代写爱尔兰都柏林大学留学生计算机硕士论文Reusable Off-line Electronic Cash Using Secret Splitting
Hitesh Tewari, Donal O’Mahony, Michael Peirce
Networks & Telecommunications Research Group,
Computer Science Department, Trinity College,
Dublin 2, Ireland.
{Hitesh.Tewari, Donal.OMahony,
Abstract
The idea of electronic cash, as a payment instrument is appealing, but has yet tobe widely deployed commercially. We outline the properties of two majorapproaches to the provision of electronic cash, and discuss their strengths andweaknesses. We then propose a new scheme based on secret splitting thatallows for off-line spending of coins with a tailored level of anonymity and
allowing reuse of the same coin many times. We then discuss a number ofpractical issues such as the trade off between coin size and the ability to detectdouble spending.
Introduction
The rapid growth of data communications networks in recent years has led to a massive growthin electronic commerce. Large organizations such as banks are always looking for means forspeeding up and simplifying the financial transaction process. The cost associated with printing,transporting and securing cash is quite high. This has led to a great deal of research on theconcept of a cashless society, which would result in elimination of all forms of paper based cash.
However in the digital world, it is easy to duplicate a piece of information that is stored in acomputer’s memory or hard disk. Security mechanisms have to be put in place that will prevent
unscrupulous users from defrauding the system.
There is a need to invent new electronic payment protocols with strong cryptographic algorithmsthat will eventually replace present day paper based cash schemes. Over the years a number ofelectronic cash schemes have been proposed, which try to mimic today’s cash based schemes.
There are a number of features, that one might expect from an electronic cash scheme. We
outline some of these below.
Anonymity – Privacy advocates believe that it should not be easy for a bank or governments to
be able to trace serial numbers of notes to a particular transaction or individual. It should also notbe possible to monitor the activities of individual users and build profiles about their spendinghabits. On the other hand, from the point of view of governments fully anonymous cash is notdesirable, as it could be used as a tool by criminals for illegal activities such as moneylaundering.
Reusability – One should be able to reuse the same piece of cash multiple times. It can pass
from person to person before it is destroyed or deleted by the issuer. This feature in turn can helpwith the previous requirement of anonymity. The more times the cash is transferred, the moredifficult it becomes to trace it to the person to whom it was issued. However, the ability to reuseelectronic currency also increases the risk of double spending and fraud in the system.
Off-line – The ability for two parties to complete a transaction without the intervention of a thirdparty such as the issuing bank or an authentication server is a highly desirable feature.Scalability –There should be no reliance on a centralized architecture, as this can become apoint of failure in the system. It also acts as bottleneck during periods of high usage. For any
scheme to be successful for mass deployment, it must be capable of distributed operation.In this paper, we present an electronic cash scheme that exhibits all the above properties. Thepaper begins with a discussion of a number of important cash-like payment schemes that have
gained significant importance in the area. We then focus on the cryptographic techniques that wehave made use of in our proposed scheme and then go on to describe the payment protocol indetail. Finally we discuss the advantages and disadvantages of the features of our scheme and
make a number of conclusions.
Related Work
A number of electronic payment schemes have been proposed in the recent past. They can be
classified in two broad categories. Schemes that are pure software solutions and do not make use
of any specialized hardware such as smart cards e.g. eCash, and schemes that rely on securehardware for their security such as CAFE. We also describe a payment scheme in widespreaduse called Mondex, which though it may not be classified as a pure electronic cash scheme,exhibits some cash like properties. The analysis of these systems helps us to highlight some ofthe features that we think should be incorporated into an electronic cash scheme for it to beuniversally acceptable.
Digital Cash
A fully anonymous digital cash protocol was proposed by David Chaum in [1, 2, 3]. The schemeis essentially an on-line software solution. This means that a buyer can spend coins with amerchant, which must be validated by the issuer before the purchase can be completed. From
examining the coins, neither the issuer nor the merchant can deduce the identity of the customer.
