Execution of the ECMQV key agreement algorithm requires determination of an implicit signature, which determination involves arithmetic operations. Some of the arithmetic operations employ a long-term cryptographic key. It is the execution of these arithmetic operations that can make the execution of the ECMQV key agreement algorithm vulnerable to a power analysis attack. In particular, an attacker using a power analysis attack may determine the long-term cryptographic key. By modifying the sequence of operations involved in the determination of the implicit signature and the inputs to those operations, power analysis attacks may no longer be applied to determine the long-term cryptographic key.