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electronic payment systems

Electronic Payment Systems. Transaction reconciliationCash or check. Electronic Payment Systems. Intermediated reconciliation (credit or debit card, 3rd party money order). Electronic Payment Systems. Transactions in the U.S. economy. Electronic Payment Systems. Online transaction systemsLack of physical tokensStandard clearing methods won't workTransaction reconciliation must be intermediatedInformational tokensEcommerce enablersFirst Virtual Holdings, Inc. modelOnline payment systems (9454

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electronic payment systems

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    1. Electronic Payment Systems

    2. The diagram shows a simplified schematic of a transaction involving either cash or checks. Cash Transaction The buyer pays for the goods or services received from the seller with cash. The cash for the transaction is obtained by withdrawing money from the buyers account at Bank 2. The seller deposits the proceeds from the transaction in her account at Bank 1. Check Transaction The buyer pays for the goods or services with a check written on her account at Bank 2. The seller deposits the check in her account at Bank 1. Bank 1 presents the check to Bank 2 for payment. Bank 2 pays Bank 1 in the amount of the check, and debits the account of the buyer. When Bank 1 receives the payment, it credits the account of the seller, and the transaction is complete. The information the banks exchange regarding the accounts to be adjusted is called the notational information.The diagram shows a simplified schematic of a transaction involving either cash or checks. Cash Transaction The buyer pays for the goods or services received from the seller with cash. The cash for the transaction is obtained by withdrawing money from the buyers account at Bank 2. The seller deposits the proceeds from the transaction in her account at Bank 1. Check Transaction The buyer pays for the goods or services with a check written on her account at Bank 2. The seller deposits the check in her account at Bank 1. Bank 1 presents the check to Bank 2 for payment. Bank 2 pays Bank 1 in the amount of the check, and debits the account of the buyer. When Bank 1 receives the payment, it credits the account of the seller, and the transaction is complete. The information the banks exchange regarding the accounts to be adjusted is called the notational information.

    3. Electronic Payment Systems Intermediated reconciliation (credit or debit card, 3rd party money order) Intermediate reconciliation differs from bank-to-bank reconciliation in that the instrument of payment (i.e. the credit/debit card or money order) is issued by an intermediary (Visa, MasterCard, Western Union) who guarantees payment, and has arrangements with the various banks involved for processing the transaction. In a credit card transaction, for example, the seller takes the buyers credit information (card number, expiration date, and personal information) and confirms with the intermediary that the card is valid and in good standing. If it is, the buyer receives the good or service (essentially on credit), and the seller submits a request for payment to the intermediary. The intermediary processes the credit card information and generates a payment to the sellers account at Bank 1. When the buyer pays her credit card bill, the intermediary generates a request for payment from Bank 2 which is deposited in the intermediarys account at a third bank. The transaction process is then complete, and the intermediary notifies buyer and seller (via their monthly statements) of this fact.Intermediate reconciliation differs from bank-to-bank reconciliation in that the instrument of payment (i.e. the credit/debit card or money order) is issued by an intermediary (Visa, MasterCard, Western Union) who guarantees payment, and has arrangements with the various banks involved for processing the transaction. In a credit card transaction, for example, the seller takes the buyers credit information (card number, expiration date, and personal information) and confirms with the intermediary that the card is valid and in good standing. If it is, the buyer receives the good or service (essentially on credit), and the seller submits a request for payment to the intermediary. The intermediary processes the credit card information and generates a payment to the sellers account at Bank 1. When the buyer pays her credit card bill, the intermediary generates a request for payment from Bank 2 which is deposited in the intermediarys account at a third bank. The transaction process is then complete, and the intermediary notifies buyer and seller (via their monthly statements) of this fact.

