CS 378 - Network Security and Privacy

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CS 378 - Network Security and Privacy Powered By Docstoc
					CS 378




         Digital Cash

         Vitaly Shmatikov




                            slide 1
Digital Cash: Properties
Digital “payment message” with properties of cash
Unforgeable
  • Users cannot “mint” valid cash on their own
Anonymous and untraceable
  • Cannot link a payment to payer’s identity
  • Without this property, might as well use a credit card,
    except for micropayments (more on this later)
Does not require online intermediaries
  • Accepting merchant does not have to interact with the
    bank to verify that user’s payment is valid
                                                          slide 2
Overview of the System


     Withdraw
   digital “coins”
                                   Deposit coins
                            bank




 user
                                      merchant
                     Spend coins


                                                   slide 3
 Digital “Coins”
  User creates the coin, bank signs it and debits the
   coin’s face amount to user’s account

                                                     No anonymity from the bank!
                                                     Bank can record all serial numbers.
                                                        When a coin is presented for
         Coin                                         payment by merchant, bank will
m=(amount, serial number)                                   know who spent it.
                                    bank

                     =sigbank(m)

                    Any merchant can verify bank’s
                        signature on the coin
    user
                                                                                      slide 4
Blind Signatures
User creates a coin
User puts his coin into a digital “envelope”
Bank signs “through” the envelope
  • Electronic equivalent of embossing an envelope: bank
    signs its contents without learning what they are
User receives the signed envelope and opens it,
 extracting bank’s signature on the coin
The coin is signed by the bank, but bank does
 not know its number and cannot trace it!

                                                           slide 5
RSA Signatures Redux
Public key is (n,e), private key is d
   • Main property: for any b, bed mod n  b
   • Assume that everybody knows bank’s public key
To sign message m: s = md mod n
   • It’s infeasible to compute s on m if you don’t know d
To verify signature s on message m:
 se mod n = (md)e mod n  m
   • Anyone who knows n and e (public key) can verify
     signatures produced with d (private key)


                                                             slide 6
  Coins with Blind RSA Signatures                                                                [Chaum]


    User creates the coin, blinds it, bank signs it, user
     removes blinding and obtains a valid coin
                                                           Public key=(n,e)
     b is a secret random
    multiplier chosen by user

Bank does not see m, so
send amount separately                                                      User can cheat!
                           r=mbe,
                                                               For example, amount=$100 in m, but
                          “amount=$10”
                                            bank              amount=$10 in user’s message to bank


                                =sigbank(r)=(mbe)d=md(bed)=mdb                mod n


                                         This is bank’s signature on the actual coin m
       user                                  To extract it, user divides bank’s signature on r
                                                by his secret b. Bank has not learned m!
  Create m=(amount, serial num)
                                                                                                      slide 7
“Cut-and-Choose” Verification
 User creates and blinds K coins, bank asks to open K-1 of
  them (user doesn’t know in advance which ones)
                Pick random i
                                                    Public key=(n,e)

                                                            Extract m1 … mi-1 mi+1 … mk
                                                            and verify that they contain
                                                                  the right amount
     r1=m1b1e … rk=mkbke
            “amount=$10”
                                          bank
                                                      Probability that user can cheat
              Give me all b1 … bk                    without being detected is only 1/k
                   except bi
                    b1 … bi-1 bi+1 … bk
                                                 =sigbank(ri)=midbi   mod n

   user
                                                           Coin mi will be used
Create k coins mi=(amount, serial num)
                                                                                           slide 8
Double-Spending
Digital coins are easy to copy
  • A digital coin is simply a bitstring with certain properties
Bank must keep track of spent coins to make sure
 user does not spend the same coin twice
  • Blinding is not a problem (why?)
Can’t prevent double-spending if bank is offline…
  • User pays with same coin at many merchants; when
    they try to deposit the coin, bank refuses all but one
     – To prevent this, must involve bank in every transaction
… but can make sure that if a coin is double-
 spent, identity of cheater is revealed
                                                                 slide 9
  Preventing Double-Spending
                                                              Probability of this is 1-1/2n
               merchant #2
                                                              If bib’i for at least one i, bank
                           ri if b’i=0                     can compute (Aliceri)  ri = “Alice”
                   “Alice”ri if b’i=1
                                                              and de-anonymize the cheater

                                                                      ri if bi=0
random                     ri if b’i=0                        “Alice”ri if bi=1
 b’1…b’N           “Alice”ri if b’i=1          bank                                 Cannot extract “Alice” from
                                                                                      this if coin is spent once
                   Coin is double-spent         1 or 0

                                          random b1…bN


      Alice
                                     For each bi, send
    Create N random numbers
                                              ri if bi=0        merchant #1
      r1, … rN for each coin          “Alice”ri if bi=1

                                                                                                          slide 10
Micropayment Schemes
Credit cards are impractical for payments < $10
  • Newspaper articles, mobile downloads, etc.
  • Processing one credit-card payment costs about 25c
Many (unsuccessful) micropayment schemes
  • Millicent, PayWord, NetCard, iKP, PayTree, MicroMint
Key obstacle: implementation cost
  • Customer acquisition, disputes, overspending, fraud
Idea: aggregate small payments to reduce per-
 payment processing cost
  • Chaum’s digital coins are not good for aggregation
                                                           slide 11
Probabilistic Aggregation
User gives merchant a “lottery ticket” whose
 expected value is equal to the payment amount
  • Proposed independently by Rivest, Wheeler and others
  • For example, instead of a 1-cent payment, give “lottery
    ticket” that wins $10 with probability 1/1000
After a large number of payments, merchant’s
 total winnings from lottery tickets will be
 statistically close to the total amount of payments
  • With 5000 tickets, merchant wins $50 on average
Only winning tickets need to be presented to bank
  • Few tickets win, so processing cost greatly reduced
                                                          slide 12
Peppercoin                                                              [Rivest and Micali]




                                                                    On average, only 1 transaction out of 1000
                                                                     wins and must be presented for payment



                                               bank                 Winning checks


                                 “You owe me 1 cent”


                          siguser(“This check is worth $10 if the
    user                           three low-order digits of the
                                   hash of your digital signature            merchant
                                   on today’s date are 756”)
 Probability of this is
approximately 1/1000
                                                                                                           slide 13
Problem: Statistical Variations
Unlucky user may pay $20 for his
 first two 1-cent transactions
  • If both tickets happen to win
Payment scheme is user-fair if
 user never has to pay more than
 he would pay if all his payments
 were non-probabilistic checks for
 the exact amount
  • I.e., as if user were writing 1-cent
    checks instead of $10 lottery tickets

                                            slide 14
Achieving User-Fairness
Assume that each payment is exactly 1 cent
User sequentially numbers his payments: 1, 2, …
When merchant submits a winning payment with
 sequence number N, bank charges the user the
 difference between this N and the previous
 sequence number that has been paid
            paid     paid   paid



                                      User is charged 3 cents



  • Severely punish users for reusing sequence numbers!
                                                                slide 15

				
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