The protocols are designed such that a issuer is not able detect the serial numbers of coins that itissues to users of the system, even if it colludes with the other participants in the system. Theentities in the system are shown in figure 1.
Figure 1: The Payment Model
A client can withdraw coins from a bank against an existing account. The scheme uses what isreferred to as the blind signature protocol [2]. This protocol allows the user to mint a number ofcoins and forward these unsigned coins to the bank. As long as these coins meet certain criteria,the bank signs these with its secret-key without the knowledge of the serial numbers associatedwith the coins. This feature allows for fully anonymous cash.
/On receiving the coins back from the bank, the user removes the blinding factor and can use thecoins to pay for goods from any merchant that is participating in the system. On receipt of coins,a merchant must immediately forward them to the issuer for verification. The issuer maintains a
database of serial numbers of all coins that have been spent in the system and is thus able todetect double spending.
Advantages
· A software only solution that does not require the use of secure tamper-resistant
hardware e.g. smart cards
· Provides user anonymity and untraceable electronic cash
Disadvantages
· The merchant has to maintain an on-line link with the bank to verify the authenticityof any coins that he accepts. This is an unwanted communications overhead
· The bank has to maintain an ever growing database of serial numbers of coins thathave been spent in the system
· The scheme is difficult to scale, as it requires the spent coins database to bereplicated and synchronization between bank servers
· Coins can only be spent once, after which they must be deposited with the bank
CAFE
CAFE (Conditional Access for Europe) was a project funded under the European ESPRIT
program [6, 7] to develop a secure, anonymous, off-line electronic payment system. The CAFE
Issuer
Client Wallet Merchant Software
Withdraw/
Deposit
Coins
New Coins
Payment
Receipt
Deposit Coins
Result
protocols are based on the idea of untraceable electronic cash proposed by Chaum and are
designed to allow for multi-party security. The security of each entity in the system is guaranteedwithout the need to trust a third party. CAFE employs two types of security mechanisms toprotect the system against attack. The first line of defense is the use of secure tamper-resistant
devices with observers to store cryptographic keys and to perform all cryptographic transactions.
An observer is an embedded integrated circuit that is a trusted entity of the issuing bank. Theobserver acts on behalf of the issuing organization, ensuring that the smart card in which it isplaced dos not deviate from the prescribed protocols.
Protection against double spending is guaranteed as long as the tamper resistance of the devicesinvolved is not compromised. In situations where there is a hardware security breach, CAFE hasa cryptographic fallback mechanism, which allows the financial institutions to detect doublespending of coins and blacklist suspected users. These lists are then distributed to all merchantsin the system.
A coin in the CAFE scheme is constructed from two parts, each of which contains part of theuser identity. When a coin is used in a payment transaction, the payer opens one half of the coin.This on its own does not reveal the identity of the user to whom the coin was issued. However, ifthe user tries to double spend the coin, he will have to open the second half of the coin.Combining the two halves results in the identity of the user being revealed.
Advantages
· Does not rely on secure hardware alone for protection of system security
· It is an off-line scheme
· Banks can detect double spending by users
· Under normal circumstances, payments cannot be linked to a user even if there iscollaboration between the merchants and the banks
Disadvantages
· Need to maintain large databases of spent coins. Can lead to scalability problems
· Reusability of coins is not supported
· Makes use of strong cryptographic techniques to ensure the security of the system
Mondex
The concept of the Mondex [7] card was developed at NatWest, a major UK bankingorganization in 1990. In July 1996, Mondex International (MXI) was incorporated in the UK.The company is owned by MasterCard International and 28 major organizations world wideincluding banks in US, Canada, Australia and Asia.Mondex is an off-line smart card electronic-purse scheme that allows card-to-card transfer of
electronic cash. To use the system, a user loads the card with cash, using either a Mondexautomated teller machine (ATM) or a specially adapted telephone. Each merchant is equippedwith a value transfer terminal. This device can be used to transfer cash from the customer to acard in the merchant’s device.
