A processing device, such as logic on an integrated circuit may identify a cryptographic message stored in a first register. The processing device may determine a plurality of components for a second power of the cryptographic message using a plurality of components of the cryptographic message. The processing device may determine the plurality of components for the second power of the cryptographic message without storing the entire second power of the cryptographic message. Further, the processing device may determine a third power of the cryptographic message using modular arithmetic. The processing device may determine the third power by transforming the plurality of components for the second power of the cryptographic message and the plurality of components of the cryptographic message.