Chik How Tan

Terry Shue Chien Lau, Chik How Tan

Rank Quasi-Cyclic Signature (RQCS) is a rank metric code-based signature scheme based on the Rank Quasi-Cyclic Syndrome Decoding (RQCSD) problem proposed by Song et al. in [2]. Their paper was accepted in the 22nd International Conference on Practice and Theory of Public Key Cryptography (PKC 2019). They have also shown that RQCS is EUF-CMA in the random oracle model. This short paper describes how to recover the secret key in RQCS with practical simulations. Our experimental results show that we are able to recover the secret key of RQCS in less than 41 seconds for all the proposed schemes at 128-bit, 192-bit and 256-bit security level.

Duc-Phong Le, Nadia El Mrabet, Safia Haloui et al.

In their seminar paper, Miyaji, Nakabayashi and Takano introduced the first method to construct families of prime-order elliptic curves with small embedding degrees, namely k = 3, 4, and 6. These curves, so-called MNT curves, were then extended by Scott and Barreto, and also Galbraith, McKee and Valenca to near prime-order curves with the same embedding degrees. In this paper, we extend the method of Scott and Barreto to introduce an explicit and simple algorithm that is able to generate all families of MNT curves with any given cofactor. Furthermore, we analyze the number of potential families of these curves that could be obtained for a given embedding degree $k$ and a cofactor h. We then discuss the generalized Pell equations that allow us to construct particular curves. Finally, we provide statistics of the near prime-order MNT curves.

Duc-Phong Le, Chik How Tan

Recently, Edwards curves have received a lot of attention in the cryptographic community due to their fast scalar multiplication algorithms. Then, many works on the application of these curves to pairing-based cryptography have been introduced. Xu and Lin (CT-RSA, 2010) presented refinements to improve the Miller algorithm that is central role compute pairings on Edwards curves. In this paper, we study further refinements to Miller algorithm. Our approach is generic, hence it allow to compute both Weil and Tate pairings on pairing-friendly Edwards curves of any embedding degree. We analyze and show that our algorithm is faster than the original Miller algorithm and the Xu-Lin's refinements.

Khoongming Khoo, Chik How Tan

This paper explores the time-memory-data trade-off attack on stream and block ciphers.