Cryptographic Limitations on Polynomial-Time a Posteriori Query Learning
We investigate the polynomial-time learnability by using examples and membership queries. Angluin and Kharitonov  proved that various concept classes (e.g., Boolean formulae, non-deterministic finite automata) are not polynomial-time learnable in this learning model based on a public-key encryption scheme with a certain security (i.e., IND-CCA1). As a stronger learning model, we consider an a posteriori query learning model, and show that it is indeed stronger than the above learning model if a one-way function exists. Nevertheless, from a secure encryption scheme, we prove that many natural classes containing Boolean formula concept class is not polynomial-time learnable even in this stronger learning model. The security of an encryption scheme used in this paper is weaker than the one used by Angluin and Kharitonov.
KeywordsComputational learning theory PAC learning Query learning Cryptography Encryption Signature
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