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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Electronic Payment Systems 20-763 Lecture 11 Electronic Cash

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Electronic Cash Token money in the form of bits, except unlike token money it can be copied. This creates new problems: Copy of a real bill = counterfeit. Copy of an ecash string is not counterfeit (or a perfect counterfeit) How is it issued? Spent? Counterfeiting Loss Fraud, merchant fraud, use in crime, double spending Efficiency (offline use -- no need to visit a site) Anonymity (even with collusion) No existing system solves all these problems

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Online v. Offline Systems Online system requires access to a server for each transaction. –Example: credit card authorization. Merchant must get code from issuing bank. Offline system allows transactions with no server. –Example: cash transaction. Merchant inspects money. No communications needed. –Note: an Internet system can be “offline” if the transaction is only between buyer and seller, with no third-party access during the transaction

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Outline Non-anonymous ecash –Easy Online anonymous ecash –Not difficult with blind signatures Offline anonymous ecash –Difficult –Requires secret sharing & bit commitment

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Electronic Cash -- Idea 1 Bank sells character strings containing: –denomination, serial number, bank ID –digitally signed by the bank First person to return string to bank gets the money PROBLEMS: Can’t use offline. Must verify money not yet spent. (You might not be the first person to deposit the coin.) Not anonymous. Bank can record serial number. Sophisticated transaction processing system required with locking to prevent double spending.

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Blind Signatures (Chaum) Sometimes useful to have people sign things without seeing what they are signing –notarizing confidential documents –preserving anonymity Alice wants to have Bob sign message M. (In cryptography, a message is just a number.) Alice multiplies M by a number -- the blinding factor Alice sends the blinded message to Bob. He can’t read it -- it’s blinded. Bob signs with his private key, sends it back to Alice. Alice divides out the blinding factor. She now has M signed by Bob.

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Blind Signatures Alice wants to have Bob sign message M. Bob’s public key is (e, n). Bob’s private key is d. Alice picks a blinding factor k between 1 and n. Alice blinds the message M by computing T = M k e (mod n) She sends T to Bob. Bob signs T by computing T d = (M k e ) d (mod n) = M d k (mod n) Alice unblinds this by dividing out the blinding factor: S = T d /k = M d k (mod n)/k = M d (mod n) But this is the same as if Bob had just signed M, except Bob was unable to read T e d = 1 (mod n)

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Blind Signatures It’s a problem signing documents you can’t read Blind signatures are only used in special situations Example: –Ask a bank to sign (certify) an electronic coin for $100 –It uses a special signature good only for $100 coins Blind signatures are the basis of anonymous ecash

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS eCash (Formerly DigiCash) Withdrawal (Minting): Spending: Personal Transfer: ALICE BUYS DIGITAL COINS FROM A BANK ALICE SEND UNSIGNED BLINDED COINS TO THE BANK BANK SIGNS COINS, SENDS THEM BACK. ALICE UNBLINDS THEM ALICE PAYS BOB BOB VERIFIES COINS NOT SPENT ALICE TRANSFERS COINS TO CINDY CINDY VERIFIES COINS NOT SPENT BOB DEPOSITS CINDY GETS COINS BACK WALLET SOFTWARE

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Minting eCash Alice requests coins from the bank where she has an account Alice sends the bank { { blinded coins, denominations }Sig Alice }PK Bank Bank knows they came from Alice and have not been altered (digital signature) The message is secret (only Bank can decode it) Bank knows Alice’s account number Bank deducts the total amount from Alice’s account

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Minting eCash, cont. Bank signs the blinded coins with special signatures corresponding to the denominations –$100 coins signed with $100 signature –$5 coins signed with $5 signature Bank cannot lose if it only accepts each coin once, since it has already been paid by Alice Each of Alice’s blinded coins has a serial# Alice unblinds the coins Now they can be spent

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Spending eCash Alice sends coins to Bob Bob checks the signatures using the bank’s public keys –For a $100 coin he uses the bank’s $100 public key to verify the bank’s digital signature Coin might be good, but already spent Bob must deposit it in the bank immediately Bank checks the coin for validity; looks up the serial number If the serial number has not been seen before, bank credits Bob’s account Bank can’t identify Alice, but the protocol is online

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1.Blinded random large # (160 bits, so no collisions). Sig Alice (request for $100). 2.Sig bank_$100 (blinded(#)): signed by bank 3.Sig bank_$100 (#) 4.Sig bank_$100 (#) 5.OK from bank 6.OK from Bob AliceBob Bank 1 2 3 4 Anonymous online eCash 5 6 MINTING SPENDING SOURCE: GUY BLELLOCH

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Proving a Payment If eCash is anonymous, how can Alice ever prove she paid Bob? She can create a number (payer_code) and include a hash H(payer_code) in each coin When it accepts a coin for deposit, bank records H(payer_code) If Bob claims Alice never paid, she can reveal payer_code to the bank which can verify it by hashing

