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What If? 

{ Cloud Security for Real This Time: Homomorphic Encryption and the Future of Data Privacy Craig Stuntz Improving Enterprises 

https://speakerdeck.com/craigstuntz 

TLS Changed the Internet 

Browser Server Application TLS: Safe (mostly!), but must decrypt to do business 

What if it’s stolen? 

Consumer “I don’t want my personal information stolen.” “I’d rather not have to install software to manage my finances.” Cloud Service Provider “I don’t want the data I store to make me a target.” “I can protect my business methods by not redistributing my code.” 

Homomorphic Encryption In a Nutshell Client Server Data Cyphertext Result Cyphertext Computation Homomorphic Data Plaintext Result Plaintext 

Rot-13! 

Awesoma Powa! 

Let’s launch a startup! concatenatr Join us! 

(Using Goldwasser and Micali’s algorithm developed 20 years earlier) 

Unpadded RSA = mod 1 ∙ 2 = 1 mod ∙ (2 mod ) = (1 ∙ 2 ) mod = 1 ∙ 2 mod = E(1 ∙ 2 ) 

Pivot! multiplir We make products Awesome! Now add. Uhhh…. 

 Multiply  Add, subtract, exponents, etc.  Doesn’t have to be (quite) Turing complete  Conditional branching and loops, of a sort  Cannot perform conditional jumps based on (encrypted) user input Fully Homomorphic Encryption 

Functional Completeness and Universal Gates  NAND  NOR  AND and NOT  XOR and AND 

Addition, Multiplication Over GF(2) + 0 1 0 0 1 1 1 0 * 0 1 0 0 0 1 0 1 

> def choose(first, second, choose_first): .. return first if choose_first else second .. > choose(True, False, True) => True > choose(True, False, False) => False first choose_first second 

> def my_factorial(n): .. result = 1 .. while n > 1: .. result *= n .. n -= 1 .. return result > def my_factorial_less_than_20(n): .. result = 1; .. for i in range(2, 20): .. result *= 1 if i > n else i .. return result > my_factorial_less_than_20(4) => 24 > my_factorial_less_than_20(100) => 121645100408832000L > my_factorial_less_than_20(1000) => 121645100408832000L 

Fast! Turing Complete* Strong Encryption Practical Homomorphic Encryption 

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Craig Gentry IBM Research 

Result Cyphertext Output Homomorphic reencryption algorithm Bootstrap Lossy Multiply Lossless Add Data Cyphertext Input 

E(E(E(plaintext))) E(E(plaintext)) E(plaintext) Plaintext Bootstrappable Encryption 

 “Nevertheless, the authors of this method to concede that making this scheme practical remains an open problem.”  “There exist well known solutions for secure computation of any function… It seems hard to apply these methods to complete continuous functions or represent Real numbers, since the methods inherently work over finite fields.”  “An encryption scheme with these two properties is called a homomorphic encryption scheme. The Paillier system is one homomorphic encryption scheme, but more ones [sic] exist.” Patent Encumbrance 

Limitations  Server doesn’t have data to, e.g. hand off to third parties  Some fully homomorphic cryptosystems are relatively untested and security not proven. (Both in terms of algorithms and implementation.)  Space issues  Algorithms which operate on homomorphically encrypted data are, for now, anyway, computationally expensive  Client complexity and deployment  Not always clear when to choose fully homomorphic algorithms.  Not a cure-all. Metadata and side-channels still a problem  Moving target!  Patent encumbered 

CryptDB  Query-based encryption  Requires no changes to DB server  Tested on phpBB, OpenEMR, TPC-C, etc.  Only 14-26% slower than unmodified apps. 

Zero Knowledge Proof Image: Wikimedia Commons / User:Dake 

2 Party Secure Computation Sends c = E(x) to Bob Computes and sends c’ = E(f(x,y)), ZKP of c’ correctness to Alice Decrypt c’, compute ZKP of valid decryption, and return both to Bob HELLO M y N ame I s Alice HELLO M y N ame I s Bob 

The Future? 

 Computing Arbitrary Functions of Encrypted Data, by Craig Gentry. Communications of the ACM, Vol. 53, No.3  Building the Swiss Army Knife, by Boaz Barak and Zvika Brakerski  HElib (source code)  CryptDB: Processing Queries on an Encrypted Database, by Raluca Ada Popa, Catherine M.S. Redfield, Nickolai Zeldovich, and Hari Balakrishnan Further reading