Includes bibliographical references (pages 95-108).

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Title from PDF title page (viewed on April 28, 2015).

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1. Introduction -- 1.1 Our results -- 1.2 Brief overview -- 1.3 Organization --

2. Survey of applications -- 2.1 How flexible can we make access to encrypted data? -- 2.2 Program obfuscation -- 2.3 Other applications --

3. Multilinear maps and graded encoding systems -- 3.1 Cryptographic multilinear maps -- 3.1.1 Efficient procedures -- 3.1.2 Hardness assumptions -- 3.2 Graded encoding schemes -- 3.2.1 Efficient procedures, the dream version -- 3.2.2 Efficient procedures, the real-life version -- 3.2.3 Hardness assumptions --

4. Preliminaries I: lattices -- 4.1 Lattices -- 4.2 Gaussians on lattices -- 4.3 Sampling from discrete Gaussian --

5. Preliminaries II: algebraic number theory background -- 5.1 Number fields and rings of integers -- 5.2 Embeddings and geometry -- 5.3 Ideals in the ring of integers -- 5.4 Prime ideals, unique factorization and distributions -- 5.5 Ideal lattices --

6. The new encoding schemes -- 6.1 The basic graded encoding scheme -- 6.2 Setting the parameters -- 6.3 Extensions and variants --

7. Security of our constructions -- 7.1 Our hardness assumption -- 7.2 Simplistic models of attacks -- 7.2.1 Hardness of GCDH in the arithmetic straight-line program model -- 7.3 Cryptanalysis beyond the generic models -- 7.3.1 Easily computable quantities -- 7.3.2 Using averaging attacks -- 7.3.3 Cryptanalysis with extra help -- 7.4 Some countermeasures -- 7.5 Easiness of other problems --

8. Preliminaries III: computation in a number field -- 8.1 Some computational aspects of number fields and ideal lattices -- 8.2 Computational hardness assumptions over number fields --

9. Survey of lattice cryptanalysis -- 9.1 Averaging attacks -- 9.2 Gentry-Szydlo: recovering v from v.v and (v) -- 9.3 Nguyen-Regev: a gradient descent attack -- 9.4 Ducas-Nguyen: gradient descent over zonotopes and deformed parallelepipeds -- 9.5 A new algorithm for the closest principal ideal generator problem -- 9.6 Coppersmith attacks -- 9.7 Dimension halving in principal ideal lattices --

10. One-round key exchange -- 10.1 Definitions -- 10.2 Our construction --

Appendix A. Generalizing graded encoding systems -- Efficient procedures, the dream version -- Efficient procedures, the real-life version -- Hardness assumptions -- Bibliography -- Author's biography.

Cryptography to me is "black magic," enabling tasks that often seem paradoxical or simply just impossible. Like the space explorers, we cryptographers often wonder, "What are the boundaries of this world of 'black magic'?" This book lays one of the founding stones in furthering our understanding of these edges.

Also available in print.