On the Bit Security of Cryptographic Primitives M E T R A S 7 - PowerPoint PPT Presentation

On the Bit Security of Cryptographic Primitives M E T R A S 7 . 7 M Daniele Micciancio Michael Walter UCSD IST Austria eprint.iacr.org/2018/077

Security Security Adversary Game 1

Security Security Adversary Game 1

Security Security Adversary Game A's resources and advantage 1

Proofs of Security Precision Simplicity 2

Proofs of Security Asymptotic Proofs Precision Simplicity 2

Proofs of Security Concrete Asymptotic Security Proofs Precision Simplicity 2

Proofs of Security Concrete Asymptotic Security Proofs Bit Security Precision Simplicity 2

Proofs of Security Concrete Asymptotic Security Proofs Bit Security Precision Simplicity A's resources A's advantage 2

Adversarial Advantage 3

Adversarial Advantage 1) Search game: 3

Adversarial Advantage 1) Search game: 2) Decision game: 3

Adversarial Advantage 1) Search game: A's resources constant A's advantage 2) Decision game: 3

Adversarial Advantage 1) Search game: A's resources constant A's advantage 2) Decision game: A's resources not constant A's advantage 3

Adversarial Advantage 1) Search game: A's resources constant A's advantage 2) Decision game: A's resources not constant A's advantage no bit secure PRG: 3

Adversarial Advantage, contd. 4

Adversarial Advantage, contd. [HILL'99] 4

Adversarial Advantage, contd. [HILL'99] 4

Adversarial Advantage, contd. [HILL'99] [GL'89,L'93] 4

Adversarial Advantage, contd. [HILL'99] [GL'89,L'93] 4

Adversarial Advantage, contd. [HILL'99] [GL'89,L'93] 4

Adversarial Advantage, contd. [HILL'99] [GL'89,L'93] 4

Adversarial Advantage, contd. [HILL'99] [GL'89,L'93] 4

Adversarial Advantage, contd. [HILL'99] [GL'89,L'93] 4

General De fi nition 5

General De fi nition - unify search and decision games 5

General De fi nition - unify search and decision games - characterize information gain of A 5

General De fi nition - unify search and decision games - characterize information gain of A - specialize to search and decision games 5

General De fi nition - unify search and decision games - characterize information gain of A - specialize to search and decision games "right" advantage: 5

General De fi nition - unify search and decision games - characterize information gain of A - specialize to search and decision games "right" advantage: Search 5

General De fi nition - unify search and decision games - characterize information gain of A - specialize to search and decision games "right" advantage: Search Decision 5

Security Reductions: One-Way vs Pseudorandom OW PR 6

Security Reductions: One-Way vs Pseudorandom OW PR 6

Security Reductions: One-Way vs Pseudorandom bit secure OWF implies GL hardcore bit is bit pseudorandom [L'93] OW PR 6

Security Reductions: One-Way vs Pseudorandom bit secure OWF implies GL hardcore bit is bit pseudorandom [L'93] OW PR 6

Security Reductions: One-Way vs Pseudorandom bit secure OWF implies GL hardcore bit is bit pseudorandom [L'93] OW PR bit secure PRG is also bit secure OWF 6

Security Reductions: Further Results 7

Security Reductions: Further Results - Encryption: IND implies OW 7

Security Reductions: Further Results - Encryption: IND implies OW - Hybrid Argument 7

Security Reductions: Further Results - Encryption: IND implies OW - Hybrid Argument - Security for Approximate Samplers with Less Precision 7