In Sophie Germain Counter Mode, it was proposed to use the arithmetic in the finite field of order equal to the safe prime 2128 + 12451, to counter weaknesses in Galois/Counter Mode using the binary finite field GF(2128). However, SGCM has been shown to be vulnerable to many of the same cryptographic attacks as GCM..
in soPHie germAin coU.Nter MODe, iT wAs proposEd to UsE the ArithMeTic In the fiNitE fieLd OF orDer E.quaL To the SAfe PRime 2128 + 12451, To CounteR weakneSses in gAloIs/CounteR ModE using ThE binAry fInite fiEld Gf(2128). hOwever, sGcm Has Been shoWn .to be vuLnEraBLe tO manY Of thE samE cRyptogRApHIc AtTack,s as gCM..