The Mondex payment scheme is a closed scheme, as the company has not disclosed the detailsof the payment protocol. The scheme is presently in operation in a number of countries aroundthe world.
Advantages
· Value can be transported between cards multiple times
· User-to-user transfer of electronic cash without the intervention of a trusted third
party or an on-line connection
Disadvantages
· Little is known about the internal working of the system (Does not give much
代写留学生计算机硕士论文confidence to end-users)
· Not an anonymous system
To summarize, CAFE and Mondex are electronic payment schemes, which exhibit some cash
like properties. However, none of these schemes is able to fulfill all our requirements for an ideal
electronic cash payment scheme. In the next section, we describe in detail the functionality of
our payment scheme.
Cryptographic Design
In this section, we describe two cryptographic techniques that we have used in the design of our
electronic cash scheme. The first is a mechanism to split the identity of a user into two parts
using a technique called secret splitting. The second technique makes use of this to encode the
identity of a user into a coin.
Secret Splitting
Secret splitting is a technique that allows a message to be divided up into n parts. Each part on its
own has no meaning. However, when they are combined together, they result in the original
message. A simple implementation is to XOR (exclusive-OR) the message M with a one-time
pad R as follows:
M Å R = S
Knowledge of R or S on its own is not sufficient to generate M
In [4], Schneier proposes a digital cash protocol that makes use of the above technique to encode
the identity of a user. Below we outline a simplified version of his protocol that is used in our
proposed electronic cash scheme.
A coin in our scheme consists of a number of fields, such as the serial number, denomination,
validity period and a transaction list. This transaction list comprises of a variable number of
transactions items, where each transaction item is the result of a transfer of the coin between two
users in the system. A transaction item consists of n identity strings (I1, I2, …, In). Each of these
identity strings is generated, by splitting the identity of the user using the secret splitting
protocol.
Transaction Item:
I = (I1L, I1R)
I = (I2L, I2R)
…
I = (InL, InR) (where I is the identity of a user)
XORing the left and right corresponding halves of any pair will result in the identity of the user
(I). The last transaction item in the list is unblinded and contains the identity of the coin’s current
owner. When a coin is transferred from one user to another, the entity acting on behalf of the
bank randomly blinds the left or right half of each of the identity strings. It then adds a new
transaction item (encoding the identity of the recipient) to the transaction list, cryptographically
binds the new transaction list to the coin and forwards the coin to its new owner.
Figure 2: A Transaction Item List
Figure 2 shows a transaction list of a coin whose second last transaction item has been blinded,
while the last transaction item remains in the clear. If a user tries to spend this coin twice, during
each individual payment transaction the left or right halves of the coin will be randomly blinded.
There is a high probability that one or more corresponding left and right halves of the transaction
will remain unblinded. When two coins with the same serial numbers are deposited back to the
issuer, it will be able to look through the transaction list and combine the two halves to reveal the
identity of the user that committed the fraud.
System Overview
In this section, we give an overview of our system. It consists of a number of entities, which
communicate with each other to complete various stages of the payment process.
System Entities
The entities that comprise the system are:
Issuer – Responsible for the minting and detection of double spending of coins. It maintains a
database of coins that have been deposited and are no longer in circulation in the system. Since
the coins are reusable, the size of the database is significantly smaller compared to some of the
Transaction List
Transaction Item 1
Transaction Item 2
Transaction Item 3
Transaction Item (m-1)
Transaction Item m
:
:
:
Transaction Item m-1
7438 0
9865 0
0 9875
:
:
0 4566
3776 0
Transaction Item m
9876 9596
1654 1438
4566 4670
:
:
2165 2973
UID = 9010 Å 8410 9010 8410
UID = 1000
schemes we have previously outlined. Each coin also has validity period associated with it. This
also helps in reducing the overall size of the database
Bank – Maintains end-user accounts. It distributes and accepts coins from end-users
Buyer – Users have accounts with banks from which they can withdraw and deposit coins. They
store coins in an electronic purse or a software wallet
Merchant – Users that can accept coins in exchange for hard goods
Point of Sale (POS) Device – Secure off-line devices that act as intermediary’s during the
transfer of coins between two users. Black lists are downloaded to the device from a central
server at periodic intervals, along with the serial numbers of coins that have been deposited more
than once at the issuer
Figure 3 shows the various steps that make up the payment process. A bank may periodically ask
the issuer to mint a large quantity of coins. When a request is made by an authorized user for
new coins, the bank will bind the coins to the users identity and forward the same. A user can
then use the coins to pay for services from any merchant in the system. A POS will be involved
in the transfer of coins between the two.
