Using random search and brute force algorithm in factoring the RSA modulus

Abstract. The security of the RSA cryptosystem is directly proportional to the size of its modulus, n. The modulus n is a multiplication of two very large prime numbers, notated as p and q. Since modulus n is public, a cryptanalyst can use factorization algorithms such as Euler’s and Pollard’s algorithms to derive the private keys, p and q. Brute force is an algorithm that searches a solution to a problem by generating all the possible candidate solutions and testing those candidates one by one in order to get the most relevant solution. Random search is a numerical optimization algorithm that starts its search by generating one candidate solution randomly and iteratively compares it with other random candidate solution in order to get the most suitable solution. This work aims to compare the performance of brute force algorithm and random search in factoring the RSA modulus into its two prime factors by experimental means in Python programming language. The primality test is done by Fermat algorithm and the sieve of Eratosthenes

Computing the Value of Pi in the Manner of Lambda Function with R Statistical Programming Language

The value of π is one of the famous mathematical constant, not only to mathematicians, but also to physicists and to engineers. Numerous algorithm is used to compute what is the value of π, but most of programmer do not use lambda function and neglect the aesthetic of their script. This study aims to compute the value π by write it first as infinite series using Riemann sum, and then the computing of it is conducted in R programming language. We involved the role of anonymous function or known as lambda function to make the R code is more beautiful, artistic, and elegant

A Hybrid Cryptosystem Using Vigenère Cipher and Rabin-p Algorithm in Securing BMP Files

Vigenère cipher is a classical cryptography algorithm and similar to other classical algorithms, it produces smaller but less secure ciphertexts than a public key cryptography algorithm. Meanwhile, Rabin-p is a public key cryptography algorithm with a stronger encryption than Vigenère cipher. Nevertheless, as a public key algorithm, Rabin-p is inefficient to encrypt vast amounts of messages such as BMP image files, since the size of the cipherimages will increase manyfold and this would lead to a problem in storing and sending the cipherimages. To overcome these problems, in this study, we combined the Vigenère cipher and the Rabin-p algorithm in a hybrid cryptosystem scheme. In the experiment, the Vigenère cipher was used to encrypt the BMP files and the Rabin-p algorithm was used to encrypt the Vigenère keys. The result showed that the size of the cipherimages did not increase and the decryption procedure could recover the original BMP files while maintaining their integrity

On Factoring The RSA Modulus Using Tabu Search

It is intuitively clear that the security of RSA cryptosystem depends on the hardness of factoring a very large integer into its two prime factors. Numerous studies about integer factorization in the field of number theory have been carried out, and as a result, lots of exact factorization algorithms, such as Fermat’s factorization algorithm, quadratic sieve method, and Pollard’s rho algorithm have been found. The factorization problem is in the class of NP (non-deterministic polynomial time). Tabu search is a metaheuristic in the field of artificial intelligence which is often used to solve NP and NP-hard problems; the result of this method is expected to be close-to-optimal (suboptimal). This study aims to factorize the RSA modulus into its two prime factors using tabu search by conducting experiments in Python programming language and to compare its time performance with an exact factorization algorithm, i.e. Pollard’s algorithm. The primality test is done with Lehmann’s algorithm

Implementation and comparison of Berry-Ravindran and Zhu- Takaoka exact string matching algorithms in Indonesian-Batak Toba dictionary

Indonesia has a variety of local languages, which is the Batak Toba language. This time, there are still some Batak Toba people who do not know speak Batak Toba language fluently. Nowadays, desktop based dictionary is one of reference that very efficiently used to learn a language and also to increase vocabulary. In making the dictionary application, string matching can be implemented for word-searching process. String matching have some algorithm, which is Berry – Ravindran algorithm and Zhu-Takaoka algorithm and will be implemented on the dictionary application. Zhu-Takaoka algorithm and Berry – Ravindran algorithm have two phases, which are the preprocessing phase and the searching phase. Preprocessing phase is a process to make the shifting values according to in pattern that input by user. To know the shifting value with Zhu-Takaoka algorithm, it’s need Zhu-Takaoka Bad Character (Ztbc) and Boyer-Moore Good Suffix (Bmgs). Then, Ztbc will be compared to Bmgs to get the maximum value of them that will be set as shifting value. While Berry-Ravindran algorithm, to know the shifting value is needed Berry-Ravindran Bad Character, which the two characters right of the text at the position m + 1 and m+ 2, is needed to determine the shifting value, where m is length of the pattern

