Choonsik Park

New Public-Key Cryptosystem Using Braid Groups

The braid groups are infinite non-commutative groups naturally arising from geometric braids. The aim of this article is twofold. One is to show that the braid groups can serve as a good source to enrich cryptography. The feature that makes the braid groups useful to cryptography includes the followings: (i) The word problem is solved via a fast algorithm which computes the canonical form which can be efficiently manipulated by computers. (ii) The group operations can be performed efficiently. (iii) The braid groups have many mathematically hard problems that can be utilized to design cryptographic primitives. The other is to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in the braid groups. The efficiency of our systems is demonstrated by their speed and information rate. The security of our systems is based on topological, combinatorial and group-theoretical problems that are intractible according to our current mathematical knowledge. The foundation of our systems is quite different from widely used cryptosystems based on number theory, but there are some similarities in design.

Optical image encryption based on XOR operations

We propose a new optical image encryption technique based on exclusive-OR (XOR) operations for a security system that controls the entrance of authorized persons. The basic idea is that we convert a gray-level image to eight bit planes for image encryption. We use the XOR operation that is commonly used such as the well-known encryption method. The input image is encrypted by performing optical xOr operations with the key bit stream that are generated by digital encryption algorithms. The gray level input image is converted to eight bit planes, which are represented on a liquid crystal device (LCD). The key data represented on different LCDs is reproduced to eight bit planes by a lenslet array. The optical XOR operations between the key data and the bit planes are performed by the polarization encoding method. The results of XOR operations, which are detected by a CCD camera, are converted to an encrypted gray-level image and the image is used as an input to the binary phase extraction joint transform correlator (BPEJTC) for comparison with reference images. We present some simulation results that verify the proposed method.

New Public Key Cryptosystem Using Finite Non Abelian Groups

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.

The Vulnerabilities Analysis of Fuzzy Vault Using Password

Fingerprint is immutable and unchangeable. Thus, if it is disclosed, owner of fingerprint cannot use his fingerprint any longer. Fuzzy vault is a cryptographic framework that makes secure template storage to bind the template with a uniformly random key. In order to keep fuzzy vault secure, various schemes are studied using special data like password. K.Nandakumar proposed a scheme for hardening a fingerprint minutiae-based fuzzy vault using password. However, that scheme has vulnerabilities against several attacks. In this paper, we analyze vulnerabilities of K.Nandakumar¿s scheme and propose a new scheme which is secure against various attacks to fuzzy vaults.

Global avalanche characteristics and propagation criterion of balanced Boolean functions

Abstract The GAC (Global Avalanche Characteristics) were introduced by Zhang and Zheng (1995) as a measure of cryptographic strength of Boolean functions. Two indicators σ ƒ and Δ ƒ related to GAC are introduced. Son et al. (1998) gave a lower bound on σ ƒ for a balanced Boolean function. In this paper, we provide an improved lower bound. Moreover, we provide bounds on nonlinearity for a balanced Boolean function satisfying the propagation criterion with respect to t vectors.

S-boxes with controllable nonlinearity

In this paper, we give some relationship between the nonlinearity of rational functions over F2n and the number of points of associated hyperelliptic curve. Using this, we get a lower bound on nonlinearity of rational-typed vector Boolean functions over F2n. While the previous works give us a lower bound on nonlinearity only for special-typed monomials, our result gives us general bound applicable for all rational fuctions defined over F2n. As an application of our results, we get a lower bound on nonlinearity of n × kn S-boxes.

On the Optimal Diffusion Layers with Practical Security against Differential and Linear Cryptanalysis

In this works we examine the diffusion layers of some block ciphers referred to as substitution-permutation networks. We investigate the practical security of these diffusion layers against differential and linear cryptanalysis by using the notion of active S-boxes. We show that the minimum number of differentially active S-boxes and that of linearly active S-boxes are generally not identical and propose some special conditions in which those are identical. Moreover, we apply our results to analyze three diffusion layers used in the block ciphers E2, CRYPTON and Rijndael, respectively. It is also shown that these all diffusion layers have achieved optimal security according to their each constraints of using operations.

An alert reasoning method for intrusion detection system using attribute oriented induction

The intrusion detection system (IDS) is used as one of the solutions against the Internet attack. However the IDS reports extremely many alerts as compared with the number of the real attack. Thus the operator suffers from burden tasks that analyze floods of alerts and identify the root cause of them. The attribute oriented induction (AOI) is a kind of clustering method. By generalizing the attributes of raw alerts, it creates several clusters that include a set of alerts having similar or the same cause. However, if the attributes are excessively abstracted, the administrator does not identify the root cause of the alert. In this paper, we describe about the over generalization problem because of the unbalanced generalization hierarchy. We also discuss the solution of the problem and propose an algorithm to solve the problem.

Y-AOI: Y-means based attribute oriented induction identifying root cause for IDSs

The attribute oriented induction (AOI) is a kind of aggregation method. By generalizing the attributes of the alert, it creates several clusters that includes a set of alerts having similar or the same cause. However, if the attributes are excessively abstracted, the administrator does not identify the root cause of the attack. In addition, deciding time interval of clustering and deciding min_size are one of the most critical problems. In this paper, we describe about the over-generalization problem because of the unbalanced generalization hierarchy and discuss the solution of the problem. We also discuss problem to decide time interval and meaningful min_size, and propose reasonable method to solve these problems.

A Note on the Higher Order Differential Attack of Block Ciphers with Two-Block Structures

We study on the security against higher order differential attack on block ciphers with two-block structure which have provable security against differential and linear cryptanalysis. The two-block structures are classified three types according to the location of round function such as C(Center)-type, R(Right)-type, and L(Left)-type. We prove that in the case of 4 rounds encryption function, these three types provide an equal strength against higher order differential attack and that in the case of 5 or more rounds, R-type is weaker than C-type and L-type. Moreover, we show that these facts also hold similarly for probabilistic higher order differential attack.