Shared secret verification method and system

Method for shared secret verification e.g. to be applied in secure data exchange, in which at least two parties, hereinafter indicated as Alice and Bob, each have a secret while their challenge is to find out whether they share the same secret or not, however, without disclosing the secret itself to each other or to any third party. The method comprises the following steps. In step 1, Alice picks a random number RA, encrypts it using Bob's public key PUB, adds the value of her secret SA, and sends the result K to Bob. In step 2 Bob receives K, subtracts his secret SB, and performs a decryption using his own private key PRB. In step 3 Bob performs the one-way function H on L and sends the result M to Alice. In step 4 Alice receives M, takes her original random number RA, performs the same one-way function H and verifies whether the result equals the received M. In step 5 Alice sends her original random number RA to Bob. In step 6 Bob receives RA and verifies whether it equals to his earlier result L and concluding that, if the answer is “no”, Alice knows that Bob has the same secret and that, if the answer is “yes” Bob knows Alice doesn't have the same secret. Instead of performing the steps 6 and 7, Alice and Bob may repeat steps 1 to 5 where it is Bob who starts the exchange.