CPS 214

1. CPS 214 Bank Clearing and Settlement Quantum Key Exchange Electronic Cash

2. Clearing and Settling • Clearing: determining the amount that one party owes another • Settling: transfer of funds from one party to the other • Banks clear and settle every day (or at least on those rare days when banks are open)

3. Fedwire • Owned and operated by Federal Reserve Banks • 7500 participant banks keep accounts with Federal Reserve • Over $2,000,000,000,000 transferred per day • FEDNET proprietary telecommunications network • Physical security mechanisms difficult to uncover! • Now permits some IP or web-based transactions

4. Quantum Cryptography • In quantum mechanics, there is no way to take a measurement without potentially changing the state. E.g. • Measuring position, spreads out the momentum • Measuring spin horizontally, “spreads out” the spin probability vertically Related to Heisenberg’s uncertainty principal

5. Using photon polarization 1 0 diagonal basis rectilinear basis measurerectilinear measurediagonal Measuring using one basis changes polarization to that basis! Bennet and Brassard 1984

6. Quantum Key Exchange • Alice creates each random bit and then randomly encodes it in one of two bases: • Bob measures photons in random orientationse.g.: x + + x x x + x (orientations used) \ | - \ / / - \ (measured polarizations)and tells Alice in the open what orientations he used, but not what he measured. • Alice tells Bob in the open which orientations are correct • Bob and Alice compare a randomly chosen subset of sent/received bits to detect eavesdropper • Susceptible to a man-in-the-middle attack

7. In the “real world” • 10-node DARPA Quantum Network since 2004 • Los Alamos/NIST March 2007, 148km

8. 15-853Algorithms in the Real WorldElectronic Cash Michael I. Shamos, Ph.D., J.D. Co-Director

9. Token vs. Notational Money • Token money • Represented by a physical article (e.g. cash, traveler’s check, gift certificate, coupon) • Can be lost • Used for instantaneous value transfer • Notational money (account ledger entries) • Examples: bank accounts, frequent flyer miles • Can’t be lost • Transfer by order to account holder, usually not immediate • Requires “clearance” and “settlement” ACTUAL PAYMENT IN “REAL” MONEY WHAT IS THE NET EFFECT OF ALL THE ORDERS? (HOW MUCH DOES EACH PARTY HAVE TO PAY?)

10. Online v. Offline Systems • An online system requires access to a server for each transaction. • Example: credit card authorization. Merchant must get code from issuing bank. • An offline system allows transactions with no server. • Example: cash transaction. Merchant inspects money. No communication needed.

11. Electronic Cash • Electronic cash is token money in the form of bits, except unlike token money it can be copied. This creates a host of problems: • A copy of a real bill is a counterfeit.A copy of an ecash string is not counterfeit (it’s a perfect copy) • How is ecash issued? How is it spent? Why would anyone accept it? • Counterfeiting • Loss (it’s token money; it can be lost) • What prevents double spending? • Can it be used offline?

12. Electronic Cash -- Idea 1 • Bank issues character strings containing: • denomination • serial number • bank ID + encryption of the above • First person to return string to bank gets the money PROBLEMS: • Can’t use offline. Must verify money not yet spent. • Not anonymous. Bank can record serial number. • Sophisticated transaction processing system required with locking to prevent double spending. • Eavesdropping!

13. Blind Signatures • 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.

14. 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 ke(mod n) She sends T to Bob. • Bob signs T by computing Td = (M ke)d (mod n) = Md k (mod n) • Alice unblinds this by dividing out the blinding factor: S = Td/k = Md k (mod n)/k = Md (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))

15. Blind Signatures • It’s a problem signing documents you can’t read • But it happens. Notary public, witness, etc. • 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

16. eCash (Formerly DigiCash) ALICE SEND UNSIGNED BLINDED COINS TO THE BANK Withdrawal (Minting): WALLET SOFTWARE ALICE BUYS DIGITAL COINS FROM A BANK BANK SIGNS COINS, SENDS THEM BACK. ALICE UNBLINDS THEM BOB VERIFIES COINS NOT SPENT ALICE PAYS BOB Spending: BOB DEPOSITS CINDY VERIFIES COINS NOT SPENT ALICE TRANSFERS COINS TO CINDY PersonalTransfer: CINDY GETS COINS BACK

17. Minting eCash • Alice requests coins from the bank where she has an account • Alice sends the bank{ { blinded coins, denominations }SigAlice }PKBank • 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

18. Minting eCash, cont. • Bank now must produce signed coins for Alice • Each of Alice’s blinded coins has a serial# • Bank’s public key for $5 coins is (e5, m5) (exponent and modulus). Private key is d5. • Alice selects blinding factor r • Alice blinds serial# by multiplying by re5 (mod m5) (serial# re5) (mod m5) • Banks signs the coin with its private d5 key: (serial# re5)d5 (mod m5) = (serial#)d5 r (mod m5) • Alice divides out the blinding factor r. What’s left is (serial#)d5 (mod m5) = { serial# } SKBank5Just as if bank signed serial#. But Bank doesn’t know serial#. e5•d5 = 1 (mod m5)

19. Spending eCash • Alice orders goods from Bob • Bob’s server 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)}PKmerchant_bank } payment_info = { Alice’s_bank_ID, amount, currency, ncoins, timestamp, merchant_ID, H(description), H(payer_code) }

20. Depositing eCash • Bob receives the payment message, forwards it to the bank for deposit by sending deposit = { { payment }SigBob }PKBank • Bank decrypts the message using SKBank. • 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 }SigBank

21. 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.

22. 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 • eCash demo

23. Anonymous Ecash  Crime • Kidnapper takes hostage • Ransom demand is a series of blinded coins • Banks 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

24. 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.

25. 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 • Combines b different random numbers with her account number and the coin serial number (using exclusive-OR ) • Blinds the coin • 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 her real account number. (It picked the 100 out of 200, not Alice.)

26. Probability Cheating is Detected • If Alice sends 2n coins to the bank but k have the wrong account number, what is the probability it appears 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 n OF 2n TOTAL COINS WAYS TO PICK EXACTLY n- j OF 2n-k GOOD COINS WAYS TO PICK EXACTLY j OF k BAD COINS

27. 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 number100 x 5 = 500 • Alice chooses a random number b and creates b random numbers for this coin. Say b=6 • Alice XORs each random number with her account number:

28. Chaum Protocol • Bob receives Alice’s coin. He finds out b and picks a random b-bit number, say 111010 (bits numbered 5 4 3 2 1 0) • For every bit position in which Bob’s number has a 1, he receives 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 sends the last column to the bank when depositing the coin

29. Chaum Protocol • Now Alice tries to spend the coin again with Charlie. He finds b=6 and picks random number 010000 • Charlie goes through the same procedure as Bob and sends the numbers he receives to the bank when he deposits the coin

30. Chaum Protocol • The bank refuses to pay Charlie, since the coin was 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 this alone

31. Chaum Protocol • Now Alice tries to spend the coin again with Charlie. He finds b=6 and picks random number 010000 • Charlie goes through the same procedure as Bob and sends the numbers he receives to the bank when he deposits the coin

32. 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-bp(1) = 0.5p(10) ~ .001p(20) ~ 1/1,000,000p(30) ~ 1/1,000,000,000p(64) ~ 5 x 10-20p(128) ~ 3 x 10-39 • Chaum protocol does not guarantee detection

33. Q A &