### Abstract

Manuel Ilium raised the following interesting question : suppose we are given an approximate root of an unknown polynomial with integer coefficients and a bound on the degree and maguitude of the coefficients of the polynomial. Is it possible to infer the polynomial ? we answer his question in the affirmative. We are able to show that if a complex number α satisfies an irredueible primitive polynomial p(x) off degree d with integer coefficients each of magnitude at most H then given O(d2 + d. loglI) bits off time binary expansion of the real and complex parts of , we can find p(x) in deterministic polynomial time (and then compute in polytJomlal time arty further bit of c). Using the concept o! secure pseudo random sequences formulated by Blunt, Micali and Yao we show then that the binary (oz p-ary for arty p) expansions of algebraic numbers do not, from secure sequences in a certain well delined sence.

Original language | English |
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Title of host publication | Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984 |

Publisher | Association for Computing Machinery |

Pages | 191-200 |

Number of pages | 10 |

ISBN (Electronic) | 0897911334 |

DOIs | |

Publication status | Published - Dec 1 1984 |

Event | 16th Annual ACM Symposium on Theory of Computing, STOC 1984 - Washington, United States Duration: Apr 30 1984 → May 2 1984 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Conference

Conference | 16th Annual ACM Symposium on Theory of Computing, STOC 1984 |
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Country | United States |

City | Washington |

Period | 4/30/84 → 5/2/84 |

### Fingerprint

### ASJC Scopus subject areas

- Software

### Cite this

*Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984*(pp. 191-200). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/800057.808681

**Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers.** / Kannan, R.; Lenstra, A. K.; Lovász, L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984.*Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 191-200, 16th Annual ACM Symposium on Theory of Computing, STOC 1984, Washington, United States, 4/30/84. https://doi.org/10.1145/800057.808681

}

TY - GEN

T1 - Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers

AU - Kannan, R.

AU - Lenstra, A. K.

AU - Lovász, L.

PY - 1984/12/1

Y1 - 1984/12/1

N2 - Manuel Ilium raised the following interesting question : suppose we are given an approximate root of an unknown polynomial with integer coefficients and a bound on the degree and maguitude of the coefficients of the polynomial. Is it possible to infer the polynomial ? we answer his question in the affirmative. We are able to show that if a complex number α satisfies an irredueible primitive polynomial p(x) off degree d with integer coefficients each of magnitude at most H then given O(d2 + d. loglI) bits off time binary expansion of the real and complex parts of , we can find p(x) in deterministic polynomial time (and then compute in polytJomlal time arty further bit of c). Using the concept o! secure pseudo random sequences formulated by Blunt, Micali and Yao we show then that the binary (oz p-ary for arty p) expansions of algebraic numbers do not, from secure sequences in a certain well delined sence.

AB - Manuel Ilium raised the following interesting question : suppose we are given an approximate root of an unknown polynomial with integer coefficients and a bound on the degree and maguitude of the coefficients of the polynomial. Is it possible to infer the polynomial ? we answer his question in the affirmative. We are able to show that if a complex number α satisfies an irredueible primitive polynomial p(x) off degree d with integer coefficients each of magnitude at most H then given O(d2 + d. loglI) bits off time binary expansion of the real and complex parts of , we can find p(x) in deterministic polynomial time (and then compute in polytJomlal time arty further bit of c). Using the concept o! secure pseudo random sequences formulated by Blunt, Micali and Yao we show then that the binary (oz p-ary for arty p) expansions of algebraic numbers do not, from secure sequences in a certain well delined sence.

UR - http://www.scopus.com/inward/record.url?scp=77953531723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953531723&partnerID=8YFLogxK

U2 - 10.1145/800057.808681

DO - 10.1145/800057.808681

M3 - Conference contribution

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 191

EP - 200

BT - Proceedings of the 16th Annual ACM Symposium on Theory of Computing, STOC 1984

PB - Association for Computing Machinery

ER -