Figure 3: Overview of the System
The POS will verify the authenticity of the coins. It will blind the last transaction item in the
transaction list and add a new transaction item to the end of the list. This will bind the coin to the
recipient (e.g. merchant). The merchant can immediately reuse the coins to pay for services from
other users in the system e.g. buying supplies from a wholesaler. At some stage in the process,
an end-user will have to deposit the coins with his bank. The bank will forward the coins to the
issuer who will check for double spending and add the serial numbers of the spent coins to its
database.
Issuer Deposited Coins DB
Client Wallet
User DB
Bank 1 Bank 2
3. Withdraw/Deposit
Coin(s)
4. New Coins
1. Mint Coin(s)
2. New Coin(s)
5. Price & Goods Negotiation
6. Payment 7. Forward Coins
Merchant
10. Deposit
Remaining Coins
User DB
13. Statement
11. Coin Verification
12. Result
POS (1)
POS (2)
Wholesaler
8. Spend some of the
9. Forward Coins Coins with another User
There are a number of public-key pairs in the system, which are used for minting coins and
appending transaction items. PK is denoted as the public-key and SK as the secret-key.
· Public key pair for minting and verifying the authenticity of coins
(PKIssuer, SKIssuer)
· Public key pair for appending and verifying transaction items to a coin
(PKTrans, SKTrans)
Table 1 shows the keys which each entity in the system possess
Issuer (PKIssuer, SKIssuer) (PKTrans, SKTrans)
Bank PKIssuer (PKTrans, SKTrans)
POS PKIssuer (PKTrans, SKTrans)
Users PKIssuer PKTrans
Table 1: The System Keys
The issuer is able to mint and verify the authenticity of coins. The banks and the point of sale
devices can verify the authenticity of coins and are able to append transaction items to coins.
They are not able to mint coins.
Each end-user is assigned an identifier (UID) which is signed by the issuer. A digital signature
on a given value consists of the value, along with a hash of the same, which is encrypted with the
secret-key of the signer.
(UID)SigIssuer = {UID, (H(UID))SKIssuer}
A UID is used by the banks and the POS devices in the system to verify the identity of end-users
and to bind coins to the recipient of the same.
Structure of a Coin
A coin in the system consists of the following parameters:
{SN, Denom, Val}SigIssuer, (H(SN, Denom, Val), TranList)SigTrans}
· Serial Number (SN) – A unique system wide identifier
· Denomination (Denom) – The face value of the coin
· Validity (Val) – The period of time for which this coin remains valid. This parameter
limits the size of the database at the issuer
· Transaction List (TranList) – A list of transaction items associated with each time the
coin is transferred from one user to another. There is an upper-limit to the number of
transaction items that can be contained in a transaction list
The first three fields of the coin are signed with the secret-key of the issuer (SKIssuer). To bind a
coin and its corresponding transaction list together, a hash of the first three fields along with the
transaction list is signed with the secret-key (SKTrans). This last part of the coin can be modified
by the banks and the POS devices in the system, to bind the coin to a recipient during a coin
transfer phase.
The Payment Protocol
We now describe in detail the messages that are used to effect the various stages of the payment
process. They are the withdrawal, payment and deposit phases. We also describe how the system
is able to detect double spending of coins by users.