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Lost eCash Ecash can be “lost”. Disk crashes, passwords forgotten, numbers written on paper are lost. Alice sends a message to the bank that coins have been lost Banks re-sends Alice her last n batches of blinded coins (n = 16) If Alice still has the blinding factor, she can unblind Alice deposits all the coins bank in the bank. (The ones that were spent will be rejected.) Alice now withdraws new coins

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Anonymous Ecash Crime Kidnapper takes hostage Ransom demand is a series of blinded coins Bank signs the coins to pay ransom Kidnapper tells bank to publish the coins in the newspaper (they’re just strings) Only the kidnapper can unblind the coins (only he knows the blinding factor) Kidnapper can now use the coins and is completely anonymous

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Offline Double-Spending Double spending easy to stop in online systems: System maintains record of serial numbers of spent coins. Suppose Bob can’t check every coin online. How does he know a coin has not been spent before? Method 1: create a tamperproof dispenser (smart card) that will not dispense a coin more than once. –Problem: replay attack. Just record the bits as they come out. Method 2: protocol that provably identifies the double- spender but is anonymous for the single-spender.

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum’s Double-Spending Protocol How do we prevent double spending in an offline transaction (can’t check with bank)? Idea: –Alice stays anonymous –If Alice spends a coin twice, she is identified –If Bob deposits twice, he is caught but Alice remains anonymous –Must be secure against Alice and Bob cheating the bank together –Must be secure Alice or Bob making it look like the other is cheating

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Secret-Sharing Is there a way to divide a message into n pieces so any m pieces are sufficient to reconstruct it, but no small set is sufficient? Solution due to Shamir. Let the secret be a number s in the finite field mod p, where p is a large prime Select m-1 random elements of the field a i and form the polynomial f(x) = s + a 1 x + a 2 x 2 + … + a m-1 x m-1 Now choose n integers x i and let the secret shares be the pairs (x i, f (x i )) Any m points uniquely determine a polynomial of degree m-1, so any m pairs uniquely determine s!

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Bit Commitment Alice wants to “commit” a number M to Bob without telling him what it is “Commit” means that she can later reveal the number and prove that she hasn’t changed it Idea: Alice writes M on a piece of paper, locks it in a box and gives the box to Bob. Alice keeps the key. Later, Bob asks Alice what the number was. She produces the key and opens the box. Can this be done on a computer? It’s easy.

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Bit Commitment Alice wants to “commit” number M to Bob She picks a random nonce r (to prevent replay attack) She sends Bob y = H(r || M) (H is a one-way hash) Alice sends y to Bob. Now she can’t change it. When Bob wants to know M, Alice sends M and r. Bob H(r || M) and sees if it equals y. If so, M was in the commitment y originally

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Double-Spending Protocol Split Alice’s identity (a secret) so that any two pieces can identify her but one piece cannot Each time the coin is spent, insert another piece of the secret (secret-sharing) Have Alice to put this information in the coins through bit commitment Verify that Alice is not cheating through cut-and- choose If the coin is spent only once, no possibility of different data If the bank sees the same coin from two different parties, Alice is the double spender

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Cut-and-Choose A probabilistic method to verify that Alice is following a protocol We ask Alice to put a piece of a secret in each coin. But the coins are blinded. How do we know she did it? If Alice wants 100 coins, bank asks her to send 200 coins Bank randomly picks 100 coins and asks her for the blinding factor for each Bank unblinds the test coins and sees if they all have parts of the secret If so, they probably all have parts of the secret

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Probability Footnote If Alice sends 2n coins to the bank but k have no part of the secret, what is the probability none of the k are among the n coins the bank picks? The probability that Alice gets away with it is p(0). For k = 1, p(0) = 1/2 For n = 100, k = 10, p(0) ~ 8/10000 For n = 100, k = 100, p(0) ~ 10 -59 WAYS TO PICK EXACTLY j OF k BAD COINS WAYS TO PICK EXACTLY n OF 2n TOTAL COINS WAYS TO PICK EXACTLY n- j OF 2n- k GOOD COINS

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Double-Spending Protocol If the coin is spent only once, no possibility of seeing different pieces of the secret, so Alice stays anonymous If the bank sees the same coin from two different parties, Alice is the double spender If Bob tries to deposit the coin twice, the bank sees the same serial number and knows that Bob is the cheater

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Double-Spending Protocol Alice wants 100 five-dollar coins. Alice sends 200 five-dollar coins to the bank (twice as many as she needs). For each coin, she inserts a share of her account number Bank selects half the coins (100), signs them, gives them back to Alice Bank asks her for the random numbers for the other 100 coins and uses it to read her account number –Bank feels safe that the blinded coins it signed had a piece of her account number. (It picked the 100 out of 200, not Alice.)

