Direct anonymous attestation-based apparatus and method
A technique includes generating a direct anonymous attestation (DAA)-based signature to prove an electronic device is a member of a group. Generating the signature includes determining a reciprocal of a prime modulus, and determining the reciprocal of the prime modulus comprises left bit shifting a Barrett multiplier by a predetermined number of bits and multiplying a result of the left bit shifting of the Barrett multiplier with the prime modulus.
1. A method comprising:
an electronic device generating a Direct Anonymous Attestation (DAA) signature;
the electronic device performing multiple iterations of a Barrett reduction to determine the reciprocal of a prime number, wherein a given iteration of the multiple iterations comprises left bit shifting a Barrett multiplier by a predetermined number of bits, multiplying a result of the left bit shifting of the Barrett multiplier with the prime number, subtracting a result of multiplying the result of the left bit shifting of the Barrett multiplier with the prime number from a set of most significant bits of the Barrett multiplier, and left bit shifting a result of the subtraction to form an input for another iteration of the multiple iterations;
the electronic device determining the DAA signature based on the reciprocal of the prime number; and
the electronic device communicating the DAA signature to a server to prove the electronic device is a member of a group.
2. The method of claim 1 , wherein generating the DAA-based signature comprises generating an Enhanced Privacy Identification (EPID) signature.
3. The method of claim 1 , wherein the electronic device comprises an Internet of Things (IoT) device, and the electronic device communicating the DAA signature to the server comprises the IoT device communicating with the server to provision a resource for the IoT device.
4. The method of claim 1 , wherein the electronic device comprises an Internet of Things (IoT) device.
5. The method of claim 1 , further comprising generating an Enhanced Privacy Identification (EPID) signature based on the reciprocal of the prime number.
6. The method of claim 1 , wherein the set of most significant bits comprise 32 bits.
7. The method of claim 1 , wherein the electronic device comprises an Internet of Things (IoT) device, the server comprises a cloud-based server, and the electronic device communicating the DAA signature to the server comprises the IoT device communicating the DAA signature with the cloud-based server to register the IoT device.
8. The method of claim 1 , further comprising:
further basing the generation of the signature on a multi-exponential product of a first number raised to a first exponent, a second number raised to a second exponent, a third number raised to a third exponent and a fourth number raised to a fourth exponent; and
wherein each iteration of the plurality of iterations is associated with a different bit position of the plurality of bit positions and comprises using no more than two temporary variables in each iteration.
9. The method of claim 1 , wherein determining the DAA-based signature comprises generating the DAA-based signature based on a public key and a private key.
10. An electronic device comprising:
a network interface; and
a cryptoprocessor to generate a Direct Anonymous Attestation (DAA) signature based on a private key and a public key and communicate the DAA signature using the network interface to a server to prove membership of the electronic device in a public group, wherein the cryptoprocessor to:
perform multiple iterations of a Barrett reduction to determine the reciprocal of a prime number, wherein a given iteration of the multiple iterations comprises left bit shifting a Barrett multiplier by a predetermined number of bits, multiplying a result of the left bit shifting of the Barrett multiplier with the prime number, subtracting a result of multiplying the result of the left bit shifting of the Barrett multiplier with the prime number from a set of most significant bits of the Barrett multiplier, and left bit shifting a result of the subtraction to form an input for another iteration of the multiple iterations; and
determine the DAA signature based on the reciprocal of the prime number.
11. The electronic device of claim 10 , wherein the cryptoprocessor to generate the signature to authenticate an Internet of Things (IoT) device.
12. The electronic device of claim 10 , wherein the cryptoprocessor to generate an Enhance Privacy Identification (EPID) signature based on the reciprocal of the prime number.
13. The electronic device of claim 10 , wherein the server comprises a cloud-based server, and the cryptoprocessor to use the network interface to communicate data representing the signature with the cloud-based server to register an Internet of Things (IoT) device.
14. The electronic device of claim 10 , wherein the cryptoprocessor to:
further base the generation of the signature on a multi-exponential product of a first number raised to a first exponent, a second number raised to a second exponent, a third number raised to a third exponent and a fourth number raised to a fourth exponent; and
wherein each iteration of the plurality of iterations is associated with a different bit position of the plurality of bit positions and comprises using no more than two temporary variables in each iteration.
15. A non-transitory storage medium to store instructions readable by a processor-based machine, wherein the instructions, when executed by a processor, cause the processor to:
generate a Direct Anonymous Attestation (DAA) signature;
perform multiple iterations of a Barrett reduction to determine the reciprocal of a prime number, wherein a given iteration of the multiple iterations comprises left bit shifting a Barrett multiplier by a predetermined number of bits, multiplying a result of the left bit shifting of the Barrett multiplier with the prime number, subtracting a result of multiplying the result of the left bit shifting of the Barrett multiplier with the prime number from a set of most significant bits of the Barrett multiplier, and left bit shifting a result of the subtraction to form an input for another iteration of the multiple iterations;
determine the DAA signature based on the reciprocal of the prime number; and
communicate the DAA signature to a server to prove an electronic device is a member of a group.
16. The storage medium of claim 15 , wherein the instructions, when executed by the processor, cause the processor to generate an Enhanced Privacy Identification (EPID) signature based on the reciprocal of the prime number.
17. The storage medium of claim 15 , wherein the processor-based machine comprises an Internet of Things (IoT) device.
18. The storage medium of claim 15 , wherein the instructions, when executed by the processor, cause the processor to communicate the signature to the server to provision a resource for an Internet of Things (IoT) device.