Micropayments Revisited

1
Micropayments Revisited

• Written by
• Silvio Micali and Ronald Rivest
• Presented by
• Charles Song and Michael Wasser

2
Digital Payments

• Involves Buyers, Merchants, and Brokers
• Simplest form is electronic checks
• Usually involves manual entry/signing
• Some transactions are too small
• Sum of micropayments may not equal a macropayment

3
Micropayment Goals

• Make payments of variable size with little user
  intervention
• Aggregate small transactions into larger ones
• Simple yet secure
• All parties incur low transaction costs and
• Buyer No user intervention in process with no
  risk
• Merchant Low expenses (low transaction cost)
• Bank Verifiable transactions

4
Common Deviations

• Buyers make fake payments or underpay
• Venders try to overcharge or cheat the broker
• Collusion between two parties against the third

5
PayWord

• Buyer creates H-chain
• x0, x1, x2, ..., xn xi H(xi1) for i 0, 1,
  ... n
• where xn is random
• Sends x0 to merchant
• Buyer makes payments to merchant (xi, i)
• Merchant decides when to send bank (xi, i) and x0
• Bank verify payment amount by running H() function

6
PayWord Analysis

• Pros
• If H is good, hard for parties to cheat the
  system
• Cost of reversing the function can outweigh the
  benefit
• Cons
• Merchant cannot combine payments from multiple
  buyers, deposit might cost more than payment
  value
• Every unit of payment requires calculation

7
Rivest's Lottery

• Merchant creates H-chain and gives the buyer w0
• Buyer creates H-chain and gives the merchant x0
• Buyer makes payments to merchant (xi, i) and
  calculates (xi mod 1/s)
• Merchant gives (wi, i) to buyer and calculates
  (wi mod 1/s)

8
Rivest's Lottery

• if (xi mod 1/s) (wi mod 1/s) then payment is
  worth 1/s payment unit
• Probability of (xi mod 1/s) (wi mod 1/s) is
  exactly s
• On average buyer pays and merchant receives the
  correct amount

9
Rivest's Lottery Anaylsis

• Pros
• Lowers processing cost due to less payable
  transactions
• Cons
• Buyer and merchant must interact to determine
  payability
• Buyer has the risk of over paying in short term,
  psychological burdens for buyer

10
MR1

• T - transaction contains merchant, buyer, bank,
  merchandise, transaction time and value.
• F - public function that outputs values between 0
  and 1
• C - digital check

11
MR1

• Buyer sends C to merchant, C SIGu(T)
• Merchant calculates F(SIGm(C))
• If F(SIGm(C)) lt s then C is payable, merchant
  sends bank C and SIGm(C)
• Bank can send SIGm(C) to buyer for verification
• 1/s payment unit is made

12
MR1 Analysis

• Pros
• Two-way interaction not required for transactions
• Cons
• Buyer still suffer from psychological burdens

13
MR2

• SN - Serial number starting from 1 and
  incremented sequentially
• MaxSN - maximum serial number processed by the
  bank so far

14
MR2

• Buyer sends C to merchant, C SIGu(T), along
  with SN and time
• Merchant calculates F(SIGm(C))
• If F(SIGm(C)) lt s then C is payable, merchant
  sends bank C and SIGm(C) along with SN and time
  from buyer
• Bank makes 1/s payment unit to merchant
• Bank charge buyer SN MaxSN, set MaxSN SN

15
MR2 Anaylsis

• Pros
• Two-way interaction not required for transactions
• User has no risk of over paying
• Cons
• Bank takes on all the risk of under payment
• Punishment system might be hard to enforce
• Honest user might be blamed for wrong-doing

16
MR3

• t' and t - time of M's last and current deposit

17
MR3

• Buyer sends C to merchant, C SIGu(T), along
  with SN
• Merchant groups all Cs between t' and t into
  (L1...Ln), values are (V1...Vn), total value V
• Merchant computes Ci H(Li, Vi) then sends
  C1,...,Cn to the bank
• SIGm(t, n, V, H(L1,V1),...,H(Ln,Vn))

18
MR3

• Bank selects k indices, i1, i2,...ik, and sends
  them to merchant
• Merchant de-committing Ci1,...,Cik
• Bank credits merchant account with V and debits
  the buyers in Li1,...,Lik according to the Sns
• Selected buyers pay everything owed since last
  time they are selected

19
MR3 Analysis

• Pros
• Two-way interaction not required for transactions
• User has no risk of over paying
• Bank determines which checks are payble
• Cons
• Bank takes on all the risk of under payment
• Punishment system might be hard to enforce
• Honest user might be blamed for wrong-doing