Randomized Butterfly Operations for Side-Channel Protection in NTT

The patent applies dynamics by randomizing the order of butterfly operations in the NTT algorithm. Instead of executing operations in a fixed deterministic sequence, the system dynamically shuffles the operation order using random permutation arrays. This dynamic reordering ensures that power consumption patterns and electromagnetic emissions vary with each execution, preventing side-channel attackers from correlating consistent traces with secret polynomial coefficients.

The patent changes the parameter of operation sequencing from fixed to variable. By introducing random permutation arrays that shuffle the order of butterfly operations, the system transforms the execution parameters dynamically. This parameter change ensures that identical cryptographic operations produce different physical side-channel signatures, thereby protecting secret information while maintaining computational correctness through modular reduction.

The patent applies preliminary action by pre-generating random permutation arrays before executing the NTT algorithm. These permutation arrays are created in advance and stored for use during the cryptographic operation. By preparing the randomization structure beforehand, the system minimizes the computational overhead during the actual signature generation, as the shuffling operation simply applies pre-computed permutation indices rather than generating randomness on-the-fly.

The patent uses copying by creating multiple permutation arrays that can be reused across different NTT operations. Instead of generating entirely new random sequences for each cryptographic operation, the system can replicate and reuse validated permutation structures, reducing the computational burden of randomization while maintaining security. This copying approach allows efficient batch processing of signatures with consistent protection mechanisms.

The patent applies segmentation by dividing the NTT computation into discrete butterfly operations that can be independently shuffled. Each butterfly operation is treated as a separate executable unit with a specific index in the permutation array. This segmentation allows the system to randomize the execution order of individual operations without affecting the mathematical correctness of the overall computation, as long as each operation is applied to the correct inputs according to the permutation scheme.

The patent introduces permutation arrays as intermediary structures that mediate between the fixed algorithm specification and the randomized execution. These arrays serve as a mapping layer that translates deterministic algorithm steps into variable execution sequences. The permutation arrays act as intermediaries that preserve the logical correctness of the NTT computation while enabling physical obfuscation against side-channel analysis by decoupling algorithmic structure from execution timing.