Method for authenticating payment data, corresponding devices and programs

1. A method of authenticating at least one piece of data, implemented during a payment transaction taking place between a communications terminal and a user device of the type comprising authentication by the communications terminal of at least one message m generated by the user device, by using a near field communications wireless data link, the method comprising the following acts performed by the user device:

calculating an authentication code S 1 from the message m, a piece of random data t and a hash function H;

calculating a first signature component S 2 from the message m, the random piece of data t, a public key Z of the communications terminal, a first private key x of the user device and from the authentication code S 1 ;

calculating a second signature component S 3 from the message m, the random piece of data t, the public key of Z of the communications terminal, a second private key y of the user device and from the authentication code S 1 ; and

transmitting, to the communications terminal, the authentication code S 1 and the two signature components S 2 and S 3 .

2. The method of authentication according to claim 1 , comprising the following acts performed by the communications terminal:

obtaining a first reference value denoted as U [r1] from the first signature component S 2 , a public key X of the user device, a private key z of the communications terminal and the authentication code S 1 ;

obtaining a second reference value denoted as U [r2] from the second signature component S 3 , a public key Y of the user device, the private key z, and the authentication code S 1 ; and

verifying that the first reference value U [r1] is equal to the second reference value U [r2] ;

and, when the two values are equal:

verifying that the value H(U [r2] ) and/or H(U [r1] ) is equal to S 1 ; and

issuing an assertion of authentication when the preceding verification step is positive.

3. The method of authentication according to claim 2 , comprising, for said communications terminal and prior to the communications terminal obtaining a first reference value, a phase of determining a set of encryption parameters performed by the communication terminal comprising:

obtaining a Schnorr group (G) and a generator of this group (g);

obtaining the private key (z), said private key being an element of the group G;

computing, from the private key (z), of a public key Z such that Z is an exponentiation of the generator −g by the private key z, Z=gz.

4. The method of authentication according to claim 3 , wherein:

the act of obtaining the first reference value U[r1] implements the following computation: U[r1]=s2X−zs1;

the act of obtaining the second reference value U[r2] implements the following computation: U[r2]=s3Y−zs1.

5. The method of authentication according to claim 1 , comprising, for said user device, prior to the user device obtaining an authentication code, a phase of determining a set of encryption parameters performed by the user device comprising:

obtaining a Schnorr group (G) and a generator of this group (g);

obtaining the first private key (x), said private key being an element of the group G;

obtaining the second private key (y), said private key being an element of the group G;

computing, from the first private key (x), of a public key X such that X is an exponentiation of the generator g by the private key x, X=gx;

computing, from the first private key (y), of a public key Y such that Y is an exponentiation of the generator g by the private key y, Y=gy.

6. The method of authentication according to claim 5 , wherein:

the act of obtaining the authentication code S 1 implements the following computation: S 1 =H(m∥t), where ∥ is the concatenation operator;

the act of obtaining the first signature component S 2 implements the following computation: S2=(m∥t)·Z·x·S 1 ;

the act of obtaining the second signature component S 3 implements the following computation: S 3 =(M∥t)·Z·y·S 1 .

7. A user device comprising:

a general processing unit;

a memory;

a secured processing unit;

a secured memory; and

at least one reconfigurable circuit formed by the general processing unit and the secured processing unit for processing payment transactions with a communications terminal, said reconfigurable circuit configuring the user device to perform acts comprising:

calculating an authentication code S 1 from the message m, a piece of random data t and a hash function H;

calculating a first signature component S 2 from the message m, the random piece of data t, a public key Z of the user terminal, a first private key x of the user device and the authentication code S 1 ;

calculating a second signature component S 3 from the message m, the random piece of data t, the public key Z of the communications terminal, a second private key y of the user device and the authentication code S 1 ; and

transmitting, to the communications terminal, the authentication code S 1 , and the two signature components S 2 and S 3 .

8. A non-transitory computer readable medium comprising a computer program product stored thereon which comprises program code instructions for executing a method of authenticating at least one piece of data, when the instructions are executed by a user's device during a payment transaction taking place between a communications terminal and the user device of the type comprising authentication by the communications terminal of at least one message m generated by the user device, by using a near field communications wireless data link, the method comprising the following acts performed by the user device:

calculating an authentication code S 1 from the message m, a piece of random data t and a hash function H;

calculating a first signature component S 2 from the message m, the random piece of data t, a public key Z of the communications terminal, a first private key x of the user device and the authentication code S 1 ;

calculating a second signature component S 3 from the message m, the random piece of data t, the public key of Z of the communications terminal, a second private key y of the user device and the authentication code S 1 ; and

transmitting, to the communications terminal, the authentication code S 1 and the two signature components S 2 and S 3 .