Withdrawal
When a user wishes to withdraw some coins from his bank
1. He forwards his signed UID along with the amount of coins required to the bank
The bank:
· Verifies the user identity and account details
· May have a number of coins in storage or it may have to request coins from the
issuer
· Uses the secret splitting technique on the UID to generate the first transaction item
for the coin. It adds this unblinded transaction item to the transaction list and signs
it with (SKTrans). This binds the user to the coin
2. The bank forwards the coins to the user
Figure 4: Withdrawal of Coins
The network link between the client and the bank can be secured in a number of ways e.g. using
a shared secret, Secure Socket Layer (SSL) [8, 9] or using the Diffie-Hellman [4, 5] keyagreement
algorithm.
User DB
Bank
Coin
Serial Number
Denomination
Validity
Transaction List [… ]
Transaction List
Transaction Item 1 Transaction Item 1
5390 7416
1056 3542
4902 6864
:
:
6522 4236
7159 4609 UID = 7159 Å 4609
Client Wallet
1. {(UID)SigIssuer, Amt}
2. {(Coin)SigIssuer, (H(Coin), TranList)SigTrans)}
UID = 2550
Payment
When a customer wishes to purchase goods, he negotiates a price with the merchant. The
process of price negotiation and selection of merchandise is beyond the scope of this discussion.
Once both parties agree on the purchase details, the transfer of coins can take place. This occurs
in the presence of a POS device. This is a secure off-line device, whose role is to verify the
authenticity of the coins being transferred and to bind the coins to the recipient’s identity. Figure
5 gives an overview of the process.
Figure 5: Payment for Goods
The steps, which constitute the main payment process, are as follows
1. The customer forwards coins and his signed UID to the POS
2. The merchant also forwards his signed UID to the POS
For each coin that the POS receives from the customer it:
· Verifies the authenticity of the coin and checks the validity period
· Consults its local database of black listed users and ensures that both parties to the
transaction are valid users of the system
· Verifies that the last transaction item in the transaction list belongs to that of the
customer. This gives confidence to the POS device that the coin has not been stolen
· If either of the above steps fail the POS will reject the coin
· Randomly blinds the left or right half on individual entries in the last transaction
item. This prevents the new owner of the coins from identifying the customer
Client Wallet Merchant
POS
Price & Goods Negotiation
{Coin(s), (UIDCustomer)SigIssuer}
1. Authorize payment
{(UIDMerchant)SigIssuer}
6391 8099
1004 1208
2114 3862
4969 5181
9901 8697
3. Coin(s)
2. UID of Merchant
Transaction List
Transaction Item 1
Transaction Item 2
Transaction Item 3
Transaction Item (m-1)
Transaction Item m
:
:
:
Transaction Item m-1
:
:
Transaction Item m
:
:
UIDMerchant = 9901 Å 8697
5390 0
1056 0
0 6864
0 4236
7149 0
UIDMerchant = 1876
· Creates a new unblinded transaction item that binds the coin to the recipient
(merchant) and signs it with (SKTrans)
3. Finally, it forwards the coins to the merchant
To prevent a user from masquerading as a merchant and accepting coins on his behalf, each POS
device in the system can be personalized for the merchant to whom it is issued. The merchant
would then share a secret with the POS e.g. password, which is used to authenticate him to the
device.
Employing the above method prevents the transfer of coins between two end-users. If such
functionality were desired, one would require all users and POS devices in the system to share a
secret. Alternatively, one could assign public/secret key pairs and associate certificates to all
users of the system.
Deposit
An end-user may be required to deposit coins with his bank if the number of transaction items
has reached its maximum limit or if the validity period of a coin is about to expire. This ensures
that the size of the coin does not become too large. It also helps in minimizing the risk of not
being able to detect coins that have been double spent, for long periods.
