Cocks IBE scheme is an identity based encryption system proposed by Clifford Cocks in 2001.
[1] The security of the scheme is based on the hardness of the quadratic residuosity problem.
The PKG chooses: When user
wants to obtain his private key, he contacts the PKG through a secure channel.
The PKG To encrypt a bit (coded as
, the user To decrypt a ciphertext
, he Note that here we are assuming that the encrypting entity does not know whether
has the square root
As soon as this information is known to the encrypting entity, only one element needs to be sent.
is a quadratic residue modulo
is a square root of
[2]: Where the last step is the result of a combination of Euler's Criterion and the Chinese remainder theorem.
is a quadratic residue, same idea holds for
It can be shown that breaking the scheme is equivalent to solving the quadratic residuosity problem, which is suspected to be very hard.
The common rules for choosing a RSA modulus hold: Use a secure
, make the choice of
uniform and random and moreover include some authenticity checks for
(otherwise, an adaptive chosen ciphertext attack can be mounted by altering packets that transmit a single bit and using the oracle to observe the effect on the decrypted bit).
A major disadvantage of this scheme is that it can encrypt messages only bit per bit - therefore, it is only suitable for small data packets like a session key.
To illustrate, consider a 128 bit key that is transmitted using a 1024 bit modulus.
Then, one has to send 2 × 128 × 1024 bit = 32 KByte (when it is not known whether
is the square of a or −a), which is only acceptable for environments in which session keys change infrequently.
This scheme does not preserve key-privacy, i.e. a passive adversary can recover meaningful information about the identity of the recipient observing the ciphertext.