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| Protocol | Approach | Main results |
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| Lai et al. (2013) [38] | The security of the protocol is analyzed using the ProVerif tool [191] | Proof the mutual authentication between mobile equipment and its serving network |
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| Shao et al. (2016) [63] | (i) Decisional Diffie-Hellman (DDH) Assumption;
(ii) Decision Linear (DLIN) Assumption;
(iii) Extended Computational Diffie-Hellman (eCDH) Assumption
(iv) Computational Inverse Diffie-Hellman (ciCDH) Assumption | (i) The proposed group signature scheme satisfies unforgeability
(ii) The proposed group signature scheme satisfies anonymity
(iii) The proposed theorem satisfies the traceability |
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| Zhang et al. (2016) [65] | Based on the size of the beacon interval and the network bandwidth | Broadcasting the MAC of a message’s prediction outcome is secure |
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| Zhang et al. (2016) [52] | Bilinear Diffie-Hellman and the computational Diffie- Hellman assumptions | The protocol satisfies individual authentication, non-repudiation, vehicle privacy and traceability |
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| Dolev et al. (2016) [66] | Spi calculus [192] | The proposed session key establishment protocol respects the authenticity property and the secrecy property |
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| Chan and Zhou (2014) [48] | NXP-ATOP platform [193] | Demonstrate the two-factor cyber-physical device authentication |
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| Lai et al. (2013) [37] | The security of the protocol is analyzed using the ProVerif tool [191] | The scheme can implement mutual authentication and key agreement between multiple devices and the core network simultaneously |
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| Li and Cao (2011) [28] | Prove the existence of a pivot rank by contradiction | The total signing cost does not increase |
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| Li et al. (2012) [138] | Diagnose tools | Detect failure points and to minimize the whole fault time |
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| Nicanfar et al. (2014) [142] | Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | Providing mutual authentication and key management mechanisms |
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| Mahmood et al. (2016) [67] | The security of the protocol is analyzed using the ProVerif tool [191] | Verifies mutual authentication and session key secrecy properties of the proposed scheme |
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| Kumari et al. (2016) [68] | Burrows-Abadi-Needham Logic (BAN-logic) [195] | Prove that the proposed scheme establishes a session key between user and sensor node |
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| Chung et al. (2016) [69] | Burrows-Abadi-Needham Logic (BAN-logic) [195] | Prove the validity of authentication and key agreement protocol |
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| Amin and Biswas (2016) [70] | (i) Burrows-Abadi-Needham Logic (BAN-logic) [195].
(ii) Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | Prove that the protocol has achieved mutual authentication and session key agreement securely |
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| Das (2016) [72] | Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | The scheme is secure against the replay and man-in-the-middle attacks against an adversary |
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| Chang and Le (2016) [73] | Sequence of games under the decisional Diffie-Hellman (ECDDH) problem | The scheme provides secure and perfect forward secrecy authentication |
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| Jiang et al. (2016) [74] | Burrows-Abadi-Needham Logic (BAN-logic) [195] | The improved scheme accomplishes mutual authentication and key agreement between the user and sensor, the user, and the gateway node |
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| Farash et al. (2016) [75] | (i) Burrows-Abadi-Needham Logic (BAN-logic) [195]
(ii) Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | Prove that the scheme allows a user to establish a session key with a sensor node of his choice near the end of the authentication process |
|
| Srinivas et al. (2017) [144] | (i) Burrows-Abadi-Needham Logic (BAN-logic) [195]
(ii) Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | The scheme can resist numerous security attacks, which include the attacks, found in Amin and Biswas’s scheme [70] |
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| Kumari et al. (2016) [76] | Burrows-Abadi-Needham Logic (BAN-logic) [195] | The scheme provides secure mutual authentication between a legal user and an accessed sensor node inside WSN or not |
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| Jiang et al. (2017) [77] | Burrows-Abadi-Needham Logic (BAN-logic) [195] | Prove that an identity and a session key is agreed between the user and the sensor |
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| Wu et al. (2016) [146] | The security of the protocol is analyzed using the ProVerif tool [191] | The scheme passes the verifications according to the Dolev-Yao model [196] |
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| Das et al. (2016) [147] | (i) Burrows-Abadi-Needham Logic (BAN-logic) [195]
(ii) Random oracle model
(iii) Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | Prove secure mutual authentication between a legal user and an accessed sensor node |
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| Das et al. (2016) [197] | Automated Validation of Internet Security Protocols and Application (AVISPA) security analyzer [194] | The scheme is free from man-in-the-middle and replay attacks |
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