Hi Ben,
you can generate keys with arbitrary exponents using the genpkey command:

openssl genpkey -algorithm rsa \
  -pkeyopt rsa_keygen_bits:16384
  -pkeyopt rsa_keygen_pubexp:4711

Regards,
Ann.

Am 09.08.2014 15:21, schrieb Benny Baumann:> Hi,
>
> I'd like to propose to include the following additional two command line
> arguments for the openssl binary when creating RSA keys. While the patch
> is written to apply to LibReSSL 2.0.5 it should apply to genrsa.c of
> OpenSSL 1.0.1 just fine too.
>
> While the default of 65537 is a sane default it's not strictly forced by
> any standard. In contrast when looking at NIST SP-800-56B section 6.2.1
> bullet 2b it is described as "an odd positive integer such that 65537 <=
> e < 2**256"
>
> As the plain RSA only requires e to be co-prime to both p-1 and q-1 and
> given the obvious limitation for e=1 yielding no security, there is no
> mathematical backing for any upper bound for e (except the obvious one
> given by p*q-1).
>
> The change only affects the key generation and extends the possibility
> to use custom public exponents as has been done in certain areas
> previously. Implementations conforming to the mathematical foundation
> should be unaffected as otherwise they would have been broken for
> decryption all along.
>
> Kind regards,
> Benny Baumann
>




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