TY - GEN

T1 - Applications of two-faced processes to random number generation

AU - Ryabko, Boris

AU - Savina, Nadezhda

PY - 2016/12/9

Y1 - 2016/12/9

N2 - Random and pseudorandom number generators (RNG and PRNG) are used for many purposes including cryptographic, modeling and simulation applications. For such applications a generated bit sequence should mimic true random, i.e., by definition, such a sequence could be interpreted as the result of the flips of a fair coin with sides that are labeled 0 and 1 (i.e., it is the Bernoulli process with p(0) = p(1) = 1/2). It is known that the Shannon entropy of this process is 1 per letter, whereas for any other stationary process with binary alphabet the Shannon entopy is stricly less than 1. On the other hand, the entropy of the PRNG output should be much less than 1 bit (per letter), but the output sequence should look like truly random. We describe random processes for which these, contradictory at first glance, properties, are valid. More precisely, it is shown that there exist binary-alphabet random processes whose entropy is less than 1 bit (per letter), but the frequency of occurrence of any word u goes to 2-u, where u is the length of u. In turn, it gives a possibility to construct RNG and PRNG which possess theoretical guarantees. This possibility is important for applications such as those in cryptography. We performed some experiments in which low-entropy sequences are transformed into two-faced sequences.

AB - Random and pseudorandom number generators (RNG and PRNG) are used for many purposes including cryptographic, modeling and simulation applications. For such applications a generated bit sequence should mimic true random, i.e., by definition, such a sequence could be interpreted as the result of the flips of a fair coin with sides that are labeled 0 and 1 (i.e., it is the Bernoulli process with p(0) = p(1) = 1/2). It is known that the Shannon entropy of this process is 1 per letter, whereas for any other stationary process with binary alphabet the Shannon entopy is stricly less than 1. On the other hand, the entropy of the PRNG output should be much less than 1 bit (per letter), but the output sequence should look like truly random. We describe random processes for which these, contradictory at first glance, properties, are valid. More precisely, it is shown that there exist binary-alphabet random processes whose entropy is less than 1 bit (per letter), but the frequency of occurrence of any word u goes to 2-u, where u is the length of u. In turn, it gives a possibility to construct RNG and PRNG which possess theoretical guarantees. This possibility is important for applications such as those in cryptography. We performed some experiments in which low-entropy sequences are transformed into two-faced sequences.

UR - http://www.scopus.com/inward/record.url?scp=85013743161&partnerID=8YFLogxK

U2 - 10.1109/RED.2016.7779347

DO - 10.1109/RED.2016.7779347

M3 - Conference contribution

AN - SCOPUS:85013743161

T3 - 2016 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016

SP - 132

EP - 136

BT - 2016 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016

Y2 - 26 September 2016 through 29 September 2016

ER -