Electronic Payment Systems

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Electronic Payment Systems
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Electronic Payment Systems

• Transaction reconciliation
• Cash or check

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Electronic Payment Systems

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

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Electronic Payment Systems

• Transactions in the U.S. economy

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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

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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

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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

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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 cyphertext CPB(M). Note that C is
  thus a permutation of the set D.
• The public and secret keys are inverses of each
  other
• MSB(PB(M))
• MSA(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) of Z
• 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
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Encryption
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Encryption
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Encryption
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Encryption
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Encryption
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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

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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 allows decryption.
• Suppose x is a message, and our cyphertext is
  yax 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 xby mod n.
• When such a number exists, it is called the mod n
  inverse of a.
• A key result For any ngt1, if a and n are
  relatively prime, then the equation axb mod n
  has a unique solution modulo n.

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Encryption

• In the RSA system, the actual encryption is done
  using exponentiation.
• A key result

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Encryption

• RSA technicals
• Select 2 prime numbers p and q
• Let npq
• 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

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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

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Encryption

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

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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 npq. This
  is a computationally difficult problem.
• Some exampleshttp//econ.gsia.cmu.edu/spear/rsa
  3.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