scholarly journals Pico Without Public Keys

2015 ◽  
pp. 195-211 ◽  
Author(s):  
Frank Stajano ◽  
Bruce Christianson ◽  
Mark Lomas ◽  
Graeme Jenkinson ◽  
Jeunese Payne ◽  
...  
Keyword(s):  
Public Keys

A Public Keys Based Architecture for P2P Identification, Content Authenticity and Reputation

2009 ◽  
Author(s):  
Neander L. Brisola ◽  
Altair O. Santin ◽  
Lau C. Lung ◽  
Heverson B. Ribeiro ◽  
Marcelo H. Vithoft
Keyword(s):  
Public Keys

scholarly journals Strategic Way of Factoring Modulus ``\(N = p^r q\)

2021 ◽  
pp. 74-86
Author(s):  
Sadiq Shehu ◽  
Abdullahi Hussaini ◽  
Zahriya Lawal
Keyword(s):  
Information Security ◽  
Polynomial Time ◽  
Continued Fractions ◽  
Prime Power ◽  
Electronic Information ◽  
Lll Algorithm ◽  
Key Equation ◽  
Public Keys ◽  
Diophantine Approximations ◽  
Simultaneous Diophantine Approximations

Cryptography is fundamental to the provision of a wider notion of information security. Electronic information can easily be transmitted and stored in relatively insecure environments. This research was present to factor the prime power modulus \(N = p^r q\) for \(r \geq 2\) using the RSA key equation, if \(\frac{y}{x}\) is a convergents of the continued fractions expansions of \(\frac{e}{N - \left(2^{\frac{2r+1}{r+1}} N^{\frac{r}{r+1}} - 2^{\frac{r-1}{r+1}} N^{\frac{r-1}{r+1}}\right)}\). We furthered our analysis on \(n\) prime power moduli \(N_i = p_i^r q_i\) by transforming the generalized key equations into Simultaneous Diophantine approximations and using the LLL algorithm on \(n\) prime power public keys \((N_i,e_i)\) we were able to factorize the \(n\) prime power moduli \(N_i = p_i^r q_i\), for \(i = 1,....,n\) simultaneously in polynomial time.

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