| 摘要 |
In one embodiment, it is proposed a method for encrypting a plaintext M ˆˆ G , where is a DDH-hard group of prime order p . The method is executed by an electronic device, and is remarkable in that it comprises:
- obtaining a public key PK = GNghXHG where N is a RSA module, elements g, h are random elements belonging to said group G , X = g x �¢ h y ˆˆ G , where elements x, y are random values from a ring and H, G are hash functions;
- obtaining (201) two random elements r , s , each element belonging to the ring
- determining (202) a vector being ( C 0 , C 1 , C 2 ) = ( M. X r , g r , h r );
- determining (203) a proof À that log g ( C 1 ) = log h ( C 2 ), said proof comprising two components c, t', with c = H ( C 0 ,C 1 ,C 2 ,g s ,h s ) and t' = s + c. r mod p;
- delivering a ciphertext C = C 0 �¢ C 1 �¢ C 2 �¢ À = C 0 �¢ C 1 �¢ C 2 �¢ c �¢ t¹ ˆˆ G 3 × Z p 2 . |