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Chaum’s Double-Spending Protocol u = Alice’s account number (identifies her) r 0, r 1, …, r m-1 are m random numbers (ul i, ur i ) = a secret split of u over 2 pieces using r i so that both are required to recover u. E.g. (r i XOR u, r i ) ( XORing the pieces gives u) vl i = a bit commitment of ul i vr i = a bit commitment of ur i Coin contains: –Value –Unique ID (long random number) –(vl 0,vr 0 ), (vl 1,vr 1 ), …, (vl m-1,vr m-1 ) SOURCE: GUY BLELLOCH

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1.2n blinded coins and Alice’s account # 2.A request to unblind and prove all bit commitments for n of the 2n coins (chosen at random) 3.The blinding factors and proofs of commitment for the n coins 4.Assuming step 3. passes, bank signs the other n coins AliceBank 1 2 Chaum’s Protocol: Minting 3 4 SOURCE: GUY BLELLOCH

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1.A signed coin C (unblinded) 2.A random bit vector B of length m 3.For each i if bit B i = 0 return bit value for ul i else return bit value for ur i (not both) Include all “proofs” that the ul i or ur i match vl i or vr i Now the merchant checks that the coin is properly signed by the bank, and the ul or ur match the vl or vr AliceBob 1 2 Chaum’s Protocol: Spending 3 SOURCE: GUY BLELLOCH

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1.The signed coin, bit vector B, values of ul i or ur i that Bob received from Alice. 2.An OK, or fail If fail, i.e., already returned: 1.If B matches previous order, the Merchant is guilty 2.Otherwise Alice is guilty and can be identified since for some i (where Bs don’t match) the bank will have (ul i, ur i ), which reveals her secret u (her identity). BobBank 1 2 Chaum’s Protocol: Depositing SOURCE: GUY BLELLOCH

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Protocol If Alice’s random number has b bits, what is the probability she can spend a coin twice without being detected? Bob and Charlie’s random numbers would have to be identical. If they differ by 1 bit, the bank can identify Alice. Probability that two b-bit numbers are identical p(b) = 2 - b p(1) = 0.5 p(10) ~.001 p(20) ~ 1/1,000,000 p(30) ~ 1/1,000,000,000 p(64) ~ 5 x 10 - 20 p(128) ~ 3 x 10 - 39 Chaum protocol does not guarantee detection

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Major Ideas eCash raises great security concerns eCash provides protection against loss eCash raises significant legal problems eCash is difficult to implement with both anonymity and protection against double spending eCash may not be successful because of stored- value cards and peer-to-peer systems

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Q A &

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Spending eCash Alice orders goods from Bob Bob’s serves requests coins from Alice’s wallet: payreq = { currency, amount, timestamp, merchant_bankID, merchant_accID, description } Alice approves the request. Her wallet sends: payment = { payment_info, {coins, H(payment_info)}PK merchant_bank } payment_info = { Alice’s_bank_ID, amount, currency, ncoins, timestamp, merchant_ID, H(description), H(payer_code) }

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Depositing eCash Bob receives the payment message, forwards it to the bank for deposit by sending deposit = { { payment }Sig Bob }PK Bank Bank decrypts the message using SK Bank. Bank examines payment info to obtain serial# and verify that the coin has not been spent Bank credits Bob’s account and sends Bob a deposit receipt: deposit_ack = { deposit_data, amount }Sig Bank

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Proving an eCash Payment Alice generates payer-code before paying Bob A hash of the payer_code is included in payment_info Bob cannot tamper with H(payer_code) since payment_info is encrypted with the bank’s public key The merchant’s bank records H(payer_code) along with the deposit If Bob denies being paid, Alice can reveal her payer_code to the bank Otherwise, Alice is anonymous; Bob is not.

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Protocol Alice’s account number is 12, which in hex is 0C = 00001100 Alice picks serial number 100 and blinding number 5 She asks the bank for a coin with serial number 100 x 5 = 500 Alice chooses a number b and creates b random numbers for this coin. Say b=6 Alice’s wallet XORs each random number with her account number:

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Protocol Bob receives Alice’s coin. He obtains b and picks a random b- bit number, say 111010 For every bit position in which Bob’s number has a 1, wallet reveals Alice’s random number for that position For every 0-bit, Bob receives Alice’s account number XOR her random number for that position Bob’s wallet sends last column to the bank when depositing

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Protocol Now Alice tries to spend the coin again with Charlie. He finds b=6 and picks random number 010000 Her wallet probably sends a different set of numbers Charlie goes through the same procedure as Bob and sends the numbers he receives to the bank when he deposits the coin

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ELECTRONIC PAYMENT SYSTEMS 20-763 SPRING 2004 COPYRIGHT © 2004 MICHAEL I. SHAMOS Chaum Protocol The bank refuses to pay Charlie, since the coin was previously deposited by Bob The bank combines data from Bob and Charlie (or both) using XOR where it has different data from the two sources: This identifies Alice as the cheater! Neither Bob nor Alice nor the bank could do it alone

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