Two-in-one oblivious signatures

Abstract

Abstract Edge computing is a kind of distributed computing as opposed to the computation in a centralized cloud environment. Oblivious signatures provide similar concept which allow a signature requester and one or multiple signer(s) to cooperatively generate a valid signature. It is a kind of digital signature with privacy protection which was first introduced by Chen in 1994. Later in 2008, Tso et. al. formally defined its security model. Previous schemes provide two different constructions for two different functionalities (ie., signer-oblivious and message-oblivious). In this paper, we firstly introduced the two-in-one oblivious signature which combines the two constructions of oblivious signatures into one scheme. In our scheme, a signature requester can ask many (say n 1 ) possible signers to sign many (say n 2 ) possible messages. At the end of the protocol, our scheme guarantees that only 1 out of the n 1 signers has signed 1 out of the n 2 messages. In addition, during the signing process, no one (including the possible signers) knows who has really signed the message as well as which one of the n 2 message has been signed. Our scheme provides signer-oblivious and message-oblivious simultaneously. Oblivious signature is useful in many edge-computing applications when authentication is required. For example, e-shopping, e-lottery and e-auction etc. We give two examples on how to construct such an oblivious signature based on the hardness of discrete logarithm assumption. The first one is based on the Schnorr signature and the other one is based on a variant type of ElGamal signature. We will give a formal model on the two-in-one oblivious signature scheme and prove the security in the random oracle model.