The Internet of Things (IoT) provides transparent and seamless incorporation of heterogeneous and different end systems. It has been widely used in many applications including smart cities such as public water system, power grid, water management, and vehicle traffic control system. In these smart city applications, a large number of IoT devices are deployed that can sense, communicate, compute, and potentially actuate. The uninterrupted and accurate functioning of these devices are critical to smart city applications as crucial decisions will be made based on the data received. One of the challenging tasks is to assure the authenticity of the devices so that we can rely on the decision making process with a very high confidence. One of the characteristics of IoT devices deployed in such applications is that they have limited battery power. A challenge is to design a secure mutual authentication protocol which is affordable to resource constrained devices. In this paper, we propose a lightweight mutual authentication protocol based on a novel public key encryption scheme for smart city applications. The proposed protocol takes a balance between the efficiency and communication cost without sacrificing the security. We evaluate the performance of our protocol in software and hardware environments. On the same security level, our protocol performance is significantly better than existing RSA and ECC based protocols. We also provide security analysis of the proposed encryption scheme and the mutual authentication protocol.

Lightweight Mutual Authentication for IoT and Its Applications

Braid-based cryptography

We propose the first polynomial time algorithm for the braid Diffie-Hellman conjugacy problem (DHCP) on which the braid key exchange scheme and the braid encryption scheme are based [9]. We show the proposed method solves the DHCP for the image of braids under the Lawrence-Krammer representation and the solutions play the equivalent role of the original key for the DHCP of braids. Given a braid index n and a canonical length l, the complexity is about O(n 14.4 l 3.2) or O(n 4τ + 2e l 2e ) bit operations for τ = log2 7 ≈ 2.8 and e> log2 3 ≈ 1.57.

/pdf/a-polynomial-time-algorithm-for-the-braid-diffie-hellman-1yftraz9or.pdf

A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem

Most public key cryptosystems have been constructed based on abelian groups up to now. We propose a new public key cryptosystem built on finite non abelian groups in this paper. It is convertible to a scheme in which the encryption and decryption are much faster than other well-known public key cryptosystems, even without no message expansion. Furthermore a signature scheme can be easily derived from it, while it is difficult to find a signature scheme using a non abelian group.

New public key cryptosystem using finite non Abelian groups

A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem.

We propose a new digital signature scheme based on a non-commutative group where the conjugacy search problem is hard and the conjugacy decision problem is feasible. We implement our signature scheme in the braid groups and prove that an existential forgery of the implementation under no message attack gives a solution to a variation of conjugacy search problem. Then we discuss performance of our scheme under suggested parameters.

/pdf/new-signature-scheme-using-conjugacy-problem-21eq5ej0ks.pdf

New Signature Scheme Using Conjugacy Problem.

A graph class $\mathcal{G}$ has the strong Erd\H{o}s-Hajnal property (SEH-property) if there is a constant $c=c(\mathcal{G})>0$ such that for every member $G$ of $\mathcal{G}$, either $G$ or its complement has $K_{m, m}$ as a subgraph where $m \geq \left\lfloor c|V(G)|\right\rfloor$. We prove that the class of chordal graphs satisfy SEH-property with constant $c = 2/9$. On the other hand, a strengthening of SEH-property which we call the colorful Erd\H{o}s-Hajnal property was discussed in geometric settings by Alon et al. (2005) and by Fox et al. (2012). Inspired by their results, we show that for every pair $F_1, F_2$ of subtree families of the same size in a tree $T$ with $k$ leaves, there exists subfamilies $F'_1 \subseteq F_1$ and $F'_2 \subseteq F_2$ of size $\theta \left( \frac{\ln k}{k} \left| F_1 \right|\right)$ such that either every pair of representatives from distinct subfamilies intersect or every such pair do not intersect. Our results are asymptotically optimal.

Strong Erd\H{o}s-Hajnal properties in chordal graphs

A stacked $d$-sphere $S$ is the boundary complex of a stacked $(d+1)$-ball, which is obtained by taking cone over a free $d$-face repeatedly from a $(d+1)$-simplex. A stacked sphere $S$ is called linear if every cone is taken over a face added in the previous step. In this paper, we study the transversal number of facets of stacked $d$-spheres, denoted by $\tau(S)$, which is the minimum number of vertices intersecting with all facets. Briggs, Dobbins and Lee showed that the transversal ratio of a stacked $d$-sphere is bounded above by $\frac{2}{d+2}+o(1)$ and can be as large as $\frac{2}{d+3}$. We improve the lower bound by constructing linear stacked $d$-spheres with transversal ratio $\frac{6}{3d+8}$ and general stacked $d$-spheres with transversal ratio $\frac{2d+3}{(d+2)^2}$. Finally, we show that $\frac{6}{3d+8}$ is optimal for linear stacked $2$-spheres, that is, the transversal ratio is at most $\frac{3}{7} + o(1)$ for linear stacked $2$-spheres.

Mi Sung Cho

Papers

New Signature Scheme Using Conjugacy Problem.

Strong Erd\H{o}s-Hajnal properties in chordal graphs

Transversal numbers of stacked spheres