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.

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.

Research on the Validity Duration ofOff-Line E-cash

To solve the drawback of the present electionic cash (E-cash) schemes that the size of bank's transcripts database expands without bound, the concept of validity duration of E-cash is introduced in this paper. Through improving the users' blind transforms of Brands' scheme, we design an efficient off-line E-cash system based on the restrictive blind signature and representation problem. The security analysis shows that the users can not forge a valid electronic coin or double spend it, in addition, the bank can not trace an honest users' payment behaviours. In compare with Brand's scheme, our scheme reduces storage costs and computation overhead of the users and the banks. Most of all, the electronic cashes will be authorized within a limit period only, the size of bank's transcripts database becomes controllable. Key words E-cash - restrictive blind signature - validity duration - non-trivial representation - double spending CLC number TP 309.2 Foundation item: Supported by the National Natural Science Foundation of China (90104033)Biography: Peng Bing (1972-), male, Ph. D. candidate, research direction: information security, electronic payment and modern 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.

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.