The condition number associated with ideal lattices from odd prime degree cyclic number fields

The condition number of a generator matrix of an ideal lattice derived from the ring of integers of an algebraic number field is an important quantity associated with the equivalence between two computational problems in lattice-based cryptography, the “Ring Learning With Errors (RLWE)” and the “Polynomial Learning With Errors (PLWE)”. In this work, we compute the condition number of a generator matrix of the ideal lattice from the whole ring of integers of any odd prime degree cyclic number field using canonical embedding.