Asymmetry -- The Cryptographic Game Changer

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In the 1970s cryptography experienced a dramatic creative insight: asymmetry

For centuries the decryption key was a symmetric version of the encryption key, no one asked: is this necessarily so? After all, all that is needed is for the decryption process to convert the ciphertext back to the plaintext, whether it is done by a symmetric key, or not, does not matter!

It turned out that to find the mathematics to support an encryption key Ke, to be different from the corresponding decryption key, Kd (Ke =/= Kd) is quite simple.

Only that in most of these cases it was very easy to use the knowledge of one of the keys in order to compute the other. This is reasonable, since, while these keys are different, they are closely related; after all, one undoes the action of the other.

It turned out that such a "mutually derivable key" situation is functionally equivalent to symmetry. The explosive usage and dramatic capability asymmetry offers us today, has only come to be once we found the mathematics that would break the mutual derivability between the encryption and decryption key .

Ke and Kd are mathematically linked by the requirement for one to undo the other, and hence it is impossible to find mathematics that would prevent the derivation of one from the other , which means that asymmetry will work only if we find mathematics that would make it sufficiently difficult (intractable) to derive one from the other. So difficult that by the time our adversary will do so, it would be too late.

And here lies the problem: how can we tell how difficult is it for our adversary to accomplish a certain computational task? We have to know what computing machinery he has, and we have to know how much imagination she has to devise efficient computational methods. It would be quite difficult to know the former, and virtually impossible to know the latter. Which means -- whatever great capabilities are offered by asymmetry -- they all come with a grain of salt: what does our adversary know, and when did she know it??!!

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