# A Novel Dual Authenticated Encryption Scheme Suitable for Social Networking Services
## 1 Introduction  
With the rise of the Internet, people have changed their behavior models in daily life. Needless to say, there have been more and more transactions made online. The traditional telephone is no longer the only way for people to communicate with others. E-mails, chat rooms, and all kinds of instant messenger software are available and better options for free. However, the online security also raises serious concerns. The public key cryptography (PKC) [1] introduced by [PERSON] and [PERSON] in 1976 can provide several security properties such as confidentiality [2; 3], integrity, authenticity [4], and non-repudiation [5]. The cryptographic mechanisms of encryptions and digital signatures [6; 7; 8] are thus widely studied and adopted in various fields. A conventional digital signature is publicly verifiable since the verification key is the signer's public key. To further control the capability of validating a given signature, a hybrid scheme that combines an encryption mechanism and a signature one is the commonly utilized approach. The so-called authenticated encryption (AE) scheme introduced by [PERSON] et al. [9] is a representative of this approach. In such a scheme, the sender can designate an intended recipient as the only person who is able to decrypt the ciphertext and verify the corresponding signature. Later, [PERSON] [10] and [PERSON] and colleagues [11] also proposed different hybrid mechanisms called signcryption schemes, which employ the symmetric cryptographic operation to ensure confidentiality. Since these hybrid systems only grant a designated recipient the access privilege to recover the message and verify its signature, a malicious sender can easily frame the recipient, resulting in a later dispute over repudiation. To deal with this problem, several researchers came up with various solutions. [PERSON]'s work [12] adopted the technique of zero-knowledge proofs [13; 14; 15] along with a trusted tamper-resistant device. [PERSON] et al. 's literature [16] required the sender to cooperatively perform the arbitration process with the recipient and will increase extra computational burdens. [PERSON] and [PERSON] [17] and [PERSON] and [PERSON] [18] further incorporated the functionality of signature conversion into AE schemes and could be viewed as ideal methods. Yet, [PERSON] et al. [19] found out that both of their protocols fail to satisfy the semantic security. Specifically, an adversary can easily decrypt a ciphertext with only two candidate messages. Since then, many improved hybrid schemes [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32] have been proposed. In recent years, social networking services including Facebook, Line, and Skype are widely utilized by people of any age. In addition to traditional two-party communication, multi-party (especially three-party) communication is commonly seen due to the development of broadband networks. To guarantee confidentiality and authenticity in the above applications, the design of group-oriented cryptographic mechanisms becomes quite important. In 2011, [PERSON] and [PERSON] [33] introduced a new AE scheme supporting a group of signers to cooperatively deliver a designated ciphertext. Moreover, the private key of each user is updateable with unlimited time periods. In 2012, [PERSON] et al. [34] further addressed a variant by extending one designated verifier to a group of \(n\) participants. In 2014, [PERSON] [35] generalized the signing policy using a threshold value, i.e., only when the number of joined parties is equal to or greater than the threshold value, can they create a valid authenticated ciphertext. Nevertheless, most existing literatures focus on either the conventional two-party setting or the cooperative group environments. This motivates us to design a better alternative for more and more social networking services of three-party communication where each entity usually runs independent processes without cooperation.