Module Cryptokit.DH
The DH
module implements Diffie-Hellman key agreement. Key agreement is a protocol by which two parties can establish a shared secret (typically a key for a symmetric cipher or MAC) by exchanging messages, with the guarantee that even if an attacker eavesdrop on the messages, he cannot recover the shared secret. Diffie-Hellman is one such key agreement protocol, relying on the difficulty of computing discrete logarithms. Notice that the Diffie-Hellman protocol is vulnerable to active attacks (man-in-the-middle attacks).
The protocol executes as follows:
- Both parties must agree beforehand on a set of public parameters (type
Cryptokit.DH.parameters
). Suitable parameters can be generated by callingCryptokit.DH.new_parameters
, or fixed parameters taken from the literature can be used. - Each party computes a random private secret using the function
Cryptokit.DH.private_secret
. - From its private secrets and the public parameters, each party computes a message (a string) with the function
Cryptokit.DH.message
, and sends it to the other party. - Each party recovers the shared secret by applying the function
Cryptokit.DH.shared_secret
to its private secret and to the message received from the other party. - Fixed-size keys can then be derived from the shared secret using the function
Cryptokit.DH.derive_key
.
type parameters
=
{
p : string;
Large prime number
g : string;
Generator of
Z/pZ
privlen : int;
Length of private secrets in bits
}
The type of Diffie-Hellman parameters. These parameters need to be agreed upon by the two parties before the key agreement protocol is run. The parameters are public and can be reused for several runs of the protocol.
val new_parameters : ?rng:Random.rng -> ?privlen:int -> int -> parameters
Generate a new set of Diffie-Hellman parameters. The non-optional argument is the size in bits of the
p
parameter. It must be large enough that the discrete logarithm problem modulop
is computationally unsolvable. 2048 is a reasonable value. The optionalrng
argument specifies a random number generator to use for generating the parameters; it defaults toCryptokit.Random.secure_rng
. The optionalprivlen
argument is the size in bits of the private secrets that are generated during the key agreement protocol; the default is 160.
val private_secret : ?rng:Random.rng -> parameters -> private_secret
Generate a random private secret. The optional
rng
argument specifies a random number generator to use; it defaults toCryptokit.Random.secure_rng
.
val message : parameters -> private_secret -> string
Compute the message to be sent to the other party.
Recover the shared secret from the private secret of the present party and the message received from the other party. The shared secret returned is a string of the same length as the
p
parameter. The private secret is destroyed and can no longer be used afterwards.
val derive_key : ?diversification:string -> string -> int -> string
derive_key shared_secret numbytes
derives a secret string (typically, a key for symmetric encryption) from the given shared secret.numbytes
is the desired length for the returned string. The optionaldiversification
argument is an arbitrary string that defaults to the empty string. Different secret strings can be obtained from the same shared secret by supplying differentdiversification
argument. The computation of the secret string is performed by SHA-1 hashing of the diversification string, followed by the shared secret, followed by an integer counter. The hashing is repeated with increasing values of the counter untilnumbytes
bytes have been obtained.