Performance Analysis of Hybrid Cryptographic Algorithms Rabbit Stream and Enhanced Dual RSA

Cryptography is a technique for encoding data by encrypting plaintext into an unreadable (meaningless) form. The Rabbit Stream algorithm is a stream cipher algorithm whose system security depends on generating key bit streams (keystream). In contrast, the Enhanced Dual RSA algorithm is an asymmetric variant of RSA whose security lies in the difficulty of factoring large numbers into prime factors. It is long in the encryption process when compared to the Rabbit Stream algorithm. In this study, a hybrid of the two algorithms will be carried out using the Python programming language

Analysis of Embedding Locations in the Subband Frequency DCT on Scanned Images

Uploading an identity card as an image for the account verification process or making transactions online can be a threat to application users. Irresponsible people can commit identity card theft if the application is hacked. Therefore, protection of the image is required for authentication. In this study, the proposed technique is watermarking. A watermark in the form of a binary image will be embedded into the image as ownership using a Discrete Cosine Transform. Watermark embedding using Discrete Cosine Transform is done in the frequency domain. To meet the need for good watermarking, an analysis of the location of the embedding of different watermarks was carried out in each 88 DCT block for all frequency subbands and colour components. The results show PSNR 54 dB with a watermark strength of 0,1 and an average SSIM of 0,9 on 4 scanned images in BMP format with a resolution of 100 DPI. A good watermark embedding is done on the green component at middle frequencies to maintain a balance between imperceptibility and robustness. In contrast, the red component at low frequency is vulnerable to attacks in the form of brightness +20 with an average NCC of 0,8451 and a contrast +50 with an average NCC of 0,8425

Comparative Analysis of Ciphertext Enlargement on Generalization of the ElGamal and Multi-factor RSA

Cryptography is a field of science that has a technique or art of disguising the data sent by the sender to the recipient to maintain the authenticity and integrity of the data. The Generalization of the ElGamal algorithm is the latest derivative of the ElGamal algorithm, which has security difficulties by relying on discrete logarithms. Unlike the Multi-factor RSA Algorithm, a variant of the RSA algorithm based on a modified modulus structure from ordinary RSA, it relies on factoring a huge integer into its prime factors. This study uses the Python programming language to compare the ciphertext enlargement of the two algorithms with the same prime number digit length

The Role of Village Government In Overcoming Environmental Pollution Caused by Tofu Factory Waste

Environmental problems cannot be separated from human activities themselves which cause damage to nature and has very broad consequences for human and animal life. Environmental damage is caused by a business that is only concerned with profits, ignoring the consequences of its production which can pollute the surrounding environment. The research method used by the author in studying this problem is normative juridical. using a statutory approach. The problem that occurred in this study was the emergence of a pungent odor and damage to the irrigation river ecosystem caused by this tofu factory waste. And there is no business permit or environmental permit from the tofu factory. The issues raised are 1. What is the role of the Village Government in dealing with environmental pollution caused by this factory waste? 2. What are the Pesa Government's efforts regarding environmental pollution caused by tofu factory waste. In conducting this research the authors used a normative juridical research method. The results showed that the role of the village government in overcoming environmental pollution caused by tofu factory waste generally has 3 roles, namely as a facilitator, motivator, and mediator. Such responsibility is limited to a formal existence. However, it must still refer to the provisions stipulated in Law Number 32 of 2009 concerning PPLH and Regional Regulation 11 of 2019 concerning the Nganjuk PPLH. Permits are a juridical instrument used by the government as a system for managing conditions in people's lives that must be obeyed by all people to control activity so that their business has strong legality. By completing a business permit and environmental permit, the business complies with the la