System and method for generating hash values through true-randomness quantum hash functions

A system for generating quantum hash values through true-randomness quantum hash functions, the system comprising:

• a quantum random number generator;
• a first workstation comprising a first processing unit configured to perform instructions of a first sub-system, the first workstation deriving a Borel measure as an input factor which is a continuous random variable itself, the first sub-system including:
• 1) A sample-points collection module coupled to the quantum random number generator, the quantum random number generator collecting a plurality of sample points within a configured open-set interval of a Euclidean n-space, wherein n is a configured integer which is larger than zero;
• 2) A Borel-set generator module, the Borel-set module generating available Borel sets based on a metric space composed of the collected plurality of sample points through all combinations of union operation of countable sets, intersection operation of countable sets, and complement operation of a set;
• and
• 3) A Borel-measure derivation module, the Borel-measure derivation module deriving a Borel σ-algebra based on the available Borel sets via means of transfinite induction and iteration computing and deriving a corresponding Borel measure based on the Borel σ-algebra which is derived from the available Borel sets generated by the Borel-set generator module, according to the derived Borel σ-algebra, deriving the Borel measure in a configured close-set interval, wherein the Borel measure corresponds to the derived Borel σ-algebra and making use of the derived Borel measure collaborating an operation of normalization to obtain a probability density function (PDF) where the sum of the probability of the obtained PDF is 1 in a configured close-set interval;
• a second workstation comprising a second processing unit configured to perform instructions of a second sub-system, coupled to the first sub-system, the second workstation determining an applicable quantum hash function based on the Borel measure derived from the first sub-system by leveraging Lebesgue's dominated convergence theorem to perform a validation on the PDF and once the result of the validation showing that the validated PDF fits Lebesgue's dominated convergence, determining that the validated PDF is an applicable quantum hash function and discarding duplicated quantum hash functions;
• and
• a third workstation comprising a third processing unit configured to perform instructions of a third sub-system, coupled to the second sub-system, the third workstation getting a user input value from the configured open-set interval of a Euclidean n-space and performing an operation of isomorphism mapping to switch the user input value into a form of Lebesgue measure in the configured close-set interval and then leveraging the Lebesgue measure switched from the user input value as an index parameter of the selected quantum hash table(s) for selecting one or more quantum hash tables;
• wherein if more than one applicable quantum hash functions are selected for deriving a hash table, the value generated from the former quantum hash function is made to be the input parameter of the later quantum hash function in sequence;
• so as to generate a corresponding quantum hash value;
• wherein the quantum hash value derived through hash tables derived from the quantum hash functions are determined by the second sub-system;
• wherein the first workstation and the second workstation of the system are configured to generate various applicable quantum hash functions by performing the instructions of the first sub-system and the second sub-system in sequence repeatedly;
• and
• wherein the third workstation is configured to perform the instructions of the third sub-system to provide a required quantum hash value through true-randomness quantum hash functions.