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Functional Encryption for Regular Languages
Brent Waters
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Public Key Encryption [DH76,M78,RSA78,GM84]
Avoid Prior Secret Exchange
SK
PubK
Functional Encryption for Regular Languages Brent Waters Public Key - - PowerPoint PPT Presentation
Functional Encryption for Regular Languages Brent Waters Public Key - - PowerPoint PPT Presentation
Functional Encryption for Regular Languages Brent Waters Public Key Encryption [DH76,M78,RSA78,GM84] Avoid Prior Secret Exchange PubK SK 2 Functional Encryption [SW05] Functionality: f( , ) MSK Authority Key: y 2 {0,1}* y SK CT: x
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Functional Encryption [SW05…]
Functionality: f(¢ , ¢ )
Public Params Authority MSK
Key: y 2 {0,1}* x
SK y
CT: x 2 {0,1}* f(x,y)
Security: “Can only learn f(x,y)”
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“Key Policy” ABE [GPSW06]
Key: CT: “Public Index” Boolean Formula (or circuit) Variables Functionality: Evaluate formula, if true give message
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Limitations
Key is a single formula/circuit Fixed Size: Operates over fixed sized input
OR x1 AND x2 x3Arbitrary Length: Goal: Functional Enc. for arbitrary length inputs
Form Image Text Video
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Regular Languages
Language is regular iff strings accepted some Deterministic Finite Automata (DFA) Firewall Rules
(?i)^([^./]+\.)*(grooveshark\.com|gs-cdn\.net)(?![^/])
Search
<[^>]*>
Applications
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Determinstic Finite Automata (DFA)
Set of states Alphabet Transition Start state Accept states Note: Some Regular Expressions not efficiently expressible as DFAs.
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A Simple Example
Language = “Begins with 1 and has even parity” A B
Start 1
C
1
w = 1 0 1 0 Accept(M,w)
1
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DFA-Based F.E. System
Key: CT: “Public Index” DFA Arbitrary length string Functionality: Evaluate DFA M on w, if accepts give message
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System Overview
Key: CT: At state x after j symbols Three Mechanisms Setting: Bilinear group G of order p Decrypt: Initialization: Compute Transition: Completion: Recover message using
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Setup
2) 1) Choose Bilinear group G of order p Public Parameters: Master Secret: Input:
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Encryption
Input: Note: Only showing components for transition mechanism! “Linking”
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Key Generation
Input: Note: Only showing components for transition mechanism! Define
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Transition Mechanism (of decryption)
Suppose Compute: Transition:
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Summary & Three Problems
(1) Support Non-deterministic Finite Automata (NFA) Functional Enc. for arbitrary length inputs: Achieved DFAs Problems (2) Climb the Chomsky Hierarchy (3) Move past public index model
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Thank you