Electronic Payment Systems
Electronic Payment Systems
• Transaction reconciliation
– Cash or check
Electronic Payment Systems
– Intermediated reconciliation (credit or debit card, 3rd party money
order)
Electronic Payment Systems
• Transactions in the U.S. economy
Type of Payment Volume (%) in Millions of Transactions Value (%) in Trillions of Dollars
Checks
59,400.0 (96.3%)
68.3 (12.5%)
Fedwire
69.7 (0.1%)
207.6 (37.9%)
CHIPS
42.4 (0.1%)
262.3 (47.9%)
ACH
2,200.0 (3.5%)
9.3 (1.7%)
Total
61,712.10
547.5
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
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
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
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
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=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
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)
Encryption
1  x mod 12
2  x mod 12
Encryption
3  x mod 12
4  x mod 12
Encryption
5  x mod 12
6  x mod 12
Encryption
7  x mod 12
8  x mod 12
Encryption
9  x mod 12
10  x mod 12
Encryption
11  x mod 12
Encryption
• 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:
 Z 2  Z12 , Z 2  6  Z12  12
 Z 3  Z12 , Z 3  4  Z12  12
 Z 4  Z12 , Z 4  3  Z12  12
 Z5  Z12 , Z5  12  Z12  12
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.
Encryption
• In the RSA system, the actual encryption is done using
exponentiation.
• A key result:
Fermat’s Little Theorem
If p is pr ime, then for any a  Z p a  0,
a p 1 mod p  1
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
de  1 mod  p  1q  1
– Publish the pair P=(e,n) as the public key
– Keep secret the pair S=(d,n) as the secret key
Encryption
– For this specification of the RSA system, the message domain is Zn
– Encryption of a message M in Zn is done by defining
C  P( M )  M e mod n
– Decrypting the message is done by computing
S C   C d mod n
Encryption
– Let us verify that the RSA scheme does in fact define an invertible
mapping of the message.
 For any M  Z n
P S M   S P M   M ed mod n.
 Since d and e are modular inverses of each other
ed  1  k  p  1q  1
for some integer k . Hence,
M ed mod n  MM k ( p 1)( q 1) mod n
 MM ( p 1) M k ( q 1) mod n
 M M ( q 1)  mod n  M
(the last steps follow by applying Fermat' s theorem.)
k
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
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
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