# Enhanced pseudorandom number generator based on Blum-Blum-Shub and elliptic curves

Title | Enhanced pseudorandom number generator based on Blum-Blum-Shub and elliptic curves |

Publication Type | Conference Paper |

Year of Publication | 2018 |

Authors | Omorog, C. D., Gerardo, B. D., Medina, R. P. |

Conference Name | 2018 IEEE Symposium on Computer Applications Industrial Electronics (ISCAIE) |

Date Published | apr |

ISBN Number | 978-1-5386-3527-8 |

Keywords | BBS-ECPRNG approach, Blum-Blum-Shub, complex pseudorandom number generator, cryptographically secure bits, Curve fitting, Elliptic curve cryptography, elliptic curve point operations, elliptic curve points, Elliptic curves, enhanced pseudorandom number generator, Galois fields, Generators, Mathematical model, Metrics, NIST statistical test suite, pseudorandom number generator, pubcrawl, public key cryptography, random number generation, random processes, randomness, randomness tests, Resiliency, Scalability, squaring operation, statistical testing, Urban areas |

Abstract | Blum-Blum-Shub (BBS) is a less complex pseudorandom number generator (PRNG) that requires very large modulus and a squaring operation for the generation of each bit, which makes it computationally heavy and slow. On the other hand, the concept of elliptic curve (EC) point operations has been extended to PRNGs that prove to have good randomness properties and reduced latency, but exhibit dependence on the secrecy of point P. Given these pros and cons, this paper proposes a new BBS-ECPRNG approach such that the modulus is the product of two elliptic curve points, both primes of length, and the number of bits extracted per iteration is by binary fraction. We evaluate the algorithm performance by generating 1000 distinct sequences of 106bits each. The results were analyzed based on the overall performance of the sequences using the NIST standard statistical test suite. The average performance of the sequences was observed to be above the minimum confidence level of 99.7 percent and successfully passed all the statistical properties of randomness tests. |

URL | https://ieeexplore.ieee.org/document/8405483 |

DOI | 10.1109/ISCAIE.2018.8405483 |

Citation Key | omorog_enhanced_2018 |

- BBS-ECPRNG approach
- Blum-Blum-Shub
- complex pseudorandom number generator
- cryptographically secure bits
- Curve fitting
- Elliptic curve cryptography
- elliptic curve point operations
- elliptic curve points
- Elliptic curves
- enhanced pseudorandom number generator
- Galois fields
- Generators
- Mathematical model
- Metrics
- NIST statistical test suite
- pseudorandom number generator
- pubcrawl
- public key cryptography
- random number generation
- random processes
- randomness
- randomness tests
- Resiliency
- Scalability
- squaring operation
- statistical testing
- Urban areas