspective and pure research issue. In this paper, we present a simpler and provably secure ID-based restrictive partially blind signature （RPBS）, and then propose an ID-based fair off-line electronic cash （ID-FOLC） scheme with multiple banks based on the proposed ID-based RPBS. The proposed ID-FOLC scheme with multiple banks is more efficient than existing electronic cash schemes with multiple banks based on group blind signature.