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...on, and the total complexity of both transactions is comparable to that of a payment of a fixed amount. 1 Introduction The introduction of public key crypto-systems and digital signatures ([DH76] and =-=[RSA78]-=-) has led to the construction of many different types of payment systems. During payment at least one and often more digital signatures must be created and verified. This has the advantage that it can...

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...communication, and the total complexity of both transactions is comparable to that of a payment of a fixed amount. 1 Introduction The introduction of public key crypto-systems and digital signatures (=-=[DH76]-=- and [RSA78]) has led to the construction of many different types of payment systems. During payment at least one and often more digital signatures must be created and verified. This has the advantage...

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...ing payment makes (something like) a signature on a message describing the recipient and the amount to be paid. The method is most easily explained as an application of Lamport's password scheme (see =-=[Lam81]-=-) to encode amounts in payments. An earlier application of repeated computations of one-way functions is described in [Mer90] and attributed to Winternitz (1979). In relation to payment systems a simi...

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... most easily explained as an application of Lamport's password scheme (see [Lam81]) to encode amounts in payments. An earlier application of repeated computations of one-way functions is described in =-=[Mer90]-=- and attributed to Winternitz (1979). In relation to payment systems a similar idea is used in [BC90] to encode amounts. The encoding suggested in the following is a simplification of that in [BC90] s...

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..., Fer93, Bra94]). As this often requires a large number of coins in a payment, leading to inefficiency with respect to time, storage and communication, electronic cheques with refund were proposed in =-=[CFN90]-=-. Here, the user obtains (buys) a number of cheques during withdrawal. Each cheque has an upper limit and can be spent for any amount up to this limit. A possibly remaining amount of a cheque can late...

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...d communication, and the total complexity of both transactions is comparable to that of a payment of a xed amount. 1 Introduction The introduction of public key crypto-systems and digital signatures (=-=[DH76]-=- and [RSA78]) has led to the construction of many di erent types of payment systems. During payment at least one and often more digital signatures must be created and veri ed. This has the advantage t...

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...over all random choices during payment and deposit. Unchangeability ensures that amounts and other information encoded in m cannot be changed. The function f must be one-way on its iterates (see also =-=[Lev85]-=-): 1 A function g : IN ! IR is negligible if for all c ? 0 and k sufficiently large jg(k)jsk \Gammac . Definition 3.2 Let f : f0; 1g ! f0; 1g be a length preserving function. f is said to be one-way o...

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...based systems, but still less practical than encoding amounts as described above since the user must contact the bank in order to convert "refundable" money to "spendable" money. A=-=nother proposal, in [OO92]-=-, is to use so called divisible coins. Here the user can split a coin arbitrarily (i.e., this is much like a cheque with refund, where the refund can be spend). These systems offer more flexibility th...

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...he length of signatures. Since the computations on the users side must be performed by small devices with relatively little computation power such as smart cards or electronic wallets (see [EG84] and =-=[Cha92]-=- for two different types of wallets), it is important that the users part of all transactions can be done very efficiently. Although recent research has improved the efficiency of (privacy protecting)...

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...depend on the length of signatures. Since the computations on the users side must be performed by small devices with relatively little computation power such as smart cards or electronic wallets (see =-=[EG84]-=- and [Cha92] for two different types of wallets), it is important that the users part of all transactions can be done very efficiently. Although recent research has improved the efficiency of (privacy...

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...in payments. An earlier application of repeated computations of one-way functions is described in [Mer90] and attributed to Winternitz (1979). In relation to payment systems a similar idea is used in =-=[BC90]-=- to encode amounts. The encoding suggested in the following is a simplification of that in [BC90] specifically designed for tick payments and can be used in many different systems. The proposed soluti...

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... most easily explained as an application of Lamport's password scheme (see [Lam81]) to encode amounts in payments. An earlier application of repeated computations of one-way functions is described in =-=[Mer90]-=- and attributed to Winternitz (1979). In relation to payment systems a similar idea is used in [BC90] to encode amounts. The encoding suggested in the following is a simpli cation of that in [BC90] sp...

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...he length of signatures. Since the computations on the users side must be performed by small devices with relatively little computation power such as smart cards or electronic wallets (see [EG84] and =-=[Cha92]-=- for two di erent types of wallets), it is important that the users part of all transactions can be done very e ciently. Although recent research has improved the e ciency of (privacy protecting) elec...