Even if this break breaks due to the underlying models inadequately approximating the real world, we explain how AES still could contain “trapdoors” which would make cryptanalysis unexpectedly easy for anybody who knew the trapdoor. If AES’s designers had inserted such a trap door, it could be very easy for them to convince us of that. But if none exist, then it is probably infeasible difficult for them to convince us of that.
We then discuss how to use the theory of BLECCs to build cryptosystems provably
1. not containing trapdoors of this sort,
2. secure against our strengthened form of linear cryptanalysis,
3. secure against “differential”cryptanalysis,
4. secure against D.J.Bernstein’s timing attack.
Using this technique we prove a fundamental theorem: it is possible to thus-encrypt n bits with security 2^cn , via an circuit Qn containing < cn two-input logic gates and operating in < c log n gate-delays, where the three cs denote (possibly different) positive constants and Qn is constructible in polynomial(n) time. At the end we give tables of useful binary codes.