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One of the essential security services needed to safeguard online transactions is flaxen exchange. In e-Medical transaction protocols two parties can exchange their signatures in a fair manner, so that either each party gain the other s signature or no one obtain anything useful. This Thesis examines security solutions for achieving e-Medical transactions among Patient/Doctor/PMHIP/Bank. It proposes new security protocols based on the "Rebalanced Multi-Prime Jordan-Totient RSA Cryptosystem and Signature Scheme ". This thesis concentrates on security solutions for achieving Threshold e-Medical transactions in e-Medical Health Insurance System applications, Threshold contract signing and Threshold certified delivery of valuable data. A Threshold reasonable contract signing protocol allows two potentially mistrusted parities to exchange their commitments (i.e., digital signatures) to an agreed contract over the Internet in a fair way, so that either each of them obtains the other s signature, or neither party does.