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Electronic Payment Systems

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Transaction reconciliation

Cash or check

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Intermediated reconciliation (credit or debit card, 3rd party money

order)

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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

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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

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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

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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, orkeeps it on hand to make change, or spends the ecash at a supplier

merchants site.

Role of encryption

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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

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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 cyphertextC=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

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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) ofZ

Subgroups can be generated by applying the operation to elements of

the group

Example with mod 12 arithmetic (operation is addition)

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Encryption

121 modxv

122 xv

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Encryption

123 xv

124 xv

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Encryption

125 xv

126 xv

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Encryption

127 xv

128 xv

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Encryption

129 modxv

1210 xv

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Encryption

A key result: Lagranges Theorem

If S is a subgroupof S, thenthenumberofelements of S divides

thenumberofelements of S.

Examples:

1212,

123,

124,

126,

125125

124124

123123

122122

!z!y

!z!y

!z!y

!z!y

ZZZZ

ZZZZ

ZZZZ

ZZZZ

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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 allowsdecryption.

Suppose x is a message, and our cyphertext is y=ax modn forsome numbers a and n. To recoverx from y, then, we need to beable to find a numberb such that x=by modn.

When such a number exists, it is called the mod n inverse of a.

A key result: Foranyn>1, if a andn arerelativelyprime, thentheequation ax=b modnhas a unique solution modulon.

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Encryption

In the RSA system, the actual encryption is done using

exponentiation.

A keyresult:

1mod

,0

1 !

{

pa

aZforany aime, thenIfp is pr

remittle TheoFermats L

p

p

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Encryption

RSA technicals

Select 2 prime numbers p and q

Let n=pq

Select a small odd integere relatively prime to (p-1)(q-1)

Compute the modular inverse dofe, i.e. the solutiontothe

equation

Publish the pairP=(e,n)as the public key

Keep secret the pairS=(d,n)as the secret key

11mod1 ! qpde

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Encryption

For this specification of the RSA system, the message domain is Zn

Encryption of a message Min Znis done by defining

Decrypting the message is done by computing

nMMC e mod)( !!

nCCS d mod!

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Encryption

Note that the security of the encryption system rests on the fact that

to compute the modular inverse ofe, 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 thelarge numbern=pq. This is a computationally difficult problem.

Some examples:

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

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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

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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

Documents

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