[Cryptography] Factoring safe semiprimes

[Pierre Abbat]

https://arxiv.org/pdf/1511.04385v1 explains how to factor a safe semiprime on 
a quantum computer faster than Shor's algorithm. However, their algorithm uses 
the same quantum order-finding algorithm as Shor's algorithm, which Cài Jìn-Yī 
showed cannot factor products of large Fouvry primes in the presence of noise. 
Since all safe primes greater than 10 are Fouvry primes, I'm not worried that 
quantum computers will break public-key cryptography any time soon, unless the 
developers of quantum computers factor some products of Fouvry primes.

https://arxiv.org/abs/1411.6758 reports that a quantum computer has factored 
3599, 11663, and 56153, none of which is a product of two Fouvry primes. The 
first two are one less than squares, so trivially factorizable by Fermat's 
method. The lesser factor of each is a Fouvry prime, but the greater isn't. 
Neither factor of 56153 is a Fouvry prime. https://arxiv.org/pdf/2308.05047v2 
reports factoring 549755813701 = 712321 × 771781; neither factor is a Fouvry 
prime. What's the largest Cài semiprime that has been factored with a quantum 
computer?

Pierre
-- 
sei do'anai mi'a djuno puze'e noroi nalselganse srera