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Spending Offline Divisible Coins with Combining Capability

Eikoh ChidaContact Information, Yosuke KasaiContact Information, Masahiro MamboContact Information and Hiroki ShizuyaContact Information

(6)  Dept. of Electrical Eng., Ichinoseki National College of Technology, Takanashi, Hagisho, Ichinoseki, 021-0902 Iwate, Japan
(7)  NEC Soft, Ltd., 1-18-6 Shinkiba, Koto-ku, 136-8608 Tokyo, Japan
(8)  Graduate School of Information Sciences, Tohoku University, Kawauchi, Aoba, 980-8576 Sendai, Japan
Abstract
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.

Keywords  Offline divisible coins - Combining capability - Combined coin - Anonymity - Overspending prevention - Efficiency


Contact Information Eikoh Chida
Email: chida@ichinoseki.ac.jp

Contact Information Yosuke Kasai
Email: kasai@mxn.nes.nec.co.jp

Contact Information Masahiro Mambo
Email: mambo@icl.isc.tohoku.ac.jp

Contact Information Hiroki Shizuya
Email: shizuya@icl.isc.tohoku.ac.jp
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