A finite field inverter, comprising: an input port, configured to input an operand ( a ( x)); a search tree inverse unit, configured to perform an inverse operation of the operand ( a ( x)) in the finite field ( GF (2 n)) based on a binary search tree structure; an output port, configured to output an inversion result ( b ( x)) of the operand ( a ( x)); characterized in that the search tree inverse unit is provided with a left search tree and a right search tree; the left search tree and the right search tree each comprise tree nodes for processing inverse operations over the finite field ( GF (2 n)) and connecting wires connected between the tree nodes, the tree nodes being a root node, internal nodes and 2 n-1 leaf nodes, each path from the root node to a leaf node represents an element in the finite field ( GF (2 n)); a path representing the operand ( a ( x)) is determined through processing in the nodes; and the search tree inverse unit also comprises connecting wires connecting its leaf nodes; wherein each node has a binary value ( i 2) and comprises logic gate circuitry that is adapted to receive a coefficient (a n-1, a i, a 0) of the input operand ( a ( x)) via the input port and a further input (i 0) and to generate a first output bit ( o 0, o 1) and a second output bit ( o 2), where the first output bit (o 0, o 1) is connected to the further input (i 0) of the node's child nodes or to a connecting wire, the root nodes receiving a "1" as further input (i 0), and the second output bit (o 2) is connected to the output port; wherein the search tree inverse unit is adapted such that: - the path representing the input operand ( a ( x)) is constituted by the nodes having the first output bit (o 0, o 1) equal to "1", - if the operand ( a ( x)) is represented by a path from the root node to a first leaf node ( n 1) and the inversion result ( b ( x)) is represented by a path from the root node to a second leaf node ( n 2), then a connecting wire is provided between the first leaf node ( n 1) and the second leaf node ( n 2), and - a "1" received from a connecting wire is propagated upwards such that only the nodes in the path representing the inversion result ( b ( x)) output their value ( i 2) as a second output bit ( o 2). an input port, configured to input an operand ( a ( x)); a search tree inverse unit, configured to perform an inverse operation of the operand ( a ( x)) in the finite field ( GF (2 n)) based on a binary search tree structure; an output port, configured to output an inversion result ( b ( x)) of the operand ( a ( x)); characterized in that the search tree inverse unit is provided with a left search tree and a right search tree; the left search tree and the right search tree each comprise tree nodes for processing inverse operations over the finite field ( GF (2 n)) and connecting wires connected between the tree nodes, the tree nodes being a root node, internal nodes and 2 n-1 leaf nodes, each path from the root node to a leaf node represents an element in the finite field ( GF (2 n)); a path representing the operand ( a ( x)) is determined through processing in the nodes; and the search tree inverse unit also comprises connecting wires connecting its leaf nodes; wherein each node has a binary value ( i 2) and comprises logic gate circuitry that is adapted to receive a coefficient (a n-1, a i, a 0) of the input operand ( a ( x)) via the input port and a further input (i 0) and to generate a first output bit ( o 0, o 1) and a second output bit ( o 2), where the first output bit (o 0, o 1) is connected to the further input (i 0) of the node's child nodes or to a connecting wire, the root nodes receiving a "1" as further input (i 0), and the second output bit (o 2) is connected to the output port; wherein the search tree inverse unit is adapted such that: - the path representing the input operand ( a ( x)) is constituted by the nodes having the first output bit (o 0, o 1) equal to "1", - if the operand ( a ( x)) is represented by a path from the root node to a first leaf node ( n 1) and the inversion result ( b ( x)) is represented by a path from the root node to a second leaf node ( n 2), then a connecting wire is provided between the first leaf node ( n 1) and the second leaf node ( n 2), and - a "1" received from a connecting wire is propagated upwards such that only the nodes in the path representing the inversion result ( b ( x)) output their value ( i 2) as a second output bit ( o 2). - the path representing the input operand ( a ( x)) is constituted by the nodes having the first output bit (o 0, o 1) equal to "1", - if the operand ( a ( x)) is represented by a path from the root node to a first leaf node ( n 1) and the inversion result ( b ( x)) is represented by a path from the root node to a second leaf node ( n 2), then a connecting wire is provided between the first leaf node ( n 1) and the second leaf node ( n 2), and - a "1" received from a connecting wire is propagated upwards such that only the nodes in the path representing the inversion result ( b ( x)) output their value ( i 2) as a second output bit ( o 2).