    4. Electronic Payment Systems Transactions in the U.S. economy The standard method for clearing checks involves the clearing house services provided by the Federal Reserve System. At the end of each business day, Bank 1 sends checks drawn on other banks payable to Bank 1's customers to the regional Federal Reserve clearing house for processing. The Fed credits Bank 1's account with the Fed in the amount of these checks, then debits Bank 1's account in the amount of checks issued to other banks and drawn on Bank 1's customers' accounts. The Fed then sorts the checks and sends them out to the banks they are drawn on for further processing. When Bank 1 receives the checks written on its customers' accounts, it then debits each of these accounts in the requisite amounts, and records each transaction for inclusion in customers' monthly statements. This process for clearing checks is time-consuming, and typically takes 3-5, during which time banks in the system can enjoy a credit against their accounts with the Fed that has not yet been made available to customers (known as the float). Large banks can enjoy a considerable float (often amount to millions of dollars each day), and can use these short term funds to finance short-term investments. The float is also a matter of negotiation between large banks and their corporate customers in setting up their business relationships. The remaining transactions are handled by electronic fund transfer systems (EFTS). Fedwire (operated by the U.S. Federal Reserve System) and CHIPS (Clearing House Interbank Payments Systems of the New York Clearing House) are EFTS designed to handle large interbank fund transfers. Businesses use CHIPS to process large domestic payments (generally business-to-business) and foreign exchange transactions. ACH is the Automated Clearing House, which use electronic data interchange (EDI) networks to automate payments between large firms and their suppliers. As you can see from the data (which is from data provided by the St. Louis Federal Reserve Bank for 1995), almost all transactions in the U.S. are completed using paper checks when we measure actual numbers of transactions. In terms of dollar value transacted, though, 87.5% of the value of all transactions is conducted using electronic fund transfer systems.The standard method for clearing checks involves the clearing house services provided by the Federal Reserve System. At the end of each business day, Bank 1 sends checks drawn on other banks payable to Bank 1's customers to the regional Federal Reserve clearing house for processing. The Fed credits Bank 1's account with the Fed in the amount of these checks, then debits Bank 1's account in the amount of checks issued to other banks and drawn on Bank 1's customers' accounts. The Fed then sorts the checks and sends them out to the banks they are drawn on for further processing. When Bank 1 receives the checks written on its customers' accounts, it then debits each of these accounts in the requisite amounts, and records each transaction for inclusion in customers' monthly statements. This process for clearing checks is time-consuming, and typically takes 3-5, during which time banks in the system can enjoy a credit against their accounts with the Fed that has not yet been made available to customers (known as the float). Large banks can enjoy a considerable float (often amount to millions of dollars each day), and can use these short term funds to finance short-term investments. The float is also a matter of negotiation between large banks and their corporate customers in setting up their business relationships. The remaining transactions are handled by electronic fund transfer systems (EFTS). Fedwire (operated by the U.S. Federal Reserve System) and CHIPS (Clearing House Interbank Payments Systems of the New York Clearing House) are EFTS designed to handle large interbank fund transfers. Businesses use CHIPS to process large domestic payments (generally business-to-business) and foreign exchange transactions. ACH is the Automated Clearing House, which use electronic data interchange (EDI) networks to automate payments between large firms and their suppliers. As you can see from the data (which is from data provided by the St. Louis Federal Reserve Bank for 1995), almost all transactions in the U.S. are completed using paper checks when we measure actual numbers of transactions. In terms of dollar value transacted, though, 87.5% of the value of all transactions is conducted using electronic fund transfer systems.

