Are there any block-cipher modes (or symmetric encryption schemes in general) that are fully-deterministic, meaning same inputs lead to the same outputs (like for all modes with constant IV) and satisfy any notion of security?
ECB would for example accomplish the first but has no security properties at all) And more specifically: are there any schemes as described above that produce indistinguishable blocks in the presence of an eavesdropper? (This is weaker than CPA security)
I know that there exist papers for the public key setting but I could not find anything for the symmetric setting. Also, I don't need anything like 'searchable encryption', I need specifically the described properties above.
I have done research on this topic but could not find anything useful.