BilinearMap (math 3.1.0 API)

All Superinterfaces:

java.util.function.BiFunction<GroupElement,GroupElement,GroupElement>

All Known Implementing Classes:

BasicBilinearMap, DebugBilinearMap, LazyBilinearMap
```
public interface BilinearMap
extends java.util.function.BiFunction<GroupElement,GroupElement,GroupElement>
```
A bilinear map e : G1 x G2 -> GT.
Bilinearity means that the map e is linear in both the first and second component. G1, G2 and GT are groups.
Usually used as a wrapper around a BilinearMapImpl to offer additional evaluation capabilities. You should use BilinearMapImpl for your implementation instead.

Method Summary

All Methods Instance Methods Abstract Methods Default Methods
Modifier and Type	Method and Description
`default GroupElement`	`apply(GroupElement g1, GroupElement g2)` Corresponds to `this.apply(g1, g2, 1)`.
`GroupElement`	`apply(GroupElement g1, GroupElement g2, java.math.BigInteger exponent)` Computes \(e(g1,g2)^\text{exponent}\).
`default GroupElement`	`apply(GroupElement g1, GroupElement g2, Zn.ZnElement exponent)` Computes \(e(g1,g2)^\text{exponent}\).
`default GroupElementVector`	`apply(GroupElementVector lhs, GroupElementVector rhs)` Applies the pairing function to each element of the given vectors, resulting in a new vector containing the resulting target group elements.
`default PairingExpr`	`applyExpr(GroupElementExpression g1elem, GroupElement g2elem)`
`default PairingExpr`	`applyExpr(GroupElementExpression g1elem, GroupElementExpression g2elem)` Creates a `PairingExpr` using this pairing and given argument `GroupElementExpression`s.
`default PairingExpr`	`applyExpr(GroupElement g1elem, GroupElement g2elem)` Creates a `PairingExpr` using this pairing and given argument group elements.
`default PairingExpr`	`applyExpr(GroupElement g1elem, GroupElementExpression g2elem)`
`Group`	`getG1()` Returns the source group G1 associated with this bilinear map.
`Group`	`getG2()` Returns the source group G2 associated with this bilinear map.
`Group`	`getGT()` Returns the target group GT associated with this bilinear map.
`default GroupElement`	`innerProduct(GroupElementVector lhs, GroupElementVector rhs)` Corresponds to first calling `apply(GroupElementVector, GroupElementVector)` and then combining the resulting elements using the group operation.
`boolean`	`isSymmetric()` Returns true if `e(g,h).equals(e(h,g))` for all `g`, `h`.

Methods inherited from interface java.util.function.BiFunction
andThen

- Method Detail
  - getG1
```
Group getG1()
```
    Returns the source group G1 associated with this bilinear map.
  - getG2
```
Group getG2()
```
    Returns the source group G2 associated with this bilinear map.
  - getGT
```
Group getGT()
```
    Returns the target group GT associated with this bilinear map.
  - apply
```
GroupElement apply(GroupElement g1,
                   GroupElement g2,
                   java.math.BigInteger exponent)
```
    Computes \(e(g1,g2)^\text{exponent}\).
    Depending on the bilinear map and the involved groups, this may be more efficiently implemented than computing it directly via apply(g1,g2).pow(exponent). For example, implementations should do exponentiation in the group with the cheapest group operation.
    
    Parameters:
    
    g1 - left hand side argument for the pairing function
    
    g2 - right hand side argument for the pairing function
    
    exponent - the exponent to apply to the result of the pairing
  - apply
```
default GroupElement apply(GroupElement g1,
                           GroupElement g2)
```
    Corresponds to this.apply(g1, g2, 1).
    
    Specified by:
    
    apply in interface java.util.function.BiFunction<GroupElement,GroupElement,GroupElement>
    
    Parameters:
    
    g1 - left hand side argument for the pairing function
    
    g2 - right hand side argument for the pairing function
  - apply
```
default GroupElement apply(GroupElement g1,
                           GroupElement g2,
                           Zn.ZnElement exponent)
```
    Computes \(e(g1,g2)^\text{exponent}\).
    Depending on the bilinear map and the involved groups, this may be more efficiently implemented than computing it directly via apply(g1,g2).pow(exponent). For example, implementations should do exponentiation in the group with the cheapest group operation.
    
    Parameters:
    
    g1 - left hand side argument for the pairing function
    
    g2 - right hand side argument for the pairing function
    
    exponent - the exponent to apply to the result of the pairing
  - apply
```
default GroupElementVector apply(GroupElementVector lhs,
                                 GroupElementVector rhs)
```
    Applies the pairing function to each element of the given vectors, resulting in a new vector containing the resulting target group elements. The given vectors must have the same length for this method to work.
    Specifically, the pairing function is applied to the elements residing at the same index. For example, the first element of lhs and rhs will be used as argument, and the result will be stored as the first element of the result vector. This continues until done for each element.
    
    Parameters:
    
    lhs - GroupElementVector containing the group elements to use a left hand side arguments
    
    rhs - GroupElementVector containing the group elements to use a right hand side arguments
    
    Returns:
    
    a new GroupElementVector containing the resulting target group elements
    
    Throws:
    
    java.lang.IllegalArgumentException - if the given vectors do not have the same length
  - innerProduct
```
default GroupElement innerProduct(GroupElementVector lhs,
                                  GroupElementVector rhs)
```
    Corresponds to first calling apply(GroupElementVector, GroupElementVector) and then combining the resulting elements using the group operation. The given vectors must have the same length for this method to work.
    
    Parameters:
    
    lhs - GroupElementVector containing the group elements to use a left hand side arguments
    
    rhs - GroupElementVector containing the group elements to use a right hand side arguments
    
    Returns:
    
    the resulting group element
    
    Throws:
    
    java.lang.IllegalArgumentException - if the given vectors do not have the same length
  - applyExpr
```
default PairingExpr applyExpr(GroupElementExpression g1elem,
                              GroupElementExpression g2elem)
```
    Creates a PairingExpr using this pairing and given argument GroupElementExpressions.
    
    Parameters:
    
    g1elem - the left hand side G1 group element expression argument for the pairing function
    
    g2elem - the right hand side G2 group element expression argument for the pairing function
    
    Returns:
    
    a PairingExpr
  - applyExpr
```
default PairingExpr applyExpr(GroupElement g1elem,
                              GroupElement g2elem)
```
    Creates a PairingExpr using this pairing and given argument group elements.
    
    Parameters:
    
    g1elem - the left hand side G1 element argument for the pairing function
    
    g2elem - the right hand side G2 element argument for the pairing function
    
    Returns:
    
    a PairingExpr
  - applyExpr
```
default PairingExpr applyExpr(GroupElement g1elem,
                              GroupElementExpression g2elem)
```
  - applyExpr
```
default PairingExpr applyExpr(GroupElementExpression g1elem,
                              GroupElement g2elem)
```
  - isSymmetric
```
boolean isSymmetric()
```
    Returns true if e(g,h).equals(e(h,g)) for all g, h.

Interface BilinearMap

Method Summary

Methods inherited from interface java.util.function.BiFunction

Method Detail

getG1

getG2

getGT

apply

apply

apply

apply

innerProduct

applyExpr

applyExpr

applyExpr

applyExpr

isSymmetric