Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Pairing-based identification schemes

We propose four different identification schemes that make use of bilinear pairings, and prove their security under certain computational assumptions. Each of the schemes is more efficient and/or more secure than any known pairing-based identification scheme

Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations

Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any finite abelian group. Their algorithm stimulated a lot of interest in the cryptography community, especially in the context of `bit security'. This manuscript attempts to be a friendly and comprehensive guide to the tools and results in this field. The intended readership is cryptographers who have heard about these tools and seek an understanding of their mechanics and their usefulness and limitations. A compact overview of the algorithm is presented with emphasis on the ideas behind it. We show how these ideas can be extended to a `modulus-switching' variant of the algorithm. We survey some applications of this algorithm, and explain that several results should be taken in the right context. In particular, we point out that some of the most important bit security problems are still open. Our original contributions include: a discussion of the limitations on the usefulness of these tools; an answer to an open question about the modular inversion hidden number problem

A New PVSS Scheme with a Simple Encryption Function

A Publicly Verifiable Secret Sharing (PVSS) scheme allows anyone to verify the validity of the shares computed and distributed by a dealer. The idea of PVSS was introduced by Stadler in [18] where he presented a PVSS scheme based on Discrete Logarithm. Later, several PVSS schemes were proposed. In [2], Behnad and Eghlidos present an interesting PVSS scheme with explicit membership and disputation processes. In this paper, we present a new PVSS having the advantage of being simpler while offering the same features.Comment: In Proceedings SCSS 2012, arXiv:1307.8029. This PVSS scheme was proposed to be used to provide a distributed Timestamping schem

Cryptography: Mathematical Advancements on Cyber Security

The origin of cryptography, the study of encoding and decoding messages, dates back to ancient times around 1900 BC. The ancient Egyptians enlisted the use of basic encryption techniques to conceal personal information. Eventually, the realm of cryptography grew to include the concealment of more important information, and cryptography quickly became the backbone of cyber security. Many companies today use encryption to protect online data, and the government even uses encryption to conceal confidential information. Mathematics played a huge role in advancing the methods of cryptography. By looking at the math behind the most basic methods to the newest methods of cryptography, one can learn how cryptography has advanced and will continue to advance