SEEDLESS RANDOMNESS EXTRACTORS FOR DEVICE-INDEPENDENT QUANTUM CRYPTOGRAPHY
Systems and methods are for seedless generation of random bit strings are disclosed. A System generates a secret key from a raw key received from a quantum source of randomness using a seedless randomness extractor that generates the secret key by applying a deterministic function on the raw key to transform the partially random raw bits into a near uniformly random output random bit string without using a seed random bit string. The system determines a Bell value quantifying violation of a Bell inequality by the raw bits. A distance between the secret key and a uniform random distribution is limited by an upper bound at least partially dependent on the determined Bell value.
1 . A system for generating an output random bit string, the system comprising:
a non-transitory memory storing machine-readable instructions, and
an electronic processor configured to execute the machine-readable instructions to:
receive from a single source of randomness an input random bit string;
determine a Bell value indicative of a magnitude of violation of a Bell inequality by at least a portion of bits in the input random bit string; and
generate the output random bit string using the input random bit string based at least in part on the Bell value;
wherein the output random bit string is generated by a deterministic output generation process.
2 . The system of claim 1 , wherein an error quantifying a difference between the output random bit string and a perfect random distribution is limited by an upper bound dependent on the Bell value.
3 . The system of claim 1 , wherein the Bell value is used as an input to a deterministic extraction process to generate the output random bit string.
4 . The system of claim 3 , the deterministic output generation process comprises a deterministic function.
5 . The system of claim 4 , wherein the electronic processor executes the machine-readable instructions to generate the output random bit string by applying the deterministic function on the input random bit string.
6 . The system of claim 5 , wherein the electronic processor is configured to select the deterministic function from a plurality of deterministic functions based at least in part on the Bell value.
7 . The system of claim 4 , wherein the deterministic function is selected from a group consisting of a linear function, an XOR function, or a generator of an error-correction code.
8 . The system of claim 1 , wherein the electronic processor is configured to determine at least one output random bit string parameter based at least in part on the Bell value, the output random bit string parameter comprising a length of the output random bit string, an extraction efficiency, or an error bound, and to generate the output random bit string in accordance with the determined output random bit string parameter.
9 . The system of any one of claim 1 , wherein the electronic processor is configured to execute machine-readable instructions to determine that the Bell value is larger than a threshold value and in response to determining that the Bell value is larger than the threshold value, the electronic processor generates the output random bit string.
10 . The system of any one of claim 1 , wherein the Bell value comprises an expectation value of product of a plurality of operators associated with the Bell inequality.
11 . The system of any one of claim 1 , wherein the Bell inequality comprises the Clauser-Horne-Shimony-Holt inequality.
12 . The system of any one of claim 1 , wherein the electronic processor executes the machine-readable instructions to extract the output random bit string from the input random bit string without using a seed random bit string.
13 . The system of claim 1 , wherein the output random bit string is secure against an adversary having unbounded computational power.
14 . The system of claim 13 , wherein the adversary is a quantum adversary.
15 . The system of claim 13 , wherein the adversary is a classical adversary.
16 . The system of claim 1 , wherein the output random bit string is closer to a perfectly random distribution than the input random bit string.
17 . The system of claim 1 , wherein the electronic processor is further configured to execute machine-readable instructions to generate the output random bit string based on an output criterion stored in a memory of the system or provided by a user.
18 . The system of claim 17 , wherein the output criterion comprises a length of the output random bit string.
19 . The system of claim 17 , wherein the output criterion comprises an error quantifying a difference between the randomness of the output random bit string and a perfectly random distribution.
20 . The system of claim 17 , wherein the output criterion comprises an extraction efficiency quantifying a ratio between length of the output random bit string and a portion of the input random bit string used to generate the output random bit string.