SGCM: The Sophie Germain Counter Mode

Sophie Germain Counter Mode (SGCM) is an authenticated encryption mode of operation, to be used with 128-bit block ciphers such as AES. SGCM is a variant of the NIST standardized Galois / Counter Mode (GCM) which has been found to be susceptible to weak key / short cycle forgery attacks. The GCM attacks are made possible by its extremely smooth-order multiplicative group which splits into 512 subgroups. Instead of GCM’s GF (2), we use GF (p) with p = 2+12451, where p−1 2 is also a prime. SGCM is intended for those who want a concrete, largely technically compatible alternative to GCM. In this memo we give a technical specification of SGCM, together with some elements of its implementation, security and performance analysis. Test vectors are also included.