Cryptanalysis and improvement of Q. Peng et al.’s PVSS scheme

Abstract

A publicly verifiable secret sharing (PVSS) scheme based on the m-multilinear Diffie-Hellman hard assumption was proposed by Q. Peng et al., where the public values published by a dealer are verifiable before reconstructing a secret. In addition, the scheme has the advantages that the shares’ cheating/modification by some dishonest participants and dealer’s malicious behavior in shares’ generation and/or distribution can be detected. In this work, we cryptanalyze the scheme and find that a well-known attack called man-in-the-middle (MITM) is possible if the users’ secret shares are modified because they remain undetected and, as a result, a modified common secret is reconstructed by a group of any 1 < t ≤ n participants. We address this issue and propose some modifications of the PVSS scheme with $\left(m+1\right)$ multilinear operations and two additional public values such that the MITM attack is infeasible and the scheme becomes secure. In addition, the proposed improvement is made adeptly without hampering performance, i.e., the computation cost has been marginally increased in our proposed improvement.

Keywords:

• bilinear and multi-linear pairing
• Lagrange polynomial interpolation
• secret sharing scheme
• multilinear Diffie-Hillman hard assumption
• secret sharing scheme

Additional information

Notes on contributors

Anindya Kumar Biswas

Anindya Kumar Biswas completed his BTech in CSE, MTech in IT, and PhD at National Institute of Technology (NIT) Raipur, India, under the Ministry of Education, Govt. of India. He has published a few research articles in different reputed journals, book chapters, and conference proceedings, etc. His research interests include cryptography, information security, wireless networks, blockchain, and network security.

Mou Dasgupta

Mou Dasgupta (Senior Member, IEEE) is an Assistant Professor in the Department of Computer Application, National Institute of Technology Raipur, India. She has more than 10 years of teaching and research experience. She obtained her MTech and PhD degrees from Maulana Abul Kalam Azad University of Technology and Indian Institute of Technology (Indian School of Mines) Dhanbad, India, respectively. Her research areas includes cryptography and information security, elliptic curve cryptography, blockchain Technology, internet-of-things, underwater wireless sensor network, etc. At present, she is supervising (solely) two PhD candidates and one candidate was awarded a PhD under her sole supervision. She has published more than 50 research articles in SCI-indexed international journals, conferences of repute, book chapters, etc. and delivered more than 20 keynote lectures/expert talks in international/national conferences, workshops, seminars, faculty development programs, short-term courses, etc. Dr. Dasgupta has served as a member of advisory committees, technical committees, program committees, session chairs, etc. in several international/national conferences, seminars, workshops, etc. She is a reviewer for various international and national journals published by IEEE, Springer, Elsevier, Wiley, CSI, IETE, MDPI, Harvard, etc. She is a fellow member of IETE, senior member of IEEE, and life member of ISCA, IAENG, IACSIT and CSTA.

Sangram Ray

Sangram Ray (Senior Member, IEEE) is an Assistant Professor in the Department of Computer Science and Engineering, National Institute of Technology Sikkim, India. He has more than 13 years of teaching and research experience, and more than 8 years of administrative experience in various capacities including Dean, Head of the Department, Member of the Board of Governors, Member of Senate, Faculty In-charge Training & Placement Cell, etc. He earned his MTech and PhD from Indian Institute of Technology (Indian School of Mines) Dhanbad, India. His research areas include cryptography and information security, elliptic curve cryptography, content centric networks, internet-of-things, cyber security, blockchain technology, etc. At present, he is supervising (solely) eight PhD candidates and one post doctoral fellow. One candidate was awarded a PhD degree in the Visvesvaraya PhD Scheme, sponsored by Ministry of Electronics & IT, Govt. of India, under his sole supervision. He has published more than 50 research articles in SCI-indexed international journals, conferences of repute, book chapters, etc., and delivered around 50 keynote lectures/expert talks in international/national conferences, workshops, seminars, faculty development programs, short-term courses, etc. Dr. Ray has acted as a member of advisory committees, technical committees, program committees, session chairs, etc. in more than 100 international/national conferences, seminars, workshops, etc. He is a reviewer for around 40 international and national journals published by IEEE, Springer, Elsevier, Wiley, CSI, IETE, MDPI, Harvard, etc. He has been granted external funding of more than INR one Crore for R&D projects, FDPs, etc. Currently, he is the Chief Investigator (sole) of two R&D projects funded by the Ministry of Science and Technology, Govt. of India and the Ministry of Electronics and Information Technology, Govt. of India, respectively. He is a senior member of IEEE, member of ACM, and life member of CSI, ISTE, ISCA, IEI, IAENG, IACSIT, and CSTA.