The basic security argument underlying computational cryptography is always the fact that it withstood cryptanalysis. Even when we provide `provable security`, what the proofs really show is only that the mechanism/protocol is as secure as some other assumption. The only exception is unconditional secure systems such as one-time pad, but these are usually not practical (e.g. due to key length requirements); in particular public key systems are always `only` computationally secure.
This is not really a problem and certainly not a motivation to design new systems, without a proof of security...
Best, Amir Herzberg http://amir.herzberg.name
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