    5. Electronic Payment Systems Online transaction systems Lack of physical tokens Standard clearing methods wont work Transaction reconciliation must be intermediated Informational tokens Ecommerce enablers First Virtual Holdings, Inc. model Online payment systems (financial electronic data interchange) Secure Electronic Transaction (SET) protocol supported by Visa and MasterCard Digital currency Ecommerce enablers such as First Virtual Holdings act as a trusted third party to transactions between buyers and sellers. In this role, buyers and sellers (First Virtual account holders) grant First Virtual the authority to make electronic fund transfers from their accounts at other banks as part of clearing a transaction between the buyer and seller. Transactions are then processed by presenting FV with information about the buyer and seller identities, the good(s) involved in the transaction, prices, and other sales terms. FV then completes the transaction by debiting and crediting the buyers and sellers accounts appropriately (needing only the identities for this process), and carrying out the requisite EFT with the buyer's and seller's banks. Note that once accounts are established at FV, subsequent transactions do not require the online transfer of any sensitive financial information. Online payment systems (notational funds transfer) involve the direct communication of sensitive financial information (generally credit card numbers) between buyers and sellers. At its most primitive, such a system can work by having the buyer simply email a credit card number to the seller, who then processes the transaction as if the customer were physically present, emailing back a receipt (with an authorization number from the relevant bank or credit intermediary for the charge). More sohpisticated approaches to this process involve special software agents which act as digital wallets, keeping credit card numbers (possibly for multiple cards) and cardholder information on file on disk so that merchants capable of reading this information can do so with a simple click of the mouse. Online intermediaries can then accept the information transmitted from the merchant (regarding product information and merchant account information) together with the information from the buyer's wallet and process the payment electronically, sending messages back to both the buyer and seller about the success of the transaction. Ecommerce enablers such as First Virtual Holdings act as a trusted third party to transactions between buyers and sellers. In this role, buyers and sellers (First Virtual account holders) grant First Virtual the authority to make electronic fund transfers from their accounts at other banks as part of clearing a transaction between the buyer and seller. Transactions are then processed by presenting FV with information about the buyer and seller identities, the good(s) involved in the transaction, prices, and other sales terms. FV then completes the transaction by debiting and crediting the buyers and sellers accounts appropriately (needing only the identities for this process), and carrying out the requisite EFT with the buyer's and seller's banks. Note that once accounts are established at FV, subsequent transactions do not require the online transfer of any sensitive financial information. Online payment systems (notational funds transfer) involve the direct communication of sensitive financial information (generally credit card numbers) between buyers and sellers. At its most primitive, such a system can work by having the buyer simply email a credit card number to the seller, who then processes the transaction as if the customer were physically present, emailing back a receipt (with an authorization number from the relevant bank or credit intermediary for the charge). More sohpisticated approaches to this process involve special software agents which act as digital wallets, keeping credit card numbers (possibly for multiple cards) and cardholder information on file on disk so that merchants capable of reading this information can do so with a simple click of the mouse. Online intermediaries can then accept the information transmitted from the merchant (regarding product information and merchant account information) together with the information from the buyer's wallet and process the payment electronically, sending messages back to both the buyer and seller about the success of the transaction.

    6. Electronic Payment Systems Digital currency Non-intermediated transactions Anonymity Ecommerce benefits Privacy preserving Minimizes transactions costs Micropayments Security issues with digital currency Authenticity (non-counterfeiting) Double spending Non-refutability Currency (or cash) differs from other means of reconciling transactions in that it doesn't require the participation of an intermediary, nor does it require that the identity of the parties to a transaction be encoded in any way in the currency token. These features of currency are of potential importance in ecommerce (as well as in physical commerce). Digital currencies allow transactions on the internet which are privacy preserving. The lack of intermediary minimizes the transactions costs associated with the use of the currency, making possible so-called "micropayments" when individuals access a web site. Security issues As with any form of currency, the anonymity it allows poses some thorny security issues. Because cash is anonymous, it is impossible to trace its movements back through various transactions to the issuing source (either a bank, in the case of an inside money system, or the government). This means that a good counterfeiter can insert his own tokens into the transaction flows, thus degrading the value of the true currency, and raising doubts as to the authenticity of the circulating money. Security issues with electronic currencies are complicated further by the fact that ecurrencies have no physical manifestation, but exist only in code. Hence, it becomes possible (by virtue of the ease with which digital information can be copies) for a particular piece of digital cash to be spent twice by the same person. Non-refutability issues arise because of the need for a receipt that signifies the actual occurrance of a transaction (and prevents one party or the other from refuting it and claiming title to the object at sale). With physical tokens, the token itself serves as receipt and the possession of the token by the seller is evidence of the validity (and non-refutability) of the transaction. With digital tokens, a new piece of information must be generated to signify the actual transfer and hence, of the legitimacy of the transaction. Currency (or cash) differs from other means of reconciling transactions in that it doesn't require the participation of an intermediary, nor does it require that the identity of the parties to a transaction be encoded in any way in the currency token. These features of currency are of potential importance in ecommerce (as well as in physical commerce). Digital currencies allow transactions on the internet which are privacy preserving. The lack of intermediary minimizes the transactions costs associated with the use of the currency, making possible so-called "micropayments" when individuals access a web site. Security issues As with any form of currency, the anonymity it allows poses some thorny security issues. Because cash is anonymous, it is impossible to trace its movements back through various transactions to the issuing source (either a bank, in the case of an inside money system, or the government). This means that a good counterfeiter can insert his own tokens into the transaction flows, thus degrading the value of the true currency, and raising doubts as to the authenticity of the circulating money. Security issues with electronic currencies are complicated further by the fact that ecurrencies have no physical manifestation, but exist only in code. Hence, it becomes possible (by virtue of the ease with which digital information can be copies) for a particular piece of digital cash to be spent twice by the same person. Non-refutability issues arise because of the need for a receipt that signifies the actual occurrance of a transaction (and prevents one party or the other from refuting it and claiming title to the object at sale). With physical tokens, the token itself serves as receipt and the possession of the token by the seller is evidence of the validity (and non-refutability) of the transaction. With digital tokens, a new piece of information must be generated to signify the actual transfer and hence, of the legitimacy of the transaction.

