Device authentication

A method for determining whether a first device possesses a value h, the method to be performed by a second device that possesses the value h, the method comprising:

• receiving from a third device a product RD that was received by the third device from the first device, wherein RD is a product of a random value rD and a public key value P;
• generating a product RB and transmitting the product RB to the third device, wherein RB is a product of a random value rB and the public key value P;
• obtaining a challenge value eD and transmitting the challenge value eD to the third device;
• receiving from the third device a value yD that was received by the third device from the first device;
• receiving from the third device a challenge value eB that was received by the third device from the first device;
• calculating yDP+eDRD to obtain a first result;
• calculating hP to obtain a second result;
• comparing the first result to the second result;
• and
• determining that the first device is in possession of the value h when the first result is identical to the second result,
• wherein the public key value P generates a prime subgroup of the group E(Fq) of order p, wherein Fq is a finite field of prime order q, wherein the random values rD and rB are between the number 1 and the number (p−1), and wherein the challenge values eD and eB are between the number 1 and the number (p−1).

A program product comprising a computer readable non-transitory storage medium having executable program code stored in said medium, the executable program code being operative, when executed, to cause a first device that is in possession of a value h:

• to generate a product RD and to transmit the product RD to a third device, wherein RD is a product of a random value rD and a public key value P;
• to receive from the third device a challenge value eD that was received by the third device from a second device;
• to receive from the third device a product RB that was received by the third device from the second device, wherein RB is a product of a random value rB and the public key value P;
• to obtain a challenge value eB and to transmit the challenge value eB to the third device;
• to receive from the third device a value yB that was received by the third device from the second device;
• to calculate yBP+eBRB to obtain a first result;
• to calculate hP to obtain a second result;
• to compare the first result to the second result;
• and
• to determine that the second device is in possession of the value h when the first result is identical to the second result
• wherein the public key value P generates a prime subgroup of the group E(Fq) of order p, wherein Fq is a finite field of prime order q, wherein the random values rD and rB are between the number 1 and the number (p−1), and wherein the challenge values eD and eB are between the number 1 and the number (p−1).

A program product comprising a computer readable non-transitory storage medium having executable program code stored in said medium, the executable program code being operative, when executed, to cause a second device that is in possession of a value h:

• to receive from a third device a product RD that was received by the third device from a first device, wherein RD is a product of a random value rD and a public key value P;
• to generate a product RB and to transmit the product RB to the third device, wherein RB is a product of a random value rB and the public key value P;
• to obtain a challenge value eD and to transmit the challenge value eD to the third device;
• to receive from the third device a value yD that was received by the third device from the first device;
• to receive from the third device a challenge value eB that was received by the third device from the first device;
• to calculate yDP+eDRD to obtain a first result;
• to calculate hP to obtain a second result;
• to compare the first result to the second result;
• and
• to determine that the first device is in possession of the value h when the first result is identical to the second result,
• wherein the public key value P generates a prime subgroup of the group E(Fq) of order p, wherein Fq is a finite field of prime order q, wherein the random values rD and RB are between the number 1 and the number (p−1), and wherein the challenge values eD and eB are between the number 1 and the number (p−1).

A first device adapted:

• to possess a value h;
• to generate a product RD and to transmit the product RD to a third device, wherein RD is a product of a random value rD and a public key value P;
• to receive from the third device a challenge value eD that was received by the third device from a second device;
• to receive from the third device a product RB that was received by the third device from the second device, wherein RB is a product of a random value rB and the public key value P;
• to obtain a challenge value eB and to transmit the challenge value eB to the third device;
• to receive from the third device a value yB that was received by the third device from the second device;
• to calculate yBP+eBRB to obtain a first result;
• to calculate hP to obtain a second result;
• to compare the first result to the second result;
• and
• to determine that the second device is in possession of the value h when the first result is identical to the second result
• wherein the public key value P generates a prime subgroup of the group E(Fq) of order p, wherein Fq is a finite field of prime order q, wherein the random values rD and rB are between the number 1 and the number (p−1), and wherein the challenge values eD and eB are between the number 1 and the number (p−1).

A second device adapted:

• to possess a value h;
• to receive from a third device a product RD that was received by the third device from a first device, wherein RD is a product of a random value rD and a public key value P;
• to generate a product RB and to transmit the product RB to the third device, wherein RB is a product of a random value rB and the public key value P;
• to obtain a challenge value eD and to transmit the challenge value eD to the third device;
• to receive from the third device a value yD that was received by the third device from the first device;
• to receive from the third device a challenge value eB that was received by the third device from the first device;
• to calculate yDP+eDRD to obtain a first result;
• to calculate hP to obtain a second result;
• to compare the first result to the second result;
• and
• to determine that the first device is in possession of the value h when the first result is identical to the second result,
• wherein the public key value P generates a prime subgroup of the group E(Fq) of order p, wherein Fq is a finite field of prime order q, wherein the random values rD and rB are between the number 1 and the number (p−1), and wherein the challenge values eD and eB are between the number 1 and the number (p−1).