Paper 2019/157

Schnorr-based implicit certification: improving the security and efficiency of V2X communications

Paulo S. L. M. Barreto, Marcos A. Simplicio Jr., Jefferson E. Ricardini, and Harsh Kupwade Patil


In the implicit certification model, the process of verifying the validity of the signer's public key is combined with the verification of the signature itself. When compared to traditional, explicit certificates, the main advantage of the implicit approach lies in the shorter public key validation data. This property is particularly important in resource-constrained scenarios where public key validation is performed very often, which is common in vehicular communications (V2X) that employ pseudonym certificates. In this article, we show that an alternative, Schnorr-based implicit certification procedure can improve the efficiency of a popular V2X-oriented pseudonym certificate provisioning approach, the (unified) butterfly key expansion. As an additional contribution, we show that butterfly keys are vulnerable to existential forgery attacks under certain conditions, and also discuss how this issue can be fixed in an effective and efficient manner.

Note: We would also like to thank Zhaohui Cheng and Paul Bottinelli for their useful comments on an early version of this manuscript.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. Minor revision. IEEE Transactions on Computers.
Vehicular communications (V2X)implicit certificatesbutterfly key expansionsecurity
Contact author(s)
joliveira @ larc usp br
2020-04-22: last of 3 revisions
2019-02-20: received
See all versions
Short URL
Creative Commons Attribution


      author = {Paulo S.  L.  M.  Barreto and Marcos A.  Simplicio Jr. and Jefferson E.  Ricardini and Harsh Kupwade Patil},
      title = {Schnorr-based implicit certification: improving the security and efficiency of V2X communications},
      howpublished = {Cryptology ePrint Archive, Paper 2019/157},
      year = {2019},
      doi = {10.1109/TC.2020.2988637},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.