All you have to do is have the hashmap be HashMap<K,V,CryptographicKey> and never reveal the key, or seed it from randomness? One can use an HMAC or some other method to use the key to derive hashes.
Is there as HashMap overload with three type parameters? Yes, you can use a cryptographic hash function like SipHash does but it wouldn't perform has well as HashMap.
But there is a heavy multiplier on that O(1) with the default hasher in Rust. My benchmarking has shown that FNVHasher gave me a 24% decrease in execution time over the default hasher. My use case had a high likelihood of a poll on the hash indicating that there was no match, and I got a near doubling of speed just by setting the initial capacity sufficiently large.