Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem

Verkhovsky, Boris S.

doi:10.3844/jcssp.2009.674.679

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…The Digital Signature Algorithm (DSA) is a good example which uses in authentication and integrity techniques. Several algorithms use the DLP such as the Diffie-Hellman key exchange, ElGamal encryption and digital signature, Schnorr signature etc [5]. Elliptic Curve Discrete Logarithm Problem (ECDLP): This is another mathematical problem that also based on the DLP that defined over the group of points on an elliptic curve.…”

Section: Discrete Logarithm Problem (Dlp)mentioning

confidence: 99%

“…We have introduced a simple comparison among three different public key ciphers in the below as explained in figure(4)which illustrates the implementation of run time in seconds to achieve the encryption and decryption operation for the three messages with different size (1000 char, 2000 char, and 3000 char) respectively. Figure(5) submits the running time of the signature and verification algorithms for the same message. In this test there is no need to take different messages lengths, because the execution time will be based on the message digest of the original message.…”

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confidence: 99%

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Public Key Cipher with Signature Based on Diffie-Hellman and the Magic Square Problem

S.Rahma¹,

Hossen²,

Dawood³

2016

ETJ

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In the present paper, we developed a new variant of asymmetric cipher (Public Key) algorithm based on the Discrete Logarithm Problem (DLP) uses Diffie-Hellman key exchange protocol and the mathematical features of magic square. The proposed method exploits the DLP problem in the key exchange by using the final value of Diffie-Hellman key agreement, just as the dimension to the magic construction and through which determines the type of magic square construction if it is (odd, singly-even or doubly-even) magic square as well as through which determines starting number and the difference value. From the other point, it exploits the magic squares problem in encryption/decryption and signing/verifying operations. The developed method extremely speed in the Encryption/Decryption process as well as in the digital signature that uses a Secure Hash Algorithm SHA-1, since the proposed cipher does not use logarithm and the factorization as the traditional algorithms in ciphering and deciphering operations just in the mutual exchanging, but it depends mainly upon the magic constant and magic sum as alternate that deduced from the result of multiplied fixed value, which selected randomly and imposes to keep secret, as we shall explained in the next sections.

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Section: Discrete Logarithm Problem (Dlp)mentioning

confidence: 99%

mentioning

confidence: 99%

Public Key Cipher with Signature Based on Diffie-Hellman and the Magic Square Problem

S.Rahma¹,

Hossen²,

Dawood³

2016

ETJ

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“…Methods of counting points on elliptic curves are considered in [18,19] and more generally on modular equations with several variables in [20,21]. A relationship between integer factorization and constrained discrete logarithm problems is analyzed in [22].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations

Verkhovsky¹

2011

IJCNS

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In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that computes a factor of a semi-prime integer n=pq, where prime factors p and q are unknown. The proposed algorithm is based on counting points on a sequence of at least four elliptic curves y2=x(x2+b2)(modn) , where b is a control parameter. Although in the worst case, for some n the number of required values of parameter b that must be considered (the number of basic steps of the algorithm) substantially exceeds four, hundreds of computer experiments indicate that the average number of the basic steps does not exceed six. These experiments also confirm all important facts discussed in this paper

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“…Most the existing Cryptosystems (CRS) have the common feature that they are based on a single numbertheoretic cryptographic assumption (Diffie and Hellman, 1975) like Discrete Logarithms (DL) (Verkhovsky and Sadik, 2009) or Factoring (FAC) (Verkhovsky, 2009) a large composite number or Elliptic Curve Discrete Logarithm (ECDL) (Koblizt et al, 2000) problem. Even though such problems remain hard today, it is understood that one day in the future the FAC, DL or ECDL problems could be easily solved.…”

Section: Introductionmentioning

confidence: 99%

A New Cryptosystem Based on Factoring and Discrete Logarithm Problems

Ismail¹,

Hijazi

2011

Journal of Mathematics and Statistics

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Problem statement:A cryptosystem allows a sender to send any confidential or private message using a receiver's public key and later the receiver confirms the integrity of the received message using his secret key. Currently the existing cryptosystems were developed based on a single hard problem like factoring, discrete logarithm, residuosity, knapsack or elliptic curve discrete logarithm. Although these schemes appear secure, one day in a near future they may be broken if one finds a solution of a single hard problem. Approach: To solve this problem, we developed a new cryptosystem based on two hard problems; factoring and discrete logarithm. We integrated the two problems in our encrypting and decrypting equations so that the former depends on two public keys whereas the latter depends on two corresponding secret keys. Results: The new cryptosystem is shown secure against the most three considering attacks. The efficiency performance of our scheme only requires 3T exp +T mul + T hash time complexity for encryption and 2T exp + T mul time complexity for decryption and this magnitude of complexity is considered minimal for multiple hard problems-like cryptosystems. Conclusion: The new cryptosystem based on multiple hard problems provides longer and higher security level than that schemes based on a single hard problem. The adversary has to solve the two problems simultaneously in order to recover a corresponding plaintext (message) from the received ciphertext (encrypted message).

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Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem

Cited by 9 publications

References 19 publications

Public Key Cipher with Signature Based on Diffie-Hellman and the Magic Square Problem

Public Key Cipher with Signature Based on Diffie-Hellman and the Magic Square Problem

Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations

A New Cryptosystem Based on Factoring and Discrete Logarithm Problems

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