Abstract
Automated methods can be used to generate cryptosystems by combining the primitives in an arbitrary fashion, to weed out insecure cryptosystems, and to prove the security of those that survive. In this paper, we study several algorithmic problems arising from the verification of automatically synthesized cryptosystems built from block ciphers, in a theory that includes ACUN. One of these is static equivalence to an algorithm that produces a sequence of random terms. The other is invertibility, the problem of determining whether, given an automatically synthesized cryptosystem, built from block ciphers, and the ability to compute inverses, is it always possible to compute the original plaintext from the ciphertext? We show that static equivalence to random in this theory is undecidable in general. In addition, we identify a reasonable special case for which there is a decidable condition implying security, along with an algorithm for verifying it. For invertibility, we identify a reasonable class of cryptosystems for which invertibility is equivalent to a simple syntactic condition that can be easily verified.
This work was funded by ONR Code 311. The work of Lin, Lynch, Marshall, Narendran, Ravishankar, and Rozek, was funded via NRL grant number N00173-19-1-G012.
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Lin, H. et al. (2021). Algorithmic Problems in the Symbolic Approach to the Verification of Automatically Synthesized Cryptosystems. In: Konev, B., Reger, G. (eds) Frontiers of Combining Systems. FroCoS 2021. Lecture Notes in Computer Science(), vol 12941. Springer, Cham. https://doi.org/10.1007/978-3-030-86205-3_14
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