    7. Electronic Payment Systems Contemporary forms of digital currency Ecash Set up account with ecash issuing bank Account backed by outside money (credit card or cash) Move credit from account to ecash mint Public key encryption used to validate coins: third parties can bite the coin electronically by asking the issuing bank to verify its encryption Spend ecoin at merchant site that accepts ecash Merchant then deposits ecoin in his account at his participating bank, or keeps it on hand to make change, or spends the ecash at a supplier merchants site. Role of encryption Role of encryption An ecash coin is simple a random serial number generated at the time the coin is created. This number is encrypted with the user's public keys, then sent by the client-side software to the bank where the bank signs the coin with it's own public key encrypted signature. This guarantees that the ecoin is actually backed by outside money. When the coin returns to the bank for redemption, the bank decrypts the serial number and checks it against records of previous redemptions to be certain that it hasn't been redeemed twice for outside cash.Role of encryption An ecash coin is simple a random serial number generated at the time the coin is created. This number is encrypted with the user's public keys, then sent by the client-side software to the bank where the bank signs the coin with it's own public key encrypted signature. This guarantees that the ecoin is actually backed by outside money. When the coin returns to the bank for redemption, the bank decrypts the serial number and checks it against records of previous redemptions to be certain that it hasn't been redeemed twice for outside cash.

