Key agreement (KA) without the use of a central authority is an elementary cryptographic problem to ensure security in MANETs because such networks consist of movable nodes with no fixed infrastructure or no central administration. The nodes communicate via wireless channels that are more prone to security attacks. A majority of the existing KA protocols assume the existence of central authority and hence, not perfectly suitable for a MANET environment. Proposed 2P-NCKA (Two-Party Non-Central authority KA) protocol creates a secret key between two users for a MANET which does not assume the use of a central authority and a prior password. It uses pairings, a verifiable secret sharing scheme and routing protocol. The AOPMDV protocol allows transmission of multiple packets across multiple node-disjoint paths in parallel so that one packet is in each path. This article also cryptanalyzes Li's KA protocol and has proven its vulnerability towards a man-in-the-middle (MITM) attack. The 2P-NCKA protocol is secure against MITM attacks and all known attacks and addresses problems of Li's protocol with a small increase in execution time.