Six Constructions of Difference Families

In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these combinatorial objects. Most of the constructions work for all finite groups. Though these constructions look simple, they produce many difference families with new parameters. In addition to the six new constructions, new results about intersection numbers are also derived

Energy-Efficient ID-based Group Key Agreement Protocols for Wireless Networks

One useful application of wireless networks is for secure group communication, which can be achieved by running a Group Key Agreement (GKA) protocol. One well-known method of providing authentication in GKA protocols is through the use of digital signatures. Traditional certificate-based signature schemes require users to receive and verify digital certificates before verifying the signatures but this process is not required in ID-based signature schemes. In this paper, we present an energy-efficient ID-based authenticated GKA protocol and four energy-efficient ID-based authenticated dynamic protocols, namely Join, Leave, Merge and Partition protocol, to handle dynamic group membership events, which are frequent in wireless networks. We provide complexity and energy cost analysis of our protocols and show that our protocols are more energyefficient and suitable for wireless networks.

Cryptanalysis of Yasuda, Takagi and Sakurai\u27s Signature Scheme Using Invariant Subspaces

In PQCrypto 2013 Yasuda, Takagi and Sakurai proposed an interesting signature scheme of efficiency $O(n^2)$ with parameter $(q=6781, n=121)$ claimed to have 140-bit security level. Later on almost at the same time two independent and different attacks were then proposed by Y. Hashimoto in PQCrypto 2014 and by the authors in ICISC 2014. Hashimoto\u27s attack has complexity $O(n^4)$ and breaks $(q=6781, n=121)$ in several minutes. In this paper, we make an essential extension of our work in ICISC 2014. We develop for the our previous method a thorough and rigorous mathematical theory by applying intensively the theory of invariant subspaces, then work out a much better attack with complexity $O(n^4)$, and especially implement it successfully. Our new attack efficiently recovers equivalent private keys of many randomly generated instances, especially breaking $(q=6781, n=121)$ in only about 14.77 seconds, much faster than Y. Hashimoto\u27s attack. The approach developed here might have further applications

MI-T-HFE, a New Multivariate Signature Scheme

In this paper, we propose a new multivariate signature scheme named MI-T-HFE as a competitor of QUARTZ. The core map of MI-T-HFE is of an HFEv type but more importantly has a specially designed trapdoor. This special trapdoor makes MI-T-HFE have several attractive advantages over QUARTZ. First of all, the core map and the public map of MI-T-HFE are both surjective. This surjectivity property is important for signature schemes because any message should always have valid signatures; otherwise it may be troublesome to exclude those messages without valid signatures. However this property is missing for a few major signature schemes, including QUARTZ. A practical parameter set is proposed for MI-T-HFE with the same length of message and same level of security as QUARTZ, but it has smaller public key size, and is more efficient than (the underlying HFEv- of) QUARTZ with the only cost that its signature length is twice that of QUARTZ

On the Security and Key Generation of the ZHFE Encryption Scheme

At PQCrypto\u2714 Porras, Baena and Ding proposed a new interesting construction to overcome the security weakness of the HFE encryption scheme, and called their new encryption scheme ZHFE. They provided experimental evidence for the security of ZHFE, and proposed the parameter set $(q,n,D)= (7,55,105)$ with claimed security level $2^{80}$ estimated by experiment. However there is an important gap in the state-of-the-art cryptanalysis of ZHFE, i.e., a sound theoretical estimation for the security level of ZHFE is missing. In this paper we fill in this gap by computing upper bounds for the Q-Rank and for the degree of regularity of ZHFE in terms of $\log_q D$, and thus providing such a theoretical estimation. For instance the security level of ZHFE(7,55,105) can now be estimated theoretically as at least $2^{96}$. Moreover for the inefficient key generation of ZHFE, we also provide a solution to improve it significantly, making almost no computation needed

On Near Prime-Order Elliptic Curves with Small Embedding Degrees

Article published in the proceeding of the conference CAI 2015 http://www.ims.uni-stuttgart.de/events/CAI2015In this paper, we generalize the method of Scott and Barreto in order to construct a family of pairing-friendly elliptic curve. We present an explicit algorithm to obtain generalized MNT families curves with any cofactors. We also analyze the complex multiplication equations of these curves and transform them into generalized Pell equation. As an example, we describe a way to generate Edwards curves with embedding degree 6