# Call for Chapters

Handbook of Pairing Based Cryptography

Editors: Nadia El Mrabet and Marc Joye
## Scope

As pairings are aimed to be embedded into a large number of different devices, the efficiency of a pairing implementation is an active and living subject of research. The book will be a state of the art of the latest improvements for pairing computations. We will present up to date optimizations for a pairing implementation. We will consider the choice of the elliptic curve, the representation of the finite field and the coordinate system of points over the elliptic curves, together with software and hardware issues. The book will seek to balance the theory with practice, and the use of computational approaches.## Important dates

Abstract due: | February 15, 2015 |

Notification of acceptance: | March 15, 2015 |

Manuscript due: | July 15, 2015 |

Completion of reviews: | September 1, 2015 |

Revised manuscripts due: | October 15, 2015 |

Publication: | March 2016 |

## Topics

The book will be devoted to efficient pairing computations and implementations. Pairings are a very interesting tool for cryptographers. They provide new protocols such as Identity Based Cryptography and allows the simplification of existing protocols such as signature schemes. The implementation of a pairing involves several levels of arithmetics: the arithmetic of finite fields, extensions of finite fields, the arithmetic of elliptic curves and several algorithmic problems. We will present in the book the various pairings available for cryptographic use. We will provide all the necessary mathematical background about finite fields and elliptic curves.Each chapter will include the presentation of the problem, the mathematical formulation, discussion on the implementation issues, the solutions accompanied by code or pseudo code, several numerical results, and references to further reading and notes.

In line with our desire for accessibility, the book will attempt to be a self-contained guide to the implementation of a pairing algorithm, providing a synopsis of the required background mathematical material necessary to understand the methods in the introductory chapters.

We propose below a tentavive table of content. Of course the content of each chapter can be modified and new, different chapters can be proposed.

Contributions will particularly be expected to give a survey of a larger part of the literature, and prepared using the Latex2e template. Interested authors should send an abstract of their planned contribution to the editors by electronic mail ( elmrabet@ai.univ-paris8.fr,marc.joye@technicolor.com), by February 10th 2015. Upon acceptance, the full contributions are due by June 15th 2015. The volume is expected to appear in March 2016.

- Introduction {~10 pages}
- Uses cases will give us the security level.
- Security level will give a range for the embedding degree.
- The embedding degree will provide an elliptic curve and a finite field.
- We then have to construct the appropriate arithmetic of the finite fields.
- Given the elliptic curve we would choose a pairing (Optimal Ate, twisted Ate...)/li>
- Then the implementation part, soft, hard?

- Mathematical Background{~30 pages}
- Finite fields (definition of finite fields, properties, extensions, cyclotomic subgroup, arithmetic of finite fields multiplications)
- Elliptic curves (definition, cardinality, Hasse's boundary, super-singular, ordinary, embedding degree, twisted elliptic curve, coordinates, arithmetic, addition, doubling, algorithmic)
- Discrete logarithm several problems, recent records for elliptic curve

- Pairings{~30 pages}
- Divisors, Picard group
- Definition of the Weil and Tate pairings, properties, symmetric pairings, asymmetric pairings
- Pairing-based cryptography examples
- Denominator elimination
- Twisted elliptic curve
- Ate twisted Ate pairings
- Optimal pairing
- Pairing lattices

- Pairing friendly elliptic curves {~30 pages}
- Definition, families, characteristic 2, 3, large.
- Choice of the model of elliptic curves (Weierstras, Edwards, Jacobi,...)
- Hash into the elliptic curve
- Find the curve with the nicest parameters
- The choice of the parameters (elliptic curve, sparsity, ...)
- Example of the BN curves

- Arithmetic of finite fields {~30 pages}
- Tower field extensions
- Choice of the coordinates (projective, Jacobi, affine...)
- Cyclotomic subgroup
- Lazy reduction
- RNS representation

- Final exponentiation {~30 pages}
- Exponentiation in finite fields
- The Frobenius computation
- Decomposition of the computation
- Lucas sequences

- Algorithmic {~30 pages}
- The multiplications over the extension fields
- Fixed argument pairings
- Compressed pairing

- Software implementation {~30 pages}
- Sage code
- Library giving pairing implementation

- Hardware implementation {~30 pages}
- FPGA
- specific design

- Side Channel Attacks {~30 pages}
- DPA
- Fault attacks
- Countermeasures