25 research outputs found
Conjectures in number theory
No full textPrime numbers, whose properties are important subjects in mathematics, are
also fundamental in computer science notably in IT security, Cryptocurrencies
as Bitcoin and Blockchain, cryptography, Code theory notably Error detection
codes, integer factorization, and random number generation. Finding prime
numbers is too an active area of research in mathematics. There are many
methods for identifying and generating them and many primality tests which are
often complex and expensive in terms of calculation time, and many conjectures
and theorems related to prime numbers, such as the prime number theorem,
Goldbach's conjecture, and the Riemann hypothesis. My objective in this work is
to propose two conjectures :
the integer
is not a prime number for all or mod , and
the integer
is not a prime number for all mod .
Keywords : Prime numbers; IT security; Cryptography
Unlocking Security: Pioneering a Novel Elliptic Curve-Based Hashing Scheme
No full textLow-power networks and devices are becoming increasingly prevalent globally. These networks facilitate the exchange of concise messages, such as measurements and instructions. However, ensuring security, particularly concerning message integrity and sender authentication, presents a challenge in constrained environments. This article introduces a major breakthrough in the field of cryptography through the development of an innovative hash function leveraging the torsion subgroup on an elliptic curve. By incorporating the unique properties of this group, our approach redefines data security standards. We demonstrate the heightened resilience of our hash function against current attacks while maintaining exceptional performance. This novel method represents a significant advancement in safeguarding sensitive information, paving the way for more robust cybersecurity and practical applications across various domains. Experimental results confirm the effectiveness and security of our approach, establishing new perspectives for the evolution of modern cryptography
Unlocking Security: Pioneering a Novel Elliptic Curve-Based Hashing Scheme
No full textLow-power networks and devices are becoming increasingly prevalent globally. These networks facilitate the exchange of concise messages, such as measurements and instructions. However, ensuring security, particularly concerning message integrity and sender authentication, presents a challenge in constrained environments. This article introduces a major breakthrough in the field of cryptography through the development of an innovative hash function leveraging the torsion subgroup on an elliptic curve. By incorporating the unique properties of this group, our approach redefines data security standards. We demonstrate the heightened resilience of our hash function against current attacks while maintaining exceptional performance. This novel method represents a significant advancement in safeguarding sensitive information, paving the way for more robust cybersecurity and practical applications across various domains. Experimental results confirm the effectiveness and security of our approach, establishing new perspectives for the evolution of modern cryptography
Implementation and Evaluation of a Secure and Efficient Web Authentication Scheme using Mozilla Firefox and WAMP
No full text
