Abstract: Using the present cryptographic key exchange protocol, a first of two cryptographic units selects quantities "A" and "B." That same unit then applies a mathematical function ".PHI..sub.1 " to A and B to compute a third quantity "C.". A and B and the function .PHI..sub.1 posses the property that knowing A or B, and C, and the function .PHI..sub.1, it is mathematically impossible to compute the unknown quantity B or A. The first unit then transmits A together C to the second unit while retaining B. The second unit selects a fourth quantity "D" and then applies a second mathematical function .PHI..sub.2 to A and D to compute a quantity "E" which the second unit transmits to the first unit while retaining D. The quantities A and D and the function .PHI..sub.2 must posses the property that knowing D and E, and the function .PHI..sub.2, it is mathematically impossible to compute the unknown quantity D. Then the second unit applies a third mathematical function ".PSI..sub.2 " to D and C to compute the key "K.