Overview of the results The Framework Work in progress Simple Functional Encryption Schemes for Inner Products Michel Abdalla, Florian Bourse, Angelo De Caro, and David Pointcheval ´ Ecole normale sup´ erieure, CNRS, INRIA, PSL, Paris, France R E S E A R C H U N I V E R S I T Y PKC 2015 — Maryland, USA Wednesday, April 1 Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results The Framework Work in progress Overview of the results 1 What is Functional Encryption? Inner Product functionality What does simple mean? What do we achieve? The Framework 2 Overview of the framework Example Proof of security Generalization Work in progress 3 What is there left to do? Thank you! Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Generalizes multiple concepts: Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Generalizes multiple concepts: Identity-Based Encryption Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Generalizes multiple concepts: Identity-Based Encryption Fuzzy Identity-Based Encryption Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Generalizes multiple concepts: Identity-Based Encryption Fuzzy Identity-Based Encryption Attribute-Based Encryption Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Generalizes multiple concepts: Identity-Based Encryption Fuzzy Identity-Based Encryption Attribute-Based Encryption Predicate Encryption, etc. Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Brief history What is Functional Encryption? Introduced by Dan Boneh, Amit Sahai and Brent Waters [BSW10] Generalizes multiple concepts: Identity-Based Encryption Fuzzy Identity-Based Encryption Attribute-Based Encryption Predicate Encryption, etc. Enables keys that give partial information. Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Motivation Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Motivation Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Formal definition Functionality F : K × X → M ( k , x ) �→ F ( k , x ) Secret key for k : sk k ← msk Ciphertext for x : ct x ← pk Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Formal definition Functionality F : K × X → M ( k , x ) �→ F ( k , x ) Secret key for k : sk k ← msk Ciphertext for x : ct x ← pk Correctness Decrypt( sk k , ct x ) = F ( k , x ) Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Formal definition Functionality F : K × X → M ( k , x ) �→ F ( k , x ) ((Picture,Bob),data) �→ Pictures of Bob Secret key for k : sk k ← msk Ciphertext for x : ct x ← pk Correctness Decrypt( sk k , ct x ) = F ( k , x ) Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Formal definition Functionality F : K × X → M ( k , x ) �→ F ( k , x ) ((Picture,Bob),data) �→ Pictures of Bob Secret key for k : sk k ← msk Ciphertext for x : ct x ← pk Correctness Decrypt( sk k , ct x ) = F ( k , x ) Alice gets Bob’s pictures in her data. Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Security Intuitively: sk k doesn’t leak any more information than F ( k , x ) Even if there are collusions ! sk k and sk ′ k don’t leak more information than F ( k , x ) and F ( k ′ , x ) Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? Security Intuitively: sk k doesn’t leak any more information than F ( k , x ) The server doesn’t access Alice’s private data other than needed. Even if there are collusions ! sk k and sk ′ k don’t leak more information than F ( k , x ) and F ( k ′ , x ) Pictures of Jean and pictures of Jacques don’t make pictures of Jean-Jacques. Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? current lines of work Designing efficient functional encryption for access control... Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? current lines of work Designing efficient functional encryption for access control... nothing about partial information Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? current lines of work Designing efficient functional encryption for access control... nothing about partial information Obtain functional encryption for all circuits... Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? current lines of work Designing efficient functional encryption for access control... nothing about partial information Obtain functional encryption for all circuits... construction from inefficient primitives Florian Bourse Simple Functional Encryption Schemes for Inner Products
Overview of the results What is Functional Encryption? The Framework Inner Product functionality Work in progress What does simple mean? What do we achieve? current lines of work Designing efficient functional encryption for access control... nothing about partial information Obtain functional encryption for all circuits... construction from inefficient primitives This work: figuring out what we can do with simple assumption Florian Bourse Simple Functional Encryption Schemes for Inner Products
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