Resumen
RSA key pairs are normally generated from two large primes p and q. We consider what happens if they are generated from two integers s and r, where r is prime, but unbeknownst to the user, s is not. Under most circumstances, the correctness of encryption and decryption depends on the choice of the public and private exponents e and d. In some cases, specific (??,??)
(
s
,
r
)
pairs can be found for which encryption and decryption will be correct for any (??,??)
(
e
,
d
)
exponent pair. Certain s exist, however, for which encryption and decryption are correct for any odd prime ?????
r
?
s
. We give necessary and sufficient conditions for s with this property.