GCM-SIV1.5: Optimal Tradeoff between GCM-SIV1 and GCM-SIV2

GCM-SIV2 is a nonce-based beyond-birthday-bound (BBB)-secure authenticated encryption (AE) mode introduced by Iwata and Minematsu at FSE 2017. However, it is built by combining two instances of GCM-SIV1 and needs eight keys, which increases the costs of hardware and software implementation. This paper aims to reduce these costs by optimizing components (such as key materials, hash calls, and block cipher calls) and proposes an optimal tradeoff between GCM-SIV1 and GCM-SIV2 called GCM-SIV1.5. Moreover, we introduce the faulty nonce setting to AE and prove the BBB security of GCM-SIV1.5 with graceful security degradation in the faulty nonce setting by mirror theory. Finally, we discuss advantages of GCM-SIV1.5.