### Abstract

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).

Original language | English |
---|---|

Pages (from-to) | 165-168 |

Number of pages | 4 |

Journal | Journal of Mathematics and Statistics |

Volume | 7 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Cryptography
- Cryptology
- Cryptosystem
- Discrete logarithms
- Factoring

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of Mathematics and Statistics*,

*7*(3), 165-168. https://doi.org/10.3844/jmssp.2011.165.168

**A new cryptosystem based on factoring and discrete logarithm problems.** / Ismail, Eddie Shahril; Hijazi, M. S N.

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 7, no. 3, pp. 165-168. https://doi.org/10.3844/jmssp.2011.165.168

}

TY - JOUR

T1 - A new cryptosystem based on factoring and discrete logarithm problems

AU - Ismail, Eddie Shahril

AU - Hijazi, M. S N

PY - 2011

Y1 - 2011

N2 - 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).

AB - 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).

KW - Cryptography

KW - Cryptology

KW - Cryptosystem

KW - Discrete logarithms

KW - Factoring

UR - http://www.scopus.com/inward/record.url?scp=84855591913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855591913&partnerID=8YFLogxK

U2 - 10.3844/jmssp.2011.165.168

DO - 10.3844/jmssp.2011.165.168

M3 - Article

AN - SCOPUS:84855591913

VL - 7

SP - 165

EP - 168

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 3

ER -