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Henry avatar Crypto

Can an adversary distinguish QROM from ROM with a single query?

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Henry

I acknowledge that QROM differs from ROM (which can be considered as a specific QROM which performs a measurement to the input). For example, one can find a preimage for an arbitrary value with $O(N)$ queries to ROM while with $O(\sqrt N)$ queries to QROM by Grover's algorithm. However, this requires more than $O(\sqrt N)$ queries. What is the case when only one query is required? More generally, is there an upperbound of the advantage of distingushing them which is related to the (polynomial) number of queries $q$?

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Daniel S avatar Crypto
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Daniel S

Only $O(1)$ queries are required to distinguish a QROM oracle from a measure-and-ROM oracle.

There is no need to perform Grover's algorithm on the whole output space. We can perform Grover on a single output bit (say the leading bit 1) and after one iteration, with overwhelming probability we will measure an input that produces an output with leading bit 1.

If on the other hand we have a fake oracle who measures input and returns classical output we will measure an input that produces an output with leading bit 0 half of the time.

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