A system for computing a private key sk i for a first device i participating in a self-certified identity based signature system comprising: a secure server configured to: compute parameters for the first device based on a second random number r i2 generated by the secure server, a first set of components received from the first device, a master secret key x i and parameters associated with a master public key mpk i, wherein the first set of components comprises a first random number r i1 generated by the first device, transmit the computed parameters to the first device; the first device configured to compute the private key sk i based on the received computed parameters and the random number r i1; and characterized in that the step of computing the parameters for the first device comprises: retrieving an arbitrary first value R i1, an identity of the device id i and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk i to an additive homomorphic encryption function HEnc(), setting an arbitrary value R i of the first device and a first integer s i1 as the parameters for the first device, whereby the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2, and whereby the first integer s i1 is computed by providing the second random number r i2, the homomorphic encryption value c, the master secret key x i the arbitrary value R i of the first device, the identity id i of the first device and the prime number q to the additive homomorphic encryption function HEnc(). compute parameters for the first device based on a second random number r i2 generated by the secure server, a first set of components received from the first device, a master secret key x i and parameters associated with a master public key mpk i, wherein the first set of components comprises a first random number r i1 generated by the first device, transmit the computed parameters to the first device; the first device configured to compute the private key sk i based on the received computed parameters and the random number r i1; and characterized in that the step of computing the parameters for the first device comprises: retrieving an arbitrary first value R i1, an identity of the device id i and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk i to an additive homomorphic encryption function HEnc(), setting an arbitrary value R i of the first device and a first integer s i1 as the parameters for the first device, whereby the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2, and whereby the first integer s i1 is computed by providing the second random number r i2, the homomorphic encryption value c, the master secret key x i the arbitrary value R i of the first device, the identity id i of the first device and the prime number q to the additive homomorphic encryption function HEnc(). retrieving an arbitrary first value R i1, an identity of the device id i and a homomorphic encryption value c from the first set of components, wherein the arbitrary first value R i1 is generated based on the first random number r i1 and the homomorphic encryption value c is generated by providing the first random number r i1 and a prime number q obtained from the parameters associated with the master public key mpk i to an additive homomorphic encryption function HEnc(), setting an arbitrary value R i of the first device and a first integer s i1 as the parameters for the first device, whereby the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2, and whereby the first integer s i1 is computed by providing the second random number r i2, the homomorphic encryption value c, the master secret key x i the arbitrary value R i of the first device, the identity id i of the first device and the prime number q to the additive homomorphic encryption function HEnc(). whereby the arbitrary value R i of the first device is computed based on the arbitrary first value R i1 and the second random number r i2, and whereby the first integer s i1 is computed by providing the second random number r i2, the homomorphic encryption value c, the master secret key x i the arbitrary value R i of the first device, the identity id i of the first device and the prime number q to the additive homomorphic encryption function HEnc().