Security Features of an Asymmetric Cryptosystem based on the Diophantine Equation Hard Problem

2011/03/23 by Muhammad Rezal Kamel Ariffin, Ariffin, M. R. K., Muhammad Asyraf Asbullah +3
Computer Science · #11D45 #68P25 #94A60 #Chaos-based Image/Signal Encryption #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.1103.4433

openalex publication_date 2011/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Diophantine Equation Hard Problem (DEHP) is a potential cryptographic problem on the Diophantine equation U=∑ _i=1ⁿ V_i x_i. A proper implementation of DEHP would render an attacker to search for private parameters amongst the exponentially many solutions. However, an improper implementation would provide an attacker exponentially many choices to solve the DEHP. The AA _β-cryptosystem is an asymmetric cryptographic scheme that utilizes this concept together with the factorization problem of two large primes and is implemented only by using the multiplication operation for both encryption and decryption. With this simple mathematical structure, it would have low computational requirements and would enable communication devices with low computing power to deploy secure communication procedures efficiently.

Citations

• Elliptic curve cryptosystems
• New directions in cryptography

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