Re: Question About RSA Encryption

Unruh wrote:
Mike Amling <nospam@xxxxxxxxxx> writes:


shimshim@xxxxxxxxx wrote:

Hi,
I have two questions about RSA encryption.

1)Does double encryption increase security over single encryption in
RSA? if yes or no why?


No. And it is very hard to impliment. The second N MUST then be larger than
the first, or you will not be able to invert it.

Well, no, you could use Rivest's trick for making the encryption function map {01}**k --> {01}**k, in which case both Ns must be larger than 2**k, but the second could be smaller than the first.

RSA is already unbearably
slow. Why do you want slow it down even further.

(Note that known plaintext does not seem to be of any help in cracking RSA.
It is cracked by factoring N, which does not require any plaintext at all.
Thus double encryption is no help whatsoever in hiding the text. If double
encryption were easier to break then the attcker could encrypt any
encrypted text and thus break it more easily. )


Others have answered this.


2)Why we should not use exponents e=1 and e=2 in RSA?


e=1 would mean the ciphertext is equal to the plaintext.
e=2 can be made to work. Search for "Rabin cryptosystem".


However, as I recall you want e to be relatively prime to p-1 and q-1 and 2
is never relatively prime to them.

Yes, that's the reason e=2 won't work in RSA, which is indeed what the OP was asking.

As he says e=1 is pretty useless. (Note that any number that is encrypted
must be much larger than N/e or else inversion is trivial. For e=1 this

When Dr. Unruh says "larger than N/e", he means "larger than N**(1/e)", or "have bitlength more than lg(N)/e bits".

requirement is impossible since the numver MUST also be less than N.

--Mike Amling
.

Relevant Pages

  • Re: Symmetric encryption algorithm with group like properties
    ... >> Solutions that exist today are not as secure as they can be. ... I wouldn't expect more than PGP / GPG type encryption, ... > versions - with the key, protected by RSA encryption under a RSA public key ... > Alice needs a secure decryption mechanism to read her emails, ...
    (sci.crypt)
  • RE: rsa encrtyption
    ... It seems to work for her now and all we did was apply some Sql Server updates. ... My only guess was that the MS dll she used to apply the RSA encryption was ... According to the RSA encryption reference, I've performed some local tests, ... Export the machine-level RSA key container: ...
    (microsoft.public.dotnet.framework.aspnet.security)
  • RE: rsa encrtyption
    ... According to the RSA encryption reference, I've performed some local tests, ... Grant Read Access to the RSA Encryption Key: ... Export the machine-level RSA key container: ... Import the the machine-level RSA key container on the 2nd server: ...
    (microsoft.public.dotnet.framework.aspnet.security)
  • Re: Rabin vs. RSA/ElGamal
    ... the speed difference between RSA ... encryption and Rabin encryption probably is irrelevant. ... For RSA or ElGamal you need exponentiation. ...
    (sci.crypt)
  • Re: Rabin vs. RSA/ElGamal
    ... the speed difference between RSA ... encryption and Rabin encryption probably is irrelevant. ... What DOES takes the time is decryption. ... This also doesn't change the fact that Rabin encryption is still a lot ...
    (sci.crypt)