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Does there exist a system wherein the encryption key/algorithm can be made indecipherable despite making arbitrarily many plaintext and ciphertext pairs available to the cracker? (Does this qualify as KPA attack security? ) If so, how strong is such a system, what kind of key and algorithms should be used?

What minimum size should the keyspace be to ensure recovering key from the known plaintext-ciphertext pairs is not efficient? Are there any known attacks which can recover key faster than a brute-force attack?

Soham
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    No. If everything fails an attacker can just query the algorithm for every possible input and make a giant table of all input-output mappings. (This is not practical of course...) – SEJPM Feb 26 '17 at 16:38
  • That's an answer? – Maarten Bodewes Feb 26 '17 at 21:33
  • How would the attacker know the algorithm? He'd just see the plaintext and ciphertext. – Soham Feb 27 '17 at 02:24
  • We assume that the attacker knows the algorithm due to Kerckhoffs principle. As we're talking about impractical anyway, an attacker could simply try all known algorithms. This should work unless the algorithm acts as a secret itself (but again, this is not how modern cryptography is supposed to work, according to the principle). – Maarten Bodewes Feb 28 '17 at 13:54

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