1. Electronic Payment Systems

2. Transaction reconciliation –Cash or check

3. Electronic Payment Systems –Intermediated reconciliation (credit or debit card, 3rd party money order)

4. Electronic Payment Systems Transactions in the U.S. economy

5. Electronic Payment Systems Online transaction systems –Lack of physical tokens Standard clearing methods won’t 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

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

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 merchant’s site. Role of encryption

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 P A and P B for Alice and Bob respectively, and a secret key, denoted S A and S B respectively

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 Bob’s public key to generate the so-called cyphertext C=P B (M). Note that C is thus a permutation of the set D. The public and secret keys are inverses of each other –M=S B (P B (M)) –M=S A (P A (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 –Z 2 (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)

11. Encryption

17. A key result: Lagrange’s 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.

19. Encryption In the RSA system, the actual encryption is done using exponentiation. A key result:

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 –Publish the pair P=(e,n) as the public key –Keep secret the pair S=(d,n) as the secret key

21. Encryption –For this specification of the RSA system, the message domain is Z n –Encryption of a message M in Z n is done by defining –Decrypting the message is done by computing

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: http://econ.gsia.cmu.edu/spear/rsa3.asp

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