Because the "secret" factors A*B = C, with A prime and B prime, are the holy grail to break RSA, the asymmetric keys algorithm used world while to enforce security, with SSL, HTTPS, VPNs... Ruffly speaking, in RSA itself, C is "the public key" and its factorization, A and B "the private key". It is straightforward to find the factors for small numbers, but it happens that it is very hard to find such factors for large numbers (indeed - you need to extensively search for them). To date it has been possible to break up to a 768 bit RSA key (C is 768 bits long) by using a cluster of many hundred servers. Larger keys (1024, 2048 bits) are still considered secure (needed hundred years of cluster computing time for one single key) - and they will, until some strong improvement will be performed in number theory.
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Sigismondo Boschi
@Sigismondo Boschi