    8. Encryption The need for encryption in ecommerce Degree of risk vs. scope of risk Institutional versus individual impact Obvious need for ecurrencies. Public key cryptography: an overview One-way functions How it works Parties to the transaction will be called Alice and Bob. Each participant has a public key, denoted PA and PB for Alice and Bob respectively, and a secret key, denoted SA and SB respectively The need for strong encryption in ecommerce transactions is a matter of considerable debate. Many people are wary of using their credit cards for online purchases without the guarantee of encrypted transmission of the numbers over the internet to prevent theft. Is this fear justified? We all engage in transactions over the telephone which involve giving out our credit card numbers, or in stores where clerks process the card by hand and deposit unshredded copies of receipts (or carbons) in the trash where they might be copied and later used. Hence, to one degree or another, we take risks with our credit card information. In deciding on the need for encryption, then, we need to ask ourselves whether the risk associated with the internet is significantly greater than that associated with other forms of commerce, particularly since most credit card agreements impose limits of liability on cardholders in the event of card theft or loss. From the point of view of an individual, the answer to this question is probably no, particularly when liability is limited. From the point of view of a bank issuing the cards, however, and answer is probably a resounding yes. The reason for this has to do with the snooping technologies that are available for monitoring internet communications. Because internet messages are broadcast widely and in the clear, it is possible for fairly simple technologies to eavesdrop on these communications. The software which monitors communication can also be made to collect large amounts of information. If this includes all of the credit card transactions a busy online merchant is engaged in over a given period of time, then even if the thieves only use each card number up to the limit of liability, the banking sector can find itself down millions of dollars lost to credit card fraud very quickly. One-way function A one-way function is a function which is easy to compute, but whose inverse is very difficult to compute. Such a function can be used for public key encryption, with the easy to compute function made publicly available and serving to encrypt messages, while the inverse (which is known to the issuer of the function) serves to decrypt the message. While the inverse of such a function can be computed in principle, in practice, it is sufficiently hard that effective decryption of an encrypted message requires prior knowledge of the inverse. The need for strong encryption in ecommerce transactions is a matter of considerable debate. Many people are wary of using their credit cards for online purchases without the guarantee of encrypted transmission of the numbers over the internet to prevent theft. Is this fear justified? We all engage in transactions over the telephone which involve giving out our credit card numbers, or in stores where clerks process the card by hand and deposit unshredded copies of receipts (or carbons) in the trash where they might be copied and later used. Hence, to one degree or another, we take risks with our credit card information. In deciding on the need for encryption, then, we need to ask ourselves whether the risk associated with the internet is significantly greater than that associated with other forms of commerce, particularly since most credit card agreements impose limits of liability on cardholders in the event of card theft or loss. From the point of view of an individual, the answer to this question is probably no, particularly when liability is limited. From the point of view of a bank issuing the cards, however, and answer is probably a resounding yes. The reason for this has to do with the snooping technologies that are available for monitoring internet communications. Because internet messages are broadcast widely and in the clear, it is possible for fairly simple technologies to eavesdrop on these communications. The software which monitors communication can also be made to collect large amounts of information. If this includes all of the credit card transactions a busy online merchant is engaged in over a given period of time, then even if the thieves only use each card number up to the limit of liability, the banking sector can find itself down millions of dollars lost to credit card fraud very quickly. One-way function A one-way function is a function which is easy to compute, but whose inverse is very difficult to compute. Such a function can be used for public key encryption, with the easy to compute function made publicly available and serving to encrypt messages, while the inverse (which is known to the issuer of the function) serves to decrypt the message. While the inverse of such a function can be computed in principle, in practice, it is sufficiently hard that effective decryption of an encrypted message requires prior knowledge of the inverse.

    9. Encryption Each person publishes his or her public key, keeping the secret key secret. Let D be the set of permissible messages Example: All finite length bit strings or strings of integers The public key is required to define a one-to-one mapping from the set D to itself (without this requirements, decryption of the message is ambiguous). Given a message M from Alice to Bob, Alice would encrypt this using Bobs public key to generate the so-called cyphertext C=PB(M). Note that C is thus a permutation of the set D. The public and secret keys are inverses of each other M=SB(PB(M)) M=SA(PA(M)) The encryption is secure as long as the functions defined by the public key are one-way functions

    10. Encryption The RSA public key cryptosystem Finite groups Finite set of elements (integers) Operation that maps the set to itself (addition, multiplication) Example: Modular (clock) arithmetic Subgroups Any subset of a given group closed under the group operation Z2 (i.e. even integers) is a subgroup (under addition) of Z Subgroups can be generated by applying the operation to elements of the group Example with mod 12 arithmetic (operation is addition) RSA stands for Ravist, Shamir and Adelman, the three people who first proposed the system.RSA stands for Ravist, Shamir and Adelman, the three people who first proposed the system.

    11. Encryption

    12. Encryption

    13. Encryption

    14. Encryption

    15. Encryption

    16. Encryption

    17. Encryption A key result: Lagranges Theorem If S is a subgroup of S, then the number of elements of S divides the number of elements of S. Examples:

    18. Encryption Solving modular equations RSA uses modular groups to transform messages (or blocks of numbers representing components of messages) to encrypted form. Ability to compute the inverse of a modular transformation allows decryption. Suppose x is a message, and our cyphertext is y=ax mod n for some numbers a and n. To recover x from y, then, we need to be able to find a number b such that x=by mod n. When such a number exists, it is called the mod n inverse of a. A key result: For any n>1, if a and n are relatively prime, then the equation ax=b mod n has a unique solution modulo n. To say that a and n are relatively prime means that the greatest common divisor of a and n is one. Example: a=5 and n=12. The greatest common divisor is 1, so 5 and 12 are relatively prime. Example: a = 6 and n = 12. The gcd is 6, so 6 and 12 are not relatively prime. While we do not pursue it here, there are efficient algorithms for determining the solution to a given modular equation.To say that a and n are relatively prime means that the greatest common divisor of a and n is one. Example: a=5 and n=12. The greatest common divisor is 1, so 5 and 12 are relatively prime. Example: a = 6 and n = 12. The gcd is 6, so 6 and 12 are not relatively prime. While we do not pursue it here, there are efficient algorithms for determining the solution to a given modular equation.

