## Abstract

Frobenius expansions are representations of integers to an algebraic base which are sometimes useful for efficient (hyper)elliptic curve cryptography. The normal form of a Frobenius expansion is the polynomial with integer coefficients obtained by reducing a Frobenius expansion modulo the characteristic polynomial of Frobenius. We consider the distribution of the coefficients of reductions of Frobenius expansions and non-adjacent forms of Frobenius expansions (NAFs) to normal form. We give asymptotic bounds on the coefficients which improve on naive bounds, for both genus one and genus two. We also discuss the non-uniformity of the distribution of the coefficients (assuming a uniform distribution for Frobenius expansions).

Original language | English |
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Pages (from-to) | 71-89 |

Number of pages | 19 |

Journal | Designs, Codes, and Cryptography |

Volume | 61 |

Issue number | 1 |

DOIs | |

State | Published - Oct 2011 |

Externally published | Yes |

## Keywords

- Elliptic curves
- Frobenius expansions
- Hyperelliptic curves

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Applied Mathematics