A new mode called Sophie Germain Counter Mode (SGCM) has been proposed as a variant of the

Galois/Counter Mode In cryptography, Galois/Counter Mode (GCM) is a mode of operation for symmetric-key cryptographic block ciphers which is widely adopted for its performance. GCM throughput rates for state-of-the-art, high-speed communication channels can be achiev ...

of operation for block ciphers. Instead of the binary field GF(2¹²⁸), it uses modular arithmetic in GF(''p'') where ''p'' is a

safe prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

with corresponding

Sophie Germain prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

. SGCM does prevent the specific "weak key" attack described in its paper, however there are other ways of modifying the message that will achieve the same forgery probability against SGCM as is possible against GCM: by modifying a valid ''n''-word message, you can create a SGCM forgery with probability circa . That is, its authentication bounds are no better than those of

. SGCM when implemented in hardware has a higher gate count than GCM. However, its authors expect software implementations of SGCM to have similar or superior performance to GCM on most software platforms.

References

{{Reflist Block cipher modes of operation