16 Weil pairing defined
This chapter covers
- Weil pairing properties
- Code to compute Weil pairing
- Example with tiny numbers
In this chapter, I’ll describe Weil pairings. These will be used with the example application shown in chapter 18. In chapter 15, I covered the fundamental functions that compute all pairings. I will now explain the Weil pairing, which has properties that make it unique. For some cryptographic protocols, these properties make the Weil pairing more useful, and for other protocols, the Weil pairing does not work. All the protocols explained in chapters 18 and 19 use different base points for the pairing algorithms, so the Weil pairing could work in principle. If you run across algorithms that have the same base point for both pairing input points, the Weil pairing will not work; use the Tate pairing from chapter 17 instead.
The formula that computes the Weil pairing uses the Miller \(f_P(R)\) function from chapter 15. After showing the properties of the Weil pairing, I’ll describe formulas in gory detail so you can get a feel for why certain calculations should give specific results. This enables us to debug our code because the math has to work.