Figure 6: A Deposit Transaction
1. The user forwards the coins along with his signed UID to the bank
2. The bank compares the UID of the user against the last transaction item in the
transaction list. This gives the bank confidence that the coins were not stolen. It forwards the
coins to the issuer. This step can be performed immediately or at a later date when the bank
has a batch of coins to clear
For each coin deposited with the issuer:
· It consults the deposited coins database and checks to see that the coin has not been
deposited previously
· If not, it then adds the serial number of coin to the database
Deposited Coins DB
Issuer
Bank
User DB
User
{Coin(s), (UID)SigIssuer}
1. Deposit Coin(s)
2. Verification of Coin(s)
3. Result
4. Statement
3. The issuer returns a result to the bank
4. The bank credits the user’s account and forwards a statement to the user
Tracing Double Spenders
Since a coin is just a piece of digital data, it is possible for a user to duplicate this information
and attempt to spend a coin multiple times. There is a post-fact detection mechanism built into
the system so that double spending can be detected when the coins are being deposited at the
issuer with a high probability of identifying the offending party.
If the issuer detects a coin with the same serial number as one previously recorded in its
database, it will assume that the coin has been double spent. It will try to determine the UID of
the user that spent the coin multiple times.
Figure 7:Post-fact Detection of Double Spending
It does this by traversing through the transaction items in the transaction list of the two coins,
and identifying corresponding transaction items where different left and right half entries have
been opened. Remember that each POS device will randomly blind the right and left halves of a
transaction item. Once the issuer finds an entry where the corresponding left and right halves are
in the clear in the two coins, it does a simple XOR of the two values to reveal the UID of the
culprit.
Users that are caught double spending are eliminated from the system. Their UID is distributed
in black lists to all POS devices in the system along with the serial numbers of the coins.
Transaction Item 1
Transaction Item 2
Transaction Item 3
Transaction Item (n-1)
Transaction Item n
:
:
:
:
Transaction Item 1
Transaction Item 2
Transaction Item 3
Transaction Item (n-1)
Transaction Item n
:
:
:
:
:
:
:
:
Original Coin Duplicate Coin
UID = 1056 Å 3542
UID = 6522 Å 4236
5390 0
1056 0
0 6864
0 4236
7149 0
5390 0
0 3542
4902 6864
6522 0
7149 0
Critique
We have presented a cash-like electronic payment scheme combines the benefits of off-line
functionality with detection of double spending of coins by users. The two main concerns that
one might express about the scheme are to do with anonymity of transactions and the size of
coins. The latter impacts on the type of storage that may be used for the system. We address each
of these concerns below.
Anonymity
Under normal operation, the scheme allows for anonymous cash transactions. The initial
(withdrawal) and final (deposit) transactions allow a bank to associate a coin’s serial number
with the UID of the end-user. All intermediate transactions involving POS devices will hide the
identity of the last owner of the coin. Only if a user double-spends a coin will his identity be
revealed.
However, it is also possible to relax this option by allowing the POS devices in the system to
maintain a log of each transaction. This log could then be transferred to the issuer, who could use
it to create an audit trail for each coin.
Storage Requirements & Double Spending
Each of the coins in the system we propose consists of a fixed header component together with a
variable length transaction list that is enlarged each time the coin is spent. The size of this
variable length component depends on a number of factors:
· The Users Identity (U) - Users in the system are issued with numerical identities.
These are then encoded into the coin by the point of sale device
· The number of entries in each transaction item (T)
· The maximum number of times a coin can be spent (M)
When a coin is generated, the transaction list contains a single users identity encoded as a pair of
(unblinded) numbers. Thus
Minimum Transaction list size = 2 * T * U
Each time the coin is used (up to M times), a blinded transaction item is added. Given that one of
the two numbers in each entry is blinded, this can be compactly represented using just one
number, and a single bit indicating whether it is the left or the right component of the pair.
