Paper 2024/1419 Original: eprint.iacr.org/2024/1419 ↗

On the Relationship between Public Key Primitives via Indifferentiability

Abstract

Recently, Masny and Rindal [MR19] formalized a notion called Endemic Oblivious Transfer (EOT), and they proposed a generic transformation from Non-Interactive Key Exchange (NIKE) to EOT with standalone security in the random oracle (RO) model. However, from the model level, the relationship between idealized NIKE and idealized EOT and the relationship between idealized elementary public key primitives have been rarely researched. In this work, we investigate the relationship between ideal NIKE and ideal one-round EOT, as well as the relationship between ideal public key encryption (PKE) and ideal two-round Oblivious Transfer (OT), in the indifferentiability framework proposed by Maurer et al.(MRH04). Our results are threefold: Firstly, we model ideal PKE without public key validity test, ideal one-round EOT and ideal two-round OT in the indifferentiability framework. Secondly, we show that ideal NIKE and ideal one-round EOT are equivalent, and ideal PKE without public key validity test are equivalent to ideal two-round OT. Thirdly, we show a separation between ideal two-round OT and ideal one-round EOT, which implies a separation between ideal PKE and ideal NIKE.