Post-Quantum Security of COPA

COPA is a notable authenticated online cipher and was one of the winning proposals for the CAESAR competition. Current works describe how to break the existentially unforgeable under quantum chosen message attack (EUF-qCMA) of COPA. However, these works do not demonstrate the confidentiality of COPA in the quantum setting. This paper fills this gap, considers the indistinguishable under quantum chosen-plaintext attack (IND-qCPA) security for privacy, and presents the first IND-qCPA security analysis of COPA. In addition, in order to effectively avoid the problems of quantum existential forgery attack and quantum distinguishing attack, we introduce an intermediate state doubling-point technology into COPA, restrict the associated data non-emptiness, and present an enhanced variant, called COPA-ISDP, to support the IND-qCPA and EUF-qCMA security. Our work is of great significance, as it provides a simple and effective post-quantum secure design idea to resist Simon's attack.