Abstract: A method (and structure) for a party (the prover) to prove its knowledge, jointly and non-malleably, of multiple secret (fixed and/or ephemeral) Diffie-Hellman exponents (DH-exponents), corresponding to its public (fixed and/or ephemeral) DH-components and with respect to the public (fixed and/or ephemeral) challenging DH-components from another party (the verifier). The joint proof-of-knowledge (JPOK) consists of secrets made by multiplying multiple DH-secrets, which can be generated and verified by each party by its own secret DH-exponents and the public DH-components of both parties. To ensure the non-malleability of the JPOK, the method makes all these multiplied DH-secrets to be independent, and makes the session-tag committed to the multiplied DH-secrets. In addition, the invented method makes the DH-secrets to be multiplied to further satisfy at least one of the following: (1) deniability; (2) pre-computability; and (3) post-ID computability.