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Abstract
Safe primes and safe RSA moduli are used in several cryptographic schemes. The most common notion is that of a prime P, where (p  1)/2 is also prime. The latter is then a Sophie Germain prime. Under appropriate heuristics, they exist in abundance and can be generated efficiently. But the modern methods of analytic number theory have  so far  not even allowed to prove that there are infinitely many of them. Thus for this notion of safe primes, there is no algorithm in the literature that is unconditionally proven to terminate, let alone to be efficient. This paper considers a different notion of safe primes and moduli. They can be generated in polynomial time, without any unproven assumptions, and are good enough for the cryptographic applications that we are aware of.
Original language  English 

Pages (fromto)  333365 
Number of pages  33 
Journal  Journal of Mathematical Cryptology 
Volume  7 
Issue number  4 
DOIs  
Publication status  Published  1 Dec 2013 
Externally published  Yes 
Keywords
 HofheinzKiltzShoup cryptosystem
 Safe prime
 Sophie Germain prime
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Projects
 1 Finished

Lattices as a Constructive and Destructive Cryptographic Tool
Doche, C., Shparlinski, I., Steinfeld, R., Stehle, D., MQRES, M., PhD Contribution (ARC), P. C. (. & Newton, J.
31/07/11 → 31/12/14
Project: Research