### 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 language | English |
---|---|

Pages (from-to) | 1765-1769 |

Number of pages | 5 |

Journal | Journal of Computer Science |

Volume | 7 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2011 |

### Fingerprint

### 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

*Journal of Computer Science*,

*7*(12), 1765-1769. https://doi.org/10.3844/jcssp.2011.1765.1769

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

Research output: Contribution to journal › Article

*Journal of Computer Science*, vol. 7, no. 12, pp. 1765-1769. https://doi.org/10.3844/jcssp.2011.1765.1769

}

TY - JOUR

T1 - New cryptosystem using multiple cryptographic assumptions

AU - Ismail, Eddie Shahril

AU - Hijazi, M. S.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Cryptographic assumptions

KW - Cryptography

KW - Cryptology

KW - Cryptosystem

KW - Discrete logarithm attack

KW - Discrete logarithms

KW - Factoring attack

KW - Polynomial algorithm

KW - Quadratic residue

UR - http://www.scopus.com/inward/record.url?scp=84855616260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855616260&partnerID=8YFLogxK

U2 - 10.3844/jcssp.2011.1765.1769

DO - 10.3844/jcssp.2011.1765.1769

M3 - Article

AN - SCOPUS:84855616260

VL - 7

SP - 1765

EP - 1769

JO - Journal of Computer Science

JF - Journal of Computer Science

SN - 1549-3636

IS - 12

ER -