Method of sharing a strong secret between two parties, one of whom has little processing power

1. A method of sharing a strong secret F between two parties (A, B) who previously share a weak secret f, said method comprising the initial step of choosing a public exponent e of small size, and further comprising the following steps performed by the parties (A, B):

for A:

1. randomly drawing two prime numbers p, q, and calculating a modulus n=p*q;

2. from the modulus n and from the exponent e, building a pair of keys of an asymmetric algorithm, namely a public key K 1 =(n, e) and a private key K 2 =(n, d), where d is the private exponent corresponding to the public exponent e;

3. drawing a first random number for use as a salt S, and encrypting the modulus n using a symmetric algorithm by using a key KS derived from the weak secret f and from the salt S; and

4. concatenating the salt S and the resulting encrypted modulus n (C 0 ) and transmitting to B the resulting message M.

for B:

5. deriving the key KS from the weak secret f, and from the salt S extracted from the message M transmitted by A;

6. decrypting the modulus n as encrypted by A, by means of the symmetric algorithm and by using said key KS;

7. drawing a random number that constitutes the strong secret F; and

8. encrypting the strong secret F by means of the asymmetric algorithm and of the public key K 1 =(n, e) and communicating to A the strong secret F as encrypted; and

for A:

9. decrypting the strong secret F as transmitted encrypted by B, by means of the asymmetric algorithm, by using the private key K 2 =(n, d), so that at the end of the processing by A and by B, both of the parties A and B are in possession of the strong secret F.

2. A method according to claim 1 , wherein the asymmetric algorithm is of the Rivest, Shamir, Adelman (RSA) type.

3. A method according to claim 1 , wherein the symmetric algorithm is of the DES or AES type.

4. A method according to claim 1 , wherein instead of encrypting a modulus n=p*q, the first party A computes n1=(n−1)/2 and applies to n1 the step of encryption using the symmetric algorithm, and the party B then reconstructs the modulus n by computing n=n1*2+1.

5. A method according to claim 1 , further comprising a step of reinforcing by D bits the strength of the strong secret by using 2 D loops in the step of computing the key derived from the salt S and from the weak secret f.

6. A method according to claim 1 , wherein the party (A) is a server.

7. A method according to claim 6 , wherein the other party (B) is a party with limited computing resources.

8. A method according to claim 7 , wherein the other party (B) is a microprocessor card.

9. A method according to claim 1 , wherein the public exponent takes one of the values from among 3, 17, and 65537.

10. A method according to claim 6 , wherein the server is a mobile payment transaction server.

11. A method according to claim 8 , wherein the microprocessor card is a SIM card.