### Abstract

Problem statement: The security of elliptic curve cryptosystems are based on elliptic curve discrete logarithm problem (ECDLP). However, if an attacker finds a solution to ECDLP, the elliptic curve-based systems will no longer be secure. Approach: To improve this, we develop a new elliptic curve cryptosystem using one of the old/novel problem in computational number theory; factoring problem (FAC). Specifically, our encrypting and decrypting equations will heavily depends on two public keys and two secret keys respectively. Results: We show that, the newly designed cryptosystem is heuristically secure against various algebraic attacks. The complexity of the scheme shows that the time complexity for each encryption and decryption are given by 299T _{mul} and 270T _{mul}. Conclusion: The new system provides greater security than that system based on a single hard problem. The attacker has not enough resources to solve the two hard problems simultaneously in a polynomial time.

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

Pages (from-to) | 1443-1447 |

Number of pages | 5 |

Journal | American Journal of Applied Sciences |

Volume | 9 |

Issue number | 9 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Cryptosystem
- Elliptic curve
- Elliptic curve discrete logarithm problem
- Factoring problem

### ASJC Scopus subject areas

- General

### Cite this

*American Journal of Applied Sciences*,

*9*(9), 1443-1447.

**Development of a new elliptic curve cryptosystem with factoring problem.** / Ismail, Eddie Shahril; Hijazi, M. S.

Research output: Contribution to journal › Article

*American Journal of Applied Sciences*, vol. 9, no. 9, pp. 1443-1447.

}

TY - JOUR

T1 - Development of a new elliptic curve cryptosystem with factoring problem

AU - Ismail, Eddie Shahril

AU - Hijazi, M. S.

PY - 2012

Y1 - 2012

N2 - Problem statement: The security of elliptic curve cryptosystems are based on elliptic curve discrete logarithm problem (ECDLP). However, if an attacker finds a solution to ECDLP, the elliptic curve-based systems will no longer be secure. Approach: To improve this, we develop a new elliptic curve cryptosystem using one of the old/novel problem in computational number theory; factoring problem (FAC). Specifically, our encrypting and decrypting equations will heavily depends on two public keys and two secret keys respectively. Results: We show that, the newly designed cryptosystem is heuristically secure against various algebraic attacks. The complexity of the scheme shows that the time complexity for each encryption and decryption are given by 299T mul and 270T mul. Conclusion: The new system provides greater security than that system based on a single hard problem. The attacker has not enough resources to solve the two hard problems simultaneously in a polynomial time.

AB - Problem statement: The security of elliptic curve cryptosystems are based on elliptic curve discrete logarithm problem (ECDLP). However, if an attacker finds a solution to ECDLP, the elliptic curve-based systems will no longer be secure. Approach: To improve this, we develop a new elliptic curve cryptosystem using one of the old/novel problem in computational number theory; factoring problem (FAC). Specifically, our encrypting and decrypting equations will heavily depends on two public keys and two secret keys respectively. Results: We show that, the newly designed cryptosystem is heuristically secure against various algebraic attacks. The complexity of the scheme shows that the time complexity for each encryption and decryption are given by 299T mul and 270T mul. Conclusion: The new system provides greater security than that system based on a single hard problem. The attacker has not enough resources to solve the two hard problems simultaneously in a polynomial time.

KW - Cryptosystem

KW - Elliptic curve

KW - Elliptic curve discrete logarithm problem

KW - Factoring problem

UR - http://www.scopus.com/inward/record.url?scp=84867619314&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867619314&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 1443

EP - 1447

JO - American Journal of Applied Sciences

JF - American Journal of Applied Sciences

SN - 1546-9239

IS - 9

ER -