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Joe Kilian NEC Laboratories, America Aladdin Workshop on Privacy in DATA March 27, 2003

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Cryptology – The First Few Millennia Goal of cryptology – protect messages from prying eyes. Lockboxes for data: data safe as long as it is locked up. Curses! I cannot read the message! 0100101010101000111010100 Well Done! Thank you, Sir Cryptographer!

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The Last Twenty Years Then: data protected, but not used. Now: Use data, but still protect it as much as possible. Secure Computation: Can we combine information while protecting it as much as possible?

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The Love Game (AKA the AND game) Want to know if both parties are interested in each other. But… Do not want to reveal unrequited love. He loves me, he loves me not… She loves me, she loves me not… Input = 1 : I love you Input = 0: I love you Must compute F(X,Y)=X Æ Y, giving F(X,Y) to both players. Can we reveal the answer without revealing the inputs? … as a friend

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The Spoiled Children Problem (AKA The Millionaires Problem [Yao]) The Spoiled Children Problem (AKA The Millionaires Problem [Yao]) Pearl wants to know whether she has more toys than Gersh, Doesnt want to tell Gersh anything. Gersh is willing for Pearl to find out who has more toys, Doesnt want Pearl to know how many toys he has. Who has more toys? Who Cares? Pearl wants to know whether she has more toys than Gersh, Doesnt want to tell Gersh anything. Gersh is willing for Pearl to find out who has more toys, Doesnt want Pearl to know how many toys he has. Can we give Pearl the information she wants, and nothing else, without giving Gersh any information at all?

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Auction with private bids: Bids are made to the system, but kept private Only the winning bid, bidders are revealed. Can we have private bids where no one, not even the auctioneer, knows the losing bids? Normal auction: Players reveal bids – high bid is identified along with high bidders. Drawback: Revealing the losing bids gives away strategic information that bidders and auctioneers might exploit in later auctions. Auctions with Private Bids $2 $7 $3 $5 $4

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Final Tally: War: 2 Peace: 2 Nader: 1 The winner is: War Electronic Voting War Peace War Peace Nader

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Secure Computation (Yao, Goldreich-Micali-Wigderson) Secure Computation (Yao, Goldreich-Micali-Wigderson) 12345 X1X1 X2X2 X3X3 X4X4 X5X5 F 2 (X 1,…,X 5 )F 3 (X 1,…,X 5 )F 4 (X 1,…,X 5 )F 5 (X 1,…,X 5 ) F 1 (X 1,…,X 5 ) Players: 1,…,N Inputs: X 1,…,X N Outputs: F 1 (X 1,…,X N ),…,F N (X 1,…,X N ) Players should learn correct outputs and nothing else.

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A Snuff Protocol Dont worry, Ill carry your secrets to the grave! The answer is… Ill Help! (for a rea- sonable con- sulting fee…) An Ideal Protocol 16 Tons X1X1 X2X2 F 1 (X 1,X 2 )F 2 (X 1,X 2 ) Goal: Implement something that looks like ideal protocol.

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1 The Nature of the Enemy 5 24 5 71 1 00 109 7 0 1 4 0 1 Corrupting a player lets adversary: Learn its input/output See everything it knew, saw, later sees. Control its behavior (e.g., messages sent) That 80s CIA training sure came in handy… = input = output = changed

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The winner still is: War Final Tally: Red-Blooded-American Patriots: Terrorist-Sympathizing Liberals: What can go wrong? War Peace Privacy: Inputs should not be revealed. Correctness: Answer should correspond to inputs. Guantanamo The winner is: War 4 1 1 4

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What We Can/Cant Hope For Corrupted players have no privacy on inputs/outputs. Outputs may reveal inputs: If candidate received 100% of the votes, we know how you voted. Cannot complain about adversary learning what it can by (independently) selecting its inputs and looking at its outputs. Cannot complain about adversary altering outcome solely by (independently) altering its inputs. Goal is to not allow the adversary to do anything else. Definitions very subtle: Beaver, Micali-Rogaway, Canetti…

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Can We Do It? Yao (GMW,GV,K,…): Yes (for two party case)! * Cryptographic solutions require reasonable assumptions e.g., hardness of factoring * Slight issues about both players getting answer at same time. As long as functions are computable in polynomial time, solutions require polynomial computation, communication. Goldreich-Micali-Wigderson (BGW,CCD,RB,Bea,…): Yes, if number of parties corrupted is less than some constant fraction of the total number of players (e.g., <n/2, <n/3). No hardness assumptions necessary.

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Can We Really Do It? Step 1: Break computations to be performed into itsy-bitsy steps. (additions, multiplications, bitwise operations) Is there any hope? Step 3: Despair at how many itsy-bitsy steps your computation takes. General solutions as impractical as they are beautiful. Step 2: For each operation...

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Signs of Hope Naor-Pinkas-Sumner Functions computed when running auctions are simple. Can exploit algebraic structure to minimize work. Rabin: Can compute sums very efficiently Testing if two strings are equal is very practical. Sometimes, dont need too many itsy-bitsy operations. Highly optimize Yao-like constructions.

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Electronic Voting Protocols are now very practical. Many interesting issues, both human and technical: What should our definitions be? Several commercial efforts Chaum, Neff, NEC,… Most extensively researched subarea of secure computation. 100,000 voters a piece of cake, 1,000,000 voters doable.

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Killed in freak weight-falling accident. Distributed Cryptographic Entities Secret Key: S Public Key: P Trusted public servant cheerfully encrypts, decrypts, signs messages, when appropriate. S1S1 S2S2 S3S3 Blakley,Shamir,Desmedt-Frankel…: Can break secret key up among several entities, Can still encrypt, decrypt, sign, Remains secure even if a few parties are corrupted.

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Cooking with Ricin Rabid Liberalism for Dummies Cooking with Ricin Applied Cryptology Flaming 101 How I Stole the Election The Empire Strikes And Sometimes Theres Magic Chor-Goldreich-Kushilevitz-Sudan,…,Kushilevitz-Ostrovsky,… Private information retrieval: Rabid Liberalism for Dummies Applied Cryptology Flaming 101 How I Stole the Election The Empire Strikes Data Repository Can you download a data entry from a repository without letting the repository know what youre interested in? Solution 1: Download everything.Much more efficient solutions possible! Applied Cryptology

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Conclusions Secure computation is an extremely powerful framework. Very rich general theory. A few applications now ready for prime time. Keep watching this space!

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