Encryption

Sequence (biology)

NIST

Artificial intelligence

Cryptography

Mathematics

Biology

Image (mathematics)

Pseudorandom number generator

Chaotic

Computer science

Algorithm

Random number generation

Logistic map

Theoretical computer science

Lyapunov exponent

Natural language processing

Computer security

Genetics

Fuzzy logic

Entropy

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption