No fixed-construction reduction from CPA security to circular security of symmetric-key bit encryption

Conditional · against fixed-construction reductions · assuming Learning with errors · GKW17a

Statement

Under LWE, there is a semantically secure private-key bit-encryption scheme that is not 1-circular secure, so the identity map is no reduction from private-key semantic security to circular security of bit encryption — GKW17a.

Notes

• Earlier separations for bit encryption used multilinear maps or iO — GKW17a; for public-key bit encryption see No fixed-construction reduction from IND-CPA security to circular security of bit encryption — Rot13.