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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 ¶
Examples ¶
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 Pair ¶
Pair calculates an Optimal Ate pairing.
Example ¶
// This implements the tripartite Diffie-Hellman algorithm from "A One // Round Protocol for Tripartite Diffie-Hellman", A. Joux. // http://www.springerlink.com/content/cddc57yyva0hburb/fulltext.pdf // Each of three parties, a, b and c, generate a private value. a, _ := rand.Int(rand.Reader, Order) b, _ := rand.Int(rand.Reader, Order) c, _ := rand.Int(rand.Reader, Order) // Then each party calculates g₁ and g₂ times their private value. pa := new(G1).ScalarBaseMult(a) qa := new(G2).ScalarBaseMult(a) pb := new(G1).ScalarBaseMult(b) qb := new(G2).ScalarBaseMult(b) pc := new(G1).ScalarBaseMult(c) qc := new(G2).ScalarBaseMult(c) // Now each party exchanges its public values with the other two and // all parties can calculate the shared key. k1 := Pair(pb, qc) k1.ScalarMult(k1, a) k2 := Pair(pc, qa) k2.ScalarMult(k2, b) k3 := Pair(pa, qb) k3.ScalarMult(k3, c) // k1, k2 and k3 will all be equal.
Output:
func (*GT) ScalarMult ¶
ScalarMult sets e to a*k and then returns e.
Source Files