• Kyungpook Mathematical Journal
• /
• v.56 no.4
• /
• pp.1135-1140
• /
• 2016

Let A be an abelian variety over a global field K. We know [6, 7] that, in many cases, the average number of n-torsion points of A over various residue fields of K, takes the minimal possible value. In this article, we study several defect cases by calculating the number of Galois orbits.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.9
• /
• pp.4788-4813
• /
• 2019

In this paper, we introduce concepts of optimal and near optimal secret data hiding schemes. We present a new digital image steganography approach based on the Galois field $GF(p^m)$ using graph and automata to design the data hiding scheme of the general form ($k,N,{\lfloor}{\log}_2p^{mn}{\rfloor}$) for binary, gray and palette images with the given assumptions, where k, m, n, N are positive integers and p is prime, show the sufficient conditions for the existence and prove the existence of some optimal and near optimal secret data hiding schemes. These results are derived from the concept of the maximal secret data ratio of embedded bits, the module approach and the fastest optimal parity assignment method proposed by Huy et al. in 2011 and 2013. An application of the schemes to the process of hiding a finite sequence of secret data in an image is also considered. Security analyses and experimental results confirm that our approach can create steganographic schemes which achieve high efficiency in embedding capacity, visual quality, speed as well as security, which are key properties of steganography.

• Journal of Korea Multimedia Society
• /
• v.16 no.5
• /
• pp.577-590
• /
• 2013

Shamir's (k,n)-threshold secret sharing scheme is not secure against cheating by attacker because the signature of participants is omitted. To prevent cheating, many schemes have been proposed, and a proactive secret sharing is one of those. The proactive secret sharing is a method to update shares in the secret sharing scheme at irregular intervals. In this paper, a proactive image secret sharing scheme over $GF(2^8)$ is proposed for the first time. For the past 30 years, Galois field operation is widely used in order to perform the efficient and secure bit operation in cryptography, and the proposed scheme with update phase of shadow image over $GF(2^8)$) at irregular intervals provides the lossless and non-compromising of secret image. To evaluate security and efficiency of images (i.e. cover and shadow images) distortion between the proposed scheme and the previous schemes, embedding capacity and PSNR are compared in experiments. The experimental results show that the performances of the embedding capacity and image distortion ratio of the proposed scheme are superior to the previous schemes.

• Journal of Korea Multimedia Society
• /
• v.18 no.11
• /
• pp.1332-1341
• /
• 2015

This paper proposes a novel reversible secret sharing scheme using AES algorithm in encrypted images. In the proposed scheme, a role of the dealer is divided into an image provider and a data hider. The image provider encrypts the cover image with a shared secret key and sends it to the dealer. The dealer embeds the secret data into the encrypted image and transmits encrypted shadow images to the corresponding participants. We utilize Galois polynomial arithmetic operation over 2⁸ and the coefficient of the higher-order term is fixed to one in order to prevent the overflow. In experimental results, we demonstrate that the PSNR is sustained close to 44dB and the embedding capacity is 524,288 bits.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1779-1801
• /
• 2017

Let X be a minimal del Pezzo surface of degree 2 over a finite field ${\mathbb{F}}_q$. The image ${\Gamma}$ of the Galois group Gal(${\bar{\mathbb{F}}}_q/{\mathbb{F}}_q$) in the group Aut($Pic({\bar{X}})$) is a cyclic subgroup of the Weyl group W($E_7$). There are 60 conjugacy classes of cyclic subgroups in W($E_7$) and 18 of them correspond to minimal del Pezzo surfaces. In this paper we study which possibilities of these subgroups for minimal del Pezzo surfaces of degree 2 can be achieved for given q.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• v.9 no.1
• /
• pp.928-930
• /
• 2005

With an increasing importance of the information security issues, the efficienct calculation process in terms of finite field level is becoming more important in the Elliptic curve cryptosystems. Serial multiplication architectures are based on the Mastrovito's serial multiplier structure. In this paper, we manipulate the numerical expressions so that we could suggest a 3-times as fast as (3x) the Mastrovito's multiplier using the polynomial basis. The architecture was implemented with HDL, to be evaluated and verified with EDA tools. The implemented 3x GF (Galois Field) multiplier showed 3 times calculation speed as fast as the Mastrovito's, only with the additional partial-sum generation processing unit.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.23 no.3
• /
• pp.359-370
• /
• 2013

Lin and Chan proposed a reversible secret image sharing scheme in 2010. The advantages of their scheme are as follows: the low distortion ratio, high embedding capacity of shadow images and usage of the reversible. However, their scheme has some problems. First, the number of participants is limited because of modulus prime number m. Second, the overflow can be occurred by additional operations (quantized value and the result value of polynomial) in the secret sharing procedure. Finally, if the coefficient of (t-1)th degree polynomial become zero, (t-1) participants can access secret data. In this paper, an improved reversible secret image sharing scheme which solves the problems of Lin and Chan's scheme while provides the low distortion ratio and high embedding capacity is proposed. The proposed scheme solves the problems that are a limit of a total number of participants, and occurrence of overflow by new polynomial operation over GF($2^8$). Also, it solve problem that the coefficient of (t-1)th degree polynomial become zero by fixed MSB 4-bit constant. In the experimental results, PSNR of their scheme is decreased with the increase of embedding capacity. However, even if the embedding capacity increase, PSNR value of about 45dB or more is maintained uniformly in the proposed scheme.