Patent ID: 8516247

Claim:
A cryptographic method using a cryptographic scheme based on cyclic groups G 1 , G 2 and G T of order p, two respective generator elements g 1 and g 2 of groups G 1 and G 2 , and a bilinear map e of G 1 ×G 2 onto G T , where p indicates a prime number, time being subdivided into successive periods of index j=0, 1, 2, and successive integers, wherein a public key has components representative of elements u and v of the group G 1 and, for each period of index j, components representative of an integer s j between 0 and p−1, of an element g 1,j of the group G 1 , and of elements g 2,j , w j and h j of the group G 2 , wherein a first secret key includes an integer γ between 0 and p−1 such that w j =g 2,j γ , g 1,0 =g 1 1/(γ+s 0 ) , g 2,0 =g 2 1/(γ+s 0 ) and, for j>0, g 1,j =g 1,j-1 1/(γ+s j ) and g 2,j =g 2,j-1 1/(γ+s j ) , wherein a second secret key includes an integer ok between 0 and p−1 such that v=u ok , wherein a third secret key includes an integer tk between 0 and p−1 such that h j =g 2,j tk , wherein a private key of a member of a signer group has a component representative of an integer x i between 0 and p−1 and, for each period of index j, a component representative of an element A i,j of the group G 1 such that A i,n =[A i,n-1 /g 1,n-1 ] 1/(x i −s n ) for any index n between 1 and j, the cryptographic method comprising a signature procedure in which said member of the signer group obtains a signature for a message during a period of index j≧0, by executing on a processor the steps of: choosing two integers α and β between 0 and p−1; calculating elements T 1 =u α and T 2 =A i,j ·v α of the group G 1 ; calculating an element S 1 =g 2,j β of the group G 2 ; calculating an element S 2 =e(A i,j , h j ) β of the group G T ; calculating, as a function of the message, proof data confirming that the elements T 1 , T 2 , S 1 and S 2 are correctly formed with knowledge of the private key of the member of the signer group for the period of index j; and including the elements T 1 , T 2 , S 1 , S 2 and the proof data in the signature of the message.