Method for exchanging a secret which can withstand quantum computer attacks, and associated computer system and computer program

Method for transporting a secret K which can withstand quantum computer attacks, said method being implemented by a computer system containing a first and a second electronic device, said first and second electronic devices each containing a processing unit which cooperates with a data memory and means of communication with the outside world, said first electronic device R being designed to receive and use the previously produced secret K encapsulated by said second electronic device S, said transport method including:

• a step of generating and publishing general parameters par of said transport method implemented by the first electronic device R;
• a step of generating a pair {sk, pk} of secret and public keys, as well as of publishing said public key produced, said step being implemented by the first electronic device R, said pair of secret and public keys {sk, pk} being produced on the basis of said general parameters par and on the basis of a first random data item produced by a random number generator of said first electronic device R;
• a step of encapsulating the secret K in the form of an encrypted C and of transmitting this latter, said step being implemented by said second electronic device S on the basis of said general parameters par, the public key pk of said first electronic device R and a second random data item produced by the random number generator of said second electronic device S;
• a step of decapsulating said secret K implemented by said first electronic device R on the basis of said encrypted C, said general parameters par and the pair {sk, pk} of secret and public keys already produced by the first electronic device R;
• said transport method being characterized in that said second random data item serves to derive a vector of n integers {right arrow over (m[n])} and in that the step of encapsulating the secret K in the form of an encrypted C and of transmitting this latter consists of implementing two sums having the same indices m1, . . . ,mn, the encrypted C consisting of a first sum such as C←{right arrow over (m[n])} and the secret K consisting of a second sum, called “mirror sum”, such as K←{right arrow over (m[n])}, {right arrow over (s[n])}, said first sum being calculated in a first algebraic structure, said second sum being calculated in a second algebraic structure and the vectors {right arrow over (v[n])} and {right arrow over (s[n])} being extracted from the public key pk of said first electronic device R.