EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Untraceable off-line cash in wallet with observers
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Divisible Electronic Cash Scheme
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Attacking and Repairing Batch Verification Schemes
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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In the purchase with electronic money customers are sometimes required to spend multiple electronic coins at a time. In case of physical coins a customer simply grabs multiple coins and hands them out to a merchant. Likewise, the customer spends multiple electronic coins just by giving all coins to the merchant. However, we can expect one step further in the electronic coins. There is room to create a combined coin from multiple coins. If the combining leads to an efficient spending, the customer as well as the merchant and the bank can get benefit of the reduction of cost. There is a proposal by Chaum for the combining operation in the online cash, but no method has been proposed for offline coins up to now. Thus we seek a way to spend offline electronic coins in a combined form without assistance of an issuing bank. The combining reduces either computational complexity associated with the spending or communication complexity between the customer and the merchant. We propose a method to achieve combining capability in the Eng-Okamoto offline divisible electronic cash, and show that (2n - 2)|p| - (n - 1)|q| bits of the message length can be reduced in the combining of n coins under the parameter of moduli p and q satisfying q|p-1. If preliminary computation is allowed, the verification cost is also slightly reduced. Significantly, even after combining coins, the bank can identify overspenders.