    19. Encryption In the RSA system, the actual encryption is done using exponentiation. A key result: Proof: Consider any non-zero a. The multiples 0, a, 2a, 3a, ,(p-1)a generate a subgroup of Zp. By Lagranges theorem, the order of this subgroup must divide p. However, because p is prime, the order of the subgroup must be either 1 or p. If a=0 the subgroup will be simple the group consisting of zero (which has order 1). For non-zero values of a, the order of the subgroup must be p, in which case the multiples of a generate a rearrangement (i.e. a permutation) of the elements of Zp. Note that it cannot be the case that a non-zero multiple of a, ra = 0 mod p, since if this were the case, the order of the subgroup would be less than p, contradicting Lagranges theorem. Now, multiplying all of the non-zero multiples of a and using the fact that these are a rearrangement of 1, 2, , p-1, we have from which the result follows. Proof: Consider any non-zero a. The multiples 0, a, 2a, 3a, ,(p-1)a generate a subgroup of Zp. By Lagranges theorem, the order of this subgroup must divide p. However, because p is prime, the order of the subgroup must be either 1 or p. If a=0 the subgroup will be simple the group consisting of zero (which has order 1). For non-zero values of a, the order of the subgroup must be p, in which case the multiples of a generate a rearrangement (i.e. a permutation) of the elements of Zp. Note that it cannot be the case that a non-zero multiple of a, ra = 0 mod p, since if this were the case, the order of the subgroup would be less than p, contradicting Lagranges theorem. Now, multiplying all of the non-zero multiples of a and using the fact that these are a rearrangement of 1, 2, , p-1, we have from which the result follows.

    20. Encryption RSA technicals Select 2 prime numbers p and q Let n=pq Select a small odd integer e relatively prime to (p-1)(q-1) Compute the modular inverse d of e, i.e. the solution to the equation In practice, we want the primes to be large, so that their product is a large number, the factoring of which is computationally difficult.In practice, we want the primes to be large, so that their product is a large number, the factoring of which is computationally difficult.

    21. Encryption For this specification of the RSA system, the message domain is Zn Encryption of a message M in Zn is done by defining Decrypting the message is done by computing In practice, encrypting a message will generally involve converting the message from text (for example) to a numerical representation (assign each letter or character a unique number, such as its ASCII code). The numercial representation will then be broken up into blocks, and each block encrypted as if it were a separate number.In practice, encrypting a message will generally involve converting the message from text (for example) to a numerical representation (assign each letter or character a unique number, such as its ASCII code). The numercial representation will then be broken up into blocks, and each block encrypted as if it were a separate number.

