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Secure message transmission is of extreme importance in today's information-based society: military, diplomatic, and corporate data transmissions must be safeguarded; so also must the account of every individual who has an automatic-teller bank account or whose purchases are subject to point-of-sale, direct account debiting. The only known way to keep all such transactions secret and authentic is by way of cryptographic techniques. But most cryptosystems in use today are not fool-proof-- their "symmetric" nature allows them to be compromised if either the sender's or the receiver's "key" (decoding algorithm) falls into the wrong hands. This book reports on the enormous amount of work that has been done in the past on the concept, "asymmetric" cryptography.