in the case where a prover a proves the validity of a pretender b to a verifier c , b receives an initial response x &# 39 ; created by a , randomizes it with a random component and sends it as x &# 34 ;, and randomizes an inquiry β from c with the random component and sends it as β &# 39 ; to a . a proves , for the received randomized inquiry β &# 39 ;, the validity of b by a secret key s randomized with a random number r and then sends it as a proved response z to b . b removes the random component from the proved response z and sends it as a &# 39 ; s proof to c for verification . b keeps secret the procedures for randomizing the initial response x &# 39 ; and the inquiry , thereby maintaining secret the correlation between a - b interactions nand b - c interactions . in the case of proving the validity of a message m of a signature client b to the verifier c by attaching a signature of a to the message m , b receives an initial response x &# 39 ; created by a and randomizes it with a random component to create a randomized response x &# 34 ;, creates a randomized inquiry β &# 39 ; containing a random component by use of the randomized response x &# 34 ; and the message m , and sends the randomized inqiury β &# 39 ; to a . a proves , for the randomized inqiury β &# 39 ;, its validity by a secret key s randomized with a random number r and then sends it as a proved response z to b . b removes the random component from the proved response z to create a derandomized response z &# 39 ;, which is sent to c for verification .