org.cryptimeleon.math.expressions.group

Class PairingExpr

java.lang.Object

org.cryptimeleon.math.expressions.group.AbstractGroupElementExpression

org.cryptimeleon.math.expressions.group.PairingExpr

All Implemented Interfaces:

Expression, GroupElementExpression

public class PairingExpr
extends AbstractGroupElementExpression

A GroupElementExpression representing a bilinear pairing applied to two group element expressions.

Field Summary

Fields

Modifier and Type	Field and Description
protected GroupElementExpression	lhs
protected BilinearMap	map
protected GroupElementExpression	rhs

Fields inherited from class org.cryptimeleon.math.expressions.group.AbstractGroupElementExpression

group

Constructor Summary

Constructors

Constructor and Description
PairingExpr(BilinearMap map, GroupElementExpression lhs, GroupElementExpression rhs)

Method Summary

Modifier and Type	Method and Description
GroupElement	evaluate(Substitution substitutions) Evaluates the expression after substituting contained variables.
GroupOpExpr	flatten(ExponentExpr exponent) Linearizes the expression \(\text{this}^\text{exponent}\).
void	forEachChild(java.util.function.Consumer<Expression> action) Calls action on every (direct) child of this expression.
GroupElementExpression	getLhs() Retrieves the left argument of the pairing.
BilinearMap	getMap() Returns the bilinear map that is used for this pairing expression.
GroupElementExpression	getRhs() Retrieves the right argument of the pairing.
GroupOpExpr	linearize() Returns an equivalent expression of the form y * f(groupVariables, exponentVariables), where y is constant (no variables), and the expression f is linear.
PairingExpr	substitute(Substitution substitutions) Substitutes variables using the given function.

Methods inherited from class org.cryptimeleon.math.expressions.group.AbstractGroupElementExpression

getGroup, getGroupOrderIfKnown

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.cryptimeleon.math.expressions.group.GroupElementExpression

evaluate, flatten, inv, isEqualTo, isEqualTo, isEqualTo, op, op, op, opPow, opPow, opPow, opPow, opPow, opPow, opPow, opPow, pow, pow, pow, pow, pow, precompute, substitute, substitute

Methods inherited from interface org.cryptimeleon.math.expressions.Expression

accumulate, containsExprMatchingPredicate, containsVariables, getVariables, treeWalk

Field Detail

lhs

protected GroupElementExpression lhs

rhs

protected GroupElementExpression rhs

map

protected BilinearMap map

Constructor Detail

PairingExpr

public PairingExpr(BilinearMap map,
                   GroupElementExpression lhs,
                   GroupElementExpression rhs)

Method Detail

getMap

public BilinearMap getMap()

Returns the bilinear map that is used for this pairing expression.

getLhs

public GroupElementExpression getLhs()

Retrieves the left argument of the pairing.

getRhs

public GroupElementExpression getRhs()

Retrieves the right argument of the pairing.

forEachChild

public void forEachChild(java.util.function.Consumer<Expression> action)

Description copied from interface: Expression

Calls action on every (direct) child of this expression. For example, for a GroupOpExpr, this would call action on the left- and right-hand-side and then return.

evaluate

public GroupElement evaluate(Substitution substitutions)

Description copied from interface: Expression

Evaluates the expression after substituting contained variables.

Parameters:

substitutions - a function mapping variables to expressions that can be evaluated

Returns:

the result of evaluation

substitute

public PairingExpr substitute(Substitution substitutions)

Description copied from interface: Expression

Substitutes variables using the given function.

Parameters:

substitutions - a function mapping variable expressions to their replacement expressions

Returns:

the expression after substitution

linearize

public GroupOpExpr linearize()
                      throws java.lang.IllegalArgumentException

Description copied from interface: GroupElementExpression

Returns an equivalent expression of the form y * f(groupVariables, exponentVariables), where y is constant (no variables), and the expression f is linear. Linearity means that

 f(groupVariables, exponentVariables) * f(groupVariables2, exponentVariables2)
 = f(groupVariables * groupVariables2, exponentVariables + exponentVariables2)
 

The exact result is a GroupOpExpr where the left-hand-side y fulfills y.containsVariables() == false and the right-hand side is linear.

Throws:

java.lang.IllegalArgumentException - if it's not possible to form the desired output (e.g., the input is something like \(g^{x_1 \cdot x_2}\) for variables \(x_1, x_2\)).

flatten

public GroupOpExpr flatten(ExponentExpr exponent)

Description copied from interface: GroupElementExpression

Linearizes the expression \(\text{this}^\text{exponent}\).