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On Higher-Order Cryptography

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Abstract

Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes themselves higher-order? This paper gives an answer to this question, by first describing why higher-order cryptography is interesting as an object of study, then showing how the concept of probabilistic polynomial time algorithm can be generalized so as to encompass algorithms of order strictly higher than two, and finally proving some positive and negative results about the existence of higher-order cryptographic primitives, namely authentication schemes and pseudorandom functions.
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Dates and versions

hal-03120781 , version 1 (25-01-2021)

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Boaz Barak, Raphaëlle Crubillé, Ugo Dal Lago. On Higher-Order Cryptography. ICALP 2020 - 47th International Colloquium on Automata, Languages, and Programming, Jul 2020, Saarbrucken, Germany. ⟨10.4230/LIPIcs.ICALP.2020.108⟩. ⟨hal-03120781⟩
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