Efficient on-line electronic checks

Chaum proposed two electronic check schemes in 1988 and 1989, respectively [Chaum et al., Advances in Cryptology--CRYPTO'88, 1990, pp. 319-327; Efficient Offline Electronic Check, 1989, pp. 294-301]. Both of the two schemes are not efficient. Besides, the face value and payee's identification information of an electronic check has to be decided before the bank issued electronic check. In this paper, an efficient and practical electronic check scheme is proposed to make it possible for a payer to attach the desired face value and payee's identification information to his electronic check when paying. The proposed scheme not only keeps the attached information from being forged but also avoids two or more different face value being attached to the same electronic check. Furthermore, the extra computation required for information attachment is just hashing, without any time-consuming computation such as modular exponentiation or inverse computation. Since the cost of hashing computation is cheap, the proposed scheme is very efficient.