README
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BN256
This package implements a particular bilinear group. The code is imported from https://github.com/ethereum/go-ethereum/tree/master/crypto/bn256/cloudflare
🚨 WARNING This package originally claimed to operate at a 128-bit level. However, recent work suggest that this is no longer the case.
A note on the selection of the bilinear group
The parameters defined in the constants.go file follow the parameters used in alt-bn128 (libff). These parameters were selected so that r−1 has a high 2-adic order. This is key to improve efficiency of the key and proof generation algorithms of the SNARK used.
Installation
go get github.com/clearmatics/bn256
Development
This project uses go modules.
If you develop in your GOPATH and use GO 1.11, make sure to run:
export GO111MODULE=on
In fact:
(Inside $GOPATH/src, for compatibility, the go command still runs in the old GOPATH mode, even if a go.mod is found.) See: https://blog.golang.org/using-go-modules
For more fine-grained control, the module support in Go 1.11 respects a temporary environment variable, GO111MODULE, which can be set to one of three string values: off, on, or auto (the default). If GO111MODULE=off, then the go command never uses the new module support. Instead it looks in vendor directories and GOPATH to find dependencies; we now refer to this as "GOPATH mode." If GO111MODULE=on, then the go command requires the use of modules, never consulting GOPATH. We refer to this as the command being module-aware or running in "module-aware mode". If GO111MODULE=auto or is unset, then the go command enables or disables module support based on the current directory. Module support is enabled only when the current directory is outside GOPATH/src and itself contains a go.mod file or is below a directory containing a go.mod file. See: https://golang.org/cmd/go/#hdr-Preliminary_module_support
The project follows standard Go conventions using gofmt. If you wish to contribute to the project please follow standard Go conventions. The CI server automatically runs these checks.
Documentation
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Overview ¶
Package bn256 implements a particular bilinear group at the 128-bit security level.
Bilinear groups are the basis of many of the new cryptographic protocols that have been proposed over the past decade. They consist of a triplet of groups (G₁, G₂ and GT) such that there exists a function e(g₁ˣ,g₂ʸ)=gTˣʸ (where gₓ is a generator of the respective group). That function is called a pairing function.
This package specifically implements the Optimal Ate pairing over a 256-bit Barreto-Naehrig curve as described in http://cryptojedi.org/papers/dclxvi-20100714.pdf. Its output is compatible with the implementation described in that paper.
Index ¶
Constants ¶
This section is empty.
Variables ¶
var Order = bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495617")
Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.
var P = bigFromBase10("21888242871839275222246405745257275088696311157297823662689037894645226208583")
P is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.
Functions ¶
func PairingCheck ¶
PairingCheck calculates the Optimal Ate pairing for a set of points.
Types ¶
type G1 ¶
type G1 struct {
// contains filtered or unexported fields
}
G1 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.
func (*G1) ScalarBaseMult ¶
ScalarBaseMult sets e to g*k where g is the generator of the group and then returns e.
func (*G1) ScalarMult ¶
ScalarMult sets e to a*k and then returns e.
type G2 ¶
type G2 struct {
// contains filtered or unexported fields
}
G2 is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.
func (*G2) ScalarBaseMult ¶
ScalarBaseMult sets e to g*k where g is the generator of the group and then returns out.
func (*G2) ScalarMult ¶
ScalarMult sets e to a*k and then returns e.
type GT ¶
type GT struct {
// contains filtered or unexported fields
}
GT is an abstract cyclic group. The zero value is suitable for use as the output of an operation, but cannot be used as an input.
func Miller ¶
Miller applies Miller's algorithm, which is a bilinear function from the source groups to F_p^12. Miller(g1, g2).Finalize() is equivalent to Pair(g1, g2).
func (*GT) ScalarMult ¶
ScalarMult sets e to a*k and then returns e.
Source Files