Compact and Efficient Constant-Time GCD and Modular Inversion with Short-Iteration

Theoretically secure cryptosystems, digital signatures may not be after being implemented on Internet of Things (IoT) devices and PCs because side-channel attacks (SCA). Because RSA key generation ECDSA require GCD computations or modular inversions, which are often computed using the binary Euclidean algorithm (BEA) extended (BEEA), SCA weaknesses BEA BEEA become a serious concern. Constant-time (CT-GCD) constant-time inversion (CTMI) algorithms effective countermeasures in such situations. Modular based Fermat's little theorem (FLT) can work constant time, but it is efficient for general inputs. Two CTMI algorithms, named BOS BY this paper, were proposed by Bos, Bernstein Yang, respectively. Their all concept BEA. However, one iteration has complicated computations, requires more iterations. A small number iterations simple during good characteristics algorithm. Based view, study proposes new short-iteration CT-GCD over