Fully Hashed Menezes-Qu-Vanstone
Fully Hashed Menezes-Qu-Vanstone (FHMQV) is ECMQV key agreement with enhancement and additional security properties published in A Secure and Efficient Authenticated Diffie–Hellman Protocol by by Augustin P. Sarr and Philippe Elbaz–Vincent, and Jean–Claude Bajard. FHMQV is based upon Hugo Krawczyk's HMQV: A High-Performance Secure Diffie-Hellman Protocol, in which Krawczyk identified and remediated issues from the original MQV.
This page is concerned with two party key agreement. For group key agreement and multicast scenarios, see Multicast Security: A Taxonomy and Some Efficient Constructions and Provably Authenticated Group Diffie-Hellman Key Exchange.
Note: FHMQV is not in Crypto++ mainline. It is offered as a patch below. You need to apply the patch from fhmqv-diff.zip, and then the sample program from fhmqv-agree.zip should work as expected.
Crypto++'s valdat2.cpp test file performs FHMQV validation over Fp. See the ValidateFHMQV function for details.
Hashes and Curves
typedef FHMQV< ECP, DL_GroupParameters_EC< ECP >::DefaultCofactorOption, SHA1 >::Domain FHMQV160; typedef FHMQV< ECP, DL_GroupParameters_EC< ECP >::DefaultCofactorOption, SHA384 >::Domain FHMQV384;
FHMQV uses hashing at key points to harden against information leakage. Internally, the hash function is similar to below, where A and B are static public keys, and X and Y are ephemeral public keys. agreedValueLength specifies the size of the output buffer agreedValue.
Hash(sigma, XX, YY, AA, BB, agreedValue, agreedValueLength);
agreedValueLength depends on the hash block size and not the field element size. To determine the required size, call the AgreedValueLength function as shown in the example below.
Fully Hashed MQV is somewhat different than other key agreement classes, such as DH, DH2, ECDH and ECMQV. FHMQV has some symmetry, but it is necessary to specify a role: client or server. For example, in the code below, fhmqvA is assuming the client role by specifying true in its constructor, and fhmqvB is assuming the server role by specifying false.
While its not readily apparent, it does not matter which object sends the first message (ie, who takes the 'client' role and who takes the 'server' role). What matters is the roles are opposed between the parties participating in the exchange. For example, a 'server' could send the first message to a 'client'. In fact, Sarr, Elbaz–Vincent and Bajard's paper uses the terms Initiator and Recipient (the recipient responds to the initiator).
The agreed upon value is encoded as an Integer because the class overloads the output operator, which makes it easy to print. In practice, the shared secret is usually hashed before use, and then used as a Key Encryption Key (KEK) to transport a random session key; or used as a Content Encryption Key (CEK). In the case of FHMQV, the shared secret does not require hashing.
AutoSeededRandomPool rng; const OID CURVE = secp256r1(); FHMQV < ECP >::Domain fhmqvA( CURVE, true /*client*/ ), fhmqvB( CURVE, false /*server*/ ); /////////////////////////////////////////////////////////// // Party A, static (long term) key pair SecByteBlock sprivA(fhmqvA.StaticPrivateKeyLength()), spubA(fhmqvA.StaticPublicKeyLength()); // Party A, ephemeral (temporary) key pair SecByteBlock eprivA(fhmqvA.EphemeralPrivateKeyLength()), epubA(fhmqvA.EphemeralPublicKeyLength()); // Party B, static (long term) key pair SecByteBlock sprivB(fhmqvB.StaticPrivateKeyLength()), spubB(fhmqvB.StaticPublicKeyLength()); // Party B, ephemeral (temporary) key pair SecByteBlock eprivB(fhmqvB.EphemeralPrivateKeyLength()), epubB(fhmqvB.EphemeralPublicKeyLength()); /////////////////////////////////////////////////////////// // Imitate a long term (static) key fhmqvA.GenerateStaticKeyPair(rng, sprivA, spubA); // Ephemeral (temporary) key fhmqvA.GenerateEphemeralKeyPair(rng, eprivA, epubA); // Imitate a long term (static) key fhmqvB.GenerateStaticKeyPair(rng, sprivB, spubB); // Ephemeral (temporary) key fhmqvB.GenerateEphemeralKeyPair(rng, eprivB, epubB); /////////////////////////////////////////////////////////// SecByteBlock sharedA(fhmqvA.AgreedValueLength()), sharedB(fhmqvB.AgreedValueLength()); if(!fhmqvA.Agree(sharedA, sprivA, eprivA, spubB, epubB)) throw runtime_error("Failed to reach shared secret (A)"); if(!fhmqvB.Agree(sharedB, sprivB, eprivB, spubA, epubA)) throw runtime_error("Failed to reach shared secret (B)"); Integer ssa, ssb; ssa.Decode(sharedA.BytePtr(), sharedA.SizeInBytes()); cout << "(A): " << std::hex << ssa << endl; ssb.Decode(sharedB.BytePtr(), sharedB.SizeInBytes()); cout << "(B): " << std::hex << ssb << endl; if(ssa != ssb) throw runtime_error("Failed to reach shared secret (C)"); cout << "Agreed to shared secret" << endl;
In production, the test ssa != ssb cannot be performed since the values will be on different hosts. A problem with agreement will not be detected until data starts flowing - the first data packet received will not authenticate.
A typical run of the program using secp256r1 is shown below.
$ ./fhmqv-agree.exe (A): 32f11d394abc3bf499e7c35e7b88103f5aec0e8d74eae7bd8c670994d26fc95h (B): 32f11d394abc3bf499e7c35e7b88103f5aec0e8d74eae7bd8c670994d26fc95h Agreed to shared secret
fhmqv-diff.zip - Fully Hashed Menezes-Qu-Vanstone (FHMQV) key agreement patch.
fhmqv-agree.zip - Fully Hashed Menezes-Qu-Vanstone (FHMQV) key agreement (authenticated).
fhmqv-tamper.zip - Fully Hashed Menezes-Qu-Vanstone (FHMQV) key agreement run under tampering. Entity A's public key is first modified so that (x,y) -> (x,y+1), which is not on the curve. The second tampering modifies the public key so that a valid point on the curve is created (but Entity A does not have the private key).