    22. Encryption Let us verify that the RSA scheme does in fact define an invertible mapping of the message.

    23. Encryption Note that the security of the encryption system rests on the fact that to compute the modular inverse of e, you need to know the number (p-1)(q-1), which requires knowledge of the factors p and q. Getting the factors p and q, in turn, requires being able to factor the large number n=pq. This is a computationally difficult problem. Some examples: Practical issues 1. Using the exponentiation function on the computer will work for the calculations as long as the numbers involved aren't too large. As the numbers get large, however, the built-in function can't handle the arithmetic, so we need to resort to the technique of repeated squaring. Thus, to calculate 35 using this technique, we note that 5=2*2+1, so that 35=32*2+1=3*32*2=3*92=81*3=243. 2. Once the size of the numbers exceed the standard memory allocation of the computer (i.e. once you are outside the range of double precision floating point arithmetic), you must resort to storing the digits of a number in an array, using the standard algorithms of elementary arithmetic to perform the requisite multiplication. Thus, for example, if we represent 35 as an array with a 3 and another with a 5 (called the tens array and the ones array), then multiplying 35 by 7 would involve first multiplying 7*5=35, entering a 5 in the ones array, then multiplying 7*3=21+3 carried from the first multiplication, and entering a 4 in the tens array, then creating a new array (called the hundreds array) and entering 2, for a final answer 245 (or [2][4][5]).Practical issues 1. Using the exponentiation function on the computer will work for the calculations as long as the numbers involved aren't too large. As the numbers get large, however, the built-in function can't handle the arithmetic, so we need to resort to the technique of repeated squaring. Thus, to calculate 35 using this technique, we note that 5=2*2+1, so that 35=32*2+1=3*32*2=3*92=81*3=243. 2. Once the size of the numbers exceed the standard memory allocation of the computer (i.e. once you are outside the range of double precision floating point arithmetic), you must resort to storing the digits of a number in an array, using the standard algorithms of elementary arithmetic to perform the requisite multiplication. Thus, for example, if we represent 35 as an array with a 3 and another with a 5 (called the tens array and the ones array), then multiplying 35 by 7 would involve first multiplying 7*5=35, entering a 5 in the ones array, then multiplying 7*3=21+3 carried from the first multiplication, and entering a 4 in the tens array, then creating a new array (called the hundreds array) and entering 2, for a final answer 245 (or [2][4][5]).

    24. Encryption Applications Direct message encryption Digital Signatures Use secret key to encrypt signature: S(Name) Appended signature to message and send to recipient Recipient decrypts signature using public key: P(S(Name)=Name Encrypted message and signature Create digital signature as above, appended to message, encrypt message using recipients public key Recipient uses own secret key to decrypt message, then uses senders public key to decrypt signature, thus verifying sender

    25. Policy Issues Privacy and verification Transaction costs and micro-payments Monetary effects Domestic money supply control and economic policy levers International currency exchanges and exchange rate stability Market organization effects Development of new financial intermediaries Effects on government Seniorage Legal issues Monetary effects of e-payment systems can be a concern if banks that issue electronic currencies are allowed to lend ecash under terms different from those the Federal Reserve applies to standard banks. Such policy differences could make it more difficult for the Fed to manipulate the money supply for economic policy purposes, although at this stage, the Fed professes not to be worried about this. Related issues of international currency exchange and stability also pose long-range questions. What, for example, might happen if a global e-currency developed for transactions on the internet? Would this currency be pegged to one nation's currency (the dollar, for example), or would it simply constitute another international currency whose value relative to other currencies was determined by simple laws of supply and demand? What governmental authority would regulate the supply of this global currency? Among the legal issues is a curious law on the books in the U.S., known as the Stamp Payments Act of 1862, which makes it a crime punishable by fine or imprisonment for issuing "any note, check, memorandum, token or other obligation for a sum of less than $1". This law was passed during the Civil War to curtail the inflationary effects of privately-issued currency substitutes in response to the disappearance of U.S. coins, which were stockpiles by individuals when they realized that the metal content of the coin was worth more than its face value.Monetary effects of e-payment systems can be a concern if banks that issue electronic currencies are allowed to lend ecash under terms different from those the Federal Reserve applies to standard banks. Such policy differences could make it more difficult for the Fed to manipulate the money supply for economic policy purposes, although at this stage, the Fed professes not to be worried about this. Related issues of international currency exchange and stability also pose long-range questions. What, for example, might happen if a global e-currency developed for transactions on the internet? Would this currency be pegged to one nation's currency (the dollar, for example), or would it simply constitute another international currency whose value relative to other currencies was determined by simple laws of supply and demand? What governmental authority would regulate the supply of this global currency? Among the legal issues is a curious law on the books in the U.S., known as the Stamp Payments Act of 1862, which makes it a crime punishable by fine or imprisonment for issuing "any note, check, memorandum, token or other obligation for a sum of less than $1". This law was passed during the Civil War to curtail the inflationary effects of privately-issued currency substitutes in response to the disappearance of U.S. coins, which were stockpiles by individuals when they realized that the metal content of the coin was worth more than its face value.

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