Peregrine: Toward Fastest FALCON Based on GPV Framework

. FALCON and Crystals-Dilithium are the digital signatures algorithms selected as NIST PQC standards at the end of the third round. FALCON has the advantage of the shortest size of the combined public key and signature but has the disadvantage of the relatively long signing time. Since FALCON algorithm is faithfully designed based on theoretical security analysis, the implementation of the algorithms is quite complex and needs considerable complexity. In order to implement the FALCON algorithm, the isochronous discrete Gaussian sampling algorithm should be used to prevent the side-channel attack, which causes a longer signature time. Also, FFT operations with floating-point numbers should be performed in FALCON, and they cause difficulty in applying the masking technique, making it vulnerable to side-channel attacks. We propose the Peregrine signature algorithm by devising two methods to make the signing algorithm of the FALCON scheme efficient. To reduce the signing time, Peregrine replaces the discrete Gaussian sampling algorithm with the sampling algorithm from the centered binomial distribution in the key generation algorithm and the signing algorithm by adjusting the encryption parameters. Also, it replaces the fast Fourier transform (FFT) operations of floating-point numbers with the number theoretic transform (NTT) operations of integers represented in residue number system (RNS), making the scheme faster and easy to be applied with a masking technique to prevent the side channel attack.