An efficient divisible electronic cash scheme

Abstract

Recently, several “divisible” untraceable off-line electronic cash schemes have been presented [8, 11, 19, 20]. This paper presents the first practical “divisible” untraceable1 off-line cash scheme that is “single-term”2 in which every procedure can be executed in the order of log N, where N is the precision of divisibility, i.e., N = (the total coin value)/(minimum divisible unit value). Therefore, our “divisible” off-line cash scheme is more efficient and practical than the previous schemes. For example, when N = 217 (e.g., the total value is about $ 1000, and the minimum divisible unit is 1 cent), our scheme requires only about 1 Kbyte of data be transfered from a customer to a shop for one payment and about 20 modular exponentiations for one payment, while all previous divisible cash schemes require more than several Kbytes of transfered data and more than 200 modular exponentiations for one payment. In addition, we prove the security of the proposed cash scheme under some cryptographic assumptions. Our scheme is the first “practical divisible” untraceable off-line cash scheme whose cryptographic security assumptions are theoretically clarified.