• Journal of the Korea Society of Computer and Information
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• v.19 no.7
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• pp.71-76
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• 2014

There is to be virtually impossible to solve the very large digits of prime number p and q from composite number n=pq using integer factorization in typical public-key cryptosystems, RSA. When the public key e and the composite number n are known but the private key d remains unknown in an asymmetric-key RSA, message decryption is carried out by first obtaining ${\phi}(n)=(p-1)(q-1)=n+1-(p+q)$ and then using a reverse function of $d=e^{-1}(mod{\phi}(n))$. Integer factorization from n to p,q is most widely used to produce ${\phi}(n)$, which has been regarded as mathematically hard. Among various integer factorization methods, the most popularly used is the congruence of squares of $a^2{\equiv}b^2(mod\;n)$, a=(p+q)/2,b=(q-p)/2 which is more commonly used then n/p=q trial division. Despite the availability of a number of congruence of scares methods, however, many of the RSA numbers remain unfactorable. This paper thus proposes an algorithm that directly and immediately obtains ${\phi}(n)$. The proposed algorithm computes $2^k{\beta}_j{\equiv}2^i(mod\;n)$, $0{\leq}i{\leq}{\gamma}-1$, $k=1,2,{\ldots}$ or $2^k{\beta}_j=2{\beta}_j$ for $2^j{\equiv}{\beta}_j(mod\;n)$, $2^{{\gamma}-1}$ < n < $2^{\gamma}$, $j={\gamma}-1,{\gamma},{\gamma}+1$ to obtain the solution. It has been found to be capable of finding an arbitrarily located ${\phi}(n)$ in a range of $n-10{\lfloor}{\sqrt{n}}{\rfloor}$ < ${\phi}(n){\leq}n-2{\lfloor}{\sqrt{n}}{\rfloor}$ much more efficiently than conventional algorithms.

• Proceedings of the IEEK Conference
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• 2001.06c
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• pp.55-58
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• 2001

In this paper, we present the development of a JavaCard for public key crypto algorithms and its performance evaluation. To make a high performance for the public key crypto algorithm such as RSA and ECC on a JavaCard, we have implemented a crypto coprocessor in hardware and ported it to the card operating system and virtual machine environments. The performance of the public key crypto algorithms on the JavaCard shows that our JavaCard is suitable for If card applications which needs high performance and high level of security.

• The Journal of the Korea Contents Association
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• v.20 no.1
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• pp.356-363
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• 2020

As a becoming era of Internet-of-Things, various devices are connected via wire or wirless networks. Although every day life is more convenient, security problems are also increasing such as privacy, information leak, denial of services. Since ECC, a kind of public key cryptosystem, has a smaller key size compared to RSA, it is widely used for environmentally constrained devices. The key of ECC in constrained devices can be exposed to power analysis attacks during scalar multiplication operation. In this paper, a key-randomization method is suggested for scalar multiplication on SECG parameters. It is against differential power analysis and has operational efficiency. In order to increase of operational efficiency, the proposed method uses the property 2^lP=∓cP where the constant c is small compared to the order n of SECG parameters and n=2^l±c. The number of operation for the Coron's key-randomization scalar multiplication algorithm is 21, but the number of operation for the proposed method in this paper is (3/2)l. It has efficiency about 25% compared to the Coron's method using full random numbers.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.2
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• pp.75-83
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• 2008

Joye et al. introduced a new prime generation algorithm (JPV algorithm hereafter), by removing the trial division from the previous combined prime generation algorithm (combined algorithm hereafter) and claimed that JPV algorithm is $30{\sim}40%$ faster than the combined algorithm. However, they only compared the number of Fermat-test calls, instead of comparing the total running times of two algorithms. The reason why the total running times could not be compared is that there was no probabilistic analysis on the running time of the JPV algorithm even though there was a probabilistic analysis for the combined algorithm. In this paper, we present a probabilistic analysis on the running time of the JPV algorithm. With this analytic model, we compare the running times of the JPV algorithm and the combined algorithm. Our model predicts that JPV algorithm is slower than the combined algorithm when a 512-bit prime is generated on a Pentium 4 system. Although our prediction is contrary to the previous prediction from comparing Fermat-test calls, our prediction corresponds to the experimental results more exactly. In addition, we propose a method to improve the JPV algorithm. With this method, the JPV algorithm can be comparable to the combined algorithm with the same space requirement.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.2
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• pp.11-21
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• 2009

The NTRU cryptosystem proposed by Hoffstein et al. in 1990s is a public key cryptosystem based on hard lattice problems. NTRU has many advantages compared to other public key cryptosystems such as RSA and elliptic curve cryptosystems. For example, it guarantees high speed encryption and decryption with the same level of security, and there is no known quantum computing algorithm for speeding up attacks against NTRD. In this paper, we analyze the security of NTRU against the simple power analysis (SPA) attack and the statistical power analysis (STPA) attack such as the correlation power analysis (CPA) attack First, we implement NTRU operations using NesC on a Telos mote, and we show how to apply CPA to recover a private key from collected power traces. We also suggest countermeasures against these attacks. In order to prevent SPA, we propose to use a nonzero value to initialize the array which will store the result of a convolution operation. On the other hand, in order to prevent STPA, we propose two techniques to randomize power traces related to the same input. The first one is random ordering of the computation sequences in a convolution operation and the other is data randomization in convolution operation.

• Journal of KIISE:Computing Practices and Letters
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• v.8 no.1
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• pp.88-95
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• 2002

In recent years, the security of hardware and software systems is one of the most essential factor of our safe network community. As elliptic Curve Cryptosystems proposed by N. Koblitz and V. Miller independently in 1985, require fewer bits for the same security as the existing cryptosystems, for example RSA, there is a net reduction in cost size, and time. In this thesis, we propose an efficient hardware architecture of underlying field arithmetic processor for Elliptic Curve Cryptosystems, and a very useful method for implementing the architecture, especially multiplicative inverse operator over GF$GF (2^m)$ onto FPGA and futhermore VLSI, where the method is based on optimized unit operation components. We optimize the arithmetic processor for speed so that it has a resonable number of gates to implement. The proposed architecture could be applied to any finite field $F_{2m}$. According to the simulation result, though the number of gates are increased by a factor of 8.8, the multiplication speed We optimize the arithmetic processor for speed so that it has a resonable number of gates to implement. The proposed architecture could be applied to any finite field $F_{2m}$. According to the simulation result, though the number of gates are increased by a factor of 8.8, the multiplication speed and inversion speed has been improved 150 times, 480 times respectively compared with the thesis presented by Sarwono Sutikno et al. [7]. The designed underlying arithmetic processor can be also applied for implementing other crypto-processor and various finite field applications.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.850-853
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• 2008

As th Internet grew rapidly, the Electronic Commerce that is based on Internet increased. The Electronic Commerce is unsubstantial in the mutual authentication between the parties and a commerce As a solution to this issue, a Web server uses a Client Message technology. The purpose of Client Message is to validate the user and the electronic commercial transaction. Further, it increases efficiency and offers several ability at various purposes. However, the Client Message is transferred and stored as an unencrypted text file, the information can be exposed easily to the network threats, end system threats, and Client Message harvesting threats. In this paper designed by used crypto algorithm a Secure Message as a solution to the issue have proposed above. Further, designed a security service per Network transmitting message to transfer client's user input information to a Web server safety.