A new cryptosystem based on factoring and discrete logarithm problems

Eddie Shahril Ismail, M. S N Hijazi

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)165-168
Number of pages4
JournalJournal of Mathematics and Statistics
Volume7
Issue number3
DOIs
Publication statusPublished - 2011

Fingerprint

Discrete Logarithm Problem
Factoring
Cryptosystem
Discrete Logarithm
Public key
Time Complexity
Receiver
Knapsack
Elliptic Curves
Integrity
Encryption
Attack

Keywords

  • Cryptography
  • Cryptology
  • Cryptosystem
  • Discrete logarithms
  • Factoring

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

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

In: Journal of Mathematics and Statistics, Vol. 7, No. 3, 2011, p. 165-168.

Research output: Contribution to journalArticle

@article{2d4f8f0e6258400493bbfaa7b7b40e70,
title = "A new cryptosystem based on factoring and discrete logarithm problems",
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).",
keywords = "Cryptography, Cryptology, Cryptosystem, Discrete logarithms, Factoring",
author = "Ismail, {Eddie Shahril} and Hijazi, {M. S N}",
year = "2011",
doi = "10.3844/jmssp.2011.165.168",
language = "English",
volume = "7",
pages = "165--168",
journal = "Journal of Mathematics and Statistics",
issn = "1549-3644",
publisher = "Science Publications",
number = "3",

}

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 -