Maximum Transaction list size = 2 * T * U + (M - 1) (U + 1) * T
Some typical values for the above parameters and the consequent coin sizes are shown in the
following table:
Parm Values Min Size Max Size Avg Size
U=64bits,T=6,M=10 96 bytes 535 bytes 315 bytes
U=64bits,T=3,M=5 46 bytes 146 bytes 97 bytes
U=32bits,T=3,M=5 24 bytes 74 bytes 49 bytes
It is clear that coin sizes of up to half a kilobyte does mean that a significant amount of storage is
required to store a reasonable amount. For example, using the first set of parameters in table 2 :
maintaining $40 in an electronic purse in $1 denominations would occupy 12.6 kilobytes. If the
same amount were stored using 1 cent coins, the storage requirement would exceed 1 Mbyte.
These values rule out the use of current generation smart cards, but other portable hardware
devices could cope with these storage requirements.
Minimising T and M will limit the maximum size of each coin, but these values also have a
major bearing on the systems ability to detect and block double spending. Once a coin has been
double spent, it will continue to be used until all of its M transactions have been used up. Thus
the value of M is determines how long it will take before the coins return to the issuer where the
double spending may be detected. Fraudsters are likely to choose relatively 'fresh' coins to
maximise this time.
When a coin is returned to the bank, any cases of double spending will cause the issuer to match
the transaction lists of the coins in question. If there is only one entry per transaction list (T=1),
and the coin has been spent twice, the probability that the fraudsters identity can be recovered is
50%. If T=2, then this increases to 75% while with larger values such as T=6 there is a 98.5%
chance of detection.
If the coin is spent more than twice, the probability of detection goes up very quickly indeed. In
general, if the coin is used K times, the probability of detection is:
Probability of Detection = 1 – 1/2^ T(K-1)
So, for example, a fraudster spending a single coin with T=6, 3 times has a 99.97% chance of
having his identity discovered.
Balancing the penalty of increased size with choosing large values for T and M against the
increased protection, issuers may choose to use larger values for coins with high values and opt
for smaller coins to represent low values.
Conclusions
This paper presents a lightweight electronic cash payment scheme. It has the flexibility that one
would expect from present day paper based cash schemes, without the complexity that is
sometimes associated with electronic payment systems. It combines the benefits of off-line
payments, user anonymity and reusability of coins. The scheme has a post-fact detection of
double spending mechanism built into it, and is well suited for real-time payments in today’s
increasingly digital world.
References
[1] D. Chaum, A. Fiat and N. Naor, “Untraceable Electronic Cash”, Proceedings of Crypto ’88,
Springer-Verlag, v. 403, 1990, pp. 319-327
[2] D. Chaum, “Security without Identification: Transaction Systems to Make Big Brother
Obsolete”, Communications of the ACM, v. 28, n. 10, Oct 1985, pp. 1030-1044
[3] D. Chaum, “Achieving Electronic Privacy”, Scientific American, v. 267, n. 2, Aug. 1992, pp.
76-81
[4] B. Schneier, “Applied Cryptography”, 2nd Ed., John Wiley & Sons, Inc, 1996
[5] 代写留学生论文W. Diffie and M.E. Hellman, “New Directions in Cryptography”, IEEE Transactions on
Information Theory, v. IT-22, n. 6, Nov 1976, pp. 644-654
[6] J. P. Boly et al., “The ESPRIT Project CAFE – High Security Digital Payment Systems”,
ESORICS ’94, Springer-Verlag, v. 875, 1994, pp. 217-230
[7] D. O’Mahony, M. Peirce, H. Tewari, “Electronic Payment Systems”, Artech House
Publishers, Boston, 1997
[8] K. Hickman, “The SSL Protocol”, Netscape Communications Corp., 501 E. Middlefield Rd.,
Mountain View, CA 94043, Feb. 1995, [9] P. Kocker, A. Freier and P. Karlton, “The SSL Protocol Version 3.0”, Netscape
Communications Corp., March 1996, Ecash – /Mondex – NTRG – ntrg.cs.tcd.ie
NTRG Payments Page – ntrg.cs.tcd.ie/mepeirce/project.html