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During an insertion, the bits that are indexed by the hash functions are set to 1.
When the security data are stored in the secure zone, the hash value of each file is generated by the hash functions and the information of the file data, including the hash value, is recorded in the file metadata.
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The HyperLogLog algorithm is said to be probabilistic because it uses some randomness introduced by the hash function h.
If the algorithm A cannot get a, then it is hard to find x = a such that H x) = H(a) and x ≠ a such that H x) = H(a) by the hash function assumption (ii).
It can be seen from the results in Table 5 that the entropy of the random numbers generated by the hash function is very close to the ideal value (7.999994 ≈ 8) and that the serial correlation coefficient in the same table is very close to zero, which demonstrates the collision resistance nature of the algorithm.
(6) Hash Subsystem The value w q produced by the hash function is h (w q ).
During membership queries, the membership of an element in the bloom filter is confirmed if all of the bits indexed by all of the hash functions are 1.
If there are r requests to a subchannel, the probability that a certain bit is not set to 1 is by any of the hash functions is given as P negative r = ( 1 − P positive 1 ) r. Similarly, the probability that the bit is set to 1 is P positive r = 1 − ( 1 − P positive 1 ) r.
A third party auditing protocol was introduced to keep online storage secure by encrypting the data before applying the hash functions using the symmetric-keys [25].
This also works, when reverting the whole database to an old state: The PRNG is seeded with a seed unknown to the attacker, every iteration changes the state of the PRNG, which cannot be calculated backwards (this is ensured by the criteria for the hash function and the PRNG in [18]).
Exactly similar strings are be accepted by the hashing function.
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