Compute the automorphism index for a single slot index

Maps a CKKS slot index to the corresponding automorphism index in the cyclotomic ring Z[X]/(X^N + 1). The automorphism group of the ring is isomorphic to the multiplicative group (Z/2N)*; this function returns the representative of that group that corresponds to rotating the plaintext slots by the given amount.

Usage

find_automorphism_index(cc, index)

Arguments

cc

A CryptoContext.

index

Integer; the slot index (positive = left rotation, negative = right rotation).

Value

Integer; the automorphism group element corresponding to that rotation.

Details

Used as a primitive by find_automorphism_indices() and by code that needs to address automorphism keys directly (for example, selectively generating eval keys for a sparse set of rotation amounts).

R-first binding: openfhe-python does not bind FindAutomorphismIndex. Logged in notes/upstream-defects.md under R-only surface.

See also

find_automorphism_indices() for the vector form.