New cryptosystem using multiple cryptographic assumptions

Eddie Shahril Ismail, M. S. Hijazi

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Problem statement: A cryptosystem is a way for a sender and a receiver to communicate digitally by which the sender can send receiver any confidential or private message by first encrypting it using the receiver's public key. Upon receiving the encrypted message, the receiver can confirm the originality of the message's contents using his own secret key. Up to now, most of the existing cryptosystems were developed based on a single cryptographic assumption like factoring, discrete logarithms, quadratic residue or elliptic curve discrete logarithm. Although these schemes remain secure today, one day in a near future they may be broken if one finds a polynomial algorithm that can efficiently solve the underlying cryptographic assumption. Approach: By this motivation, we designed a new cryptosystem based on two cryptographic assumptions; quadratic residue and discrete logarithms. We integrated these two assumptions in our encrypting and decrypting equations so that the former depends on one public key whereas the latter depends on one corresponding secret key and two secret numbers. Each of public and secret keys in our scheme determines the assumptions we use. Results: The newly developed cryptosystem is shown secure against the three common considering algebraic attacks using a heuristic security technique. The efficiency performance of our scheme requires 2T exp+2T mul +T hash time complexity for encryption and T exp+2T mul +T srt time complexity for decryption and this magnitude of complexity is considered minimal for multiple cryptographic assumptions-like cryptosystems. Conclusion: The new cryptosystem based on multiple cryptographic assumptions offers a greater security level than that schemes based on a single cryptographic assumption. The adversary has to solve the two assumptions simultaneously to recover the original message from the received corresponding encrypted message but this is very unlikely to happen.

Original languageEnglish
Pages (from-to)1765-1769
Number of pages5
JournalJournal of Computer Science
Volume7
Issue number12
DOIs
Publication statusPublished - 2011

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Cryptography
Polynomials

Keywords

  • Cryptographic assumptions
  • Cryptography
  • Cryptology
  • Cryptosystem
  • Discrete logarithm attack
  • Discrete logarithms
  • Factoring attack
  • Polynomial algorithm
  • Quadratic residue

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence

Cite this

New cryptosystem using multiple cryptographic assumptions. / Ismail, Eddie Shahril; Hijazi, M. S.

In: Journal of Computer Science, Vol. 7, No. 12, 2011, p. 1765-1769.

Research output: Contribution to journalArticle

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