MODP

MODP refers to a class of predefined Diffie-Hellman groups used for secure key exchange. Each MODP group consists of a large prime modulus p and a generator g. In a typical exchange, party A computes A = g^a mod p and party B computes B = g^b mod p, and both derive the shared secret g^(ab) mod p. The security relies on the difficulty of the discrete logarithm problem in the chosen group, while the predefined nature of the parameters promotes interoperability between implementations without requiring on-the-fly prime generation.

Standard MODP groups are published and maintained to ensure compatibility across protocols. A widely cited set comes from the Internet Engineering Task Force (IETF) in RFC 3526 and related documents. These groups include 1024-bit Group 2, 2048-bit Group 14, 3072-bit Group 15, 4096-bit Group 16, 6144-bit Group 17, and 8192-bit Group 18. Generators commonly used with these moduli are small integers such as 2 or 5. Larger groups provide stronger protection against brute-force attacks but incur higher computational and bandwidth costs.

Usage and security: MODP groups are used to establish ephemeral, forward-secure keys in protocols such as TLS, SSH, and IPsec. To mitigate certain attacks, primes are often chosen as safe primes, and implementations should validate peer public values to ensure they lie within the expected subgroup. While widely deployed, some security practitioners advocate moving toward elliptic-curve Diffie-Hellman due to better security-per-bit and efficiency at equivalent sizes.

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