The smaller the value for e, the faster encryption is. However, some attacks
(Hasted's and Coppersmith's) work better for smaller e. I believe all of
these attacks are blocked by using PKCS#1 block type 2 formatting, but just
for an extra security comfort margin, a larger value of e is often chosen.
Also, I don't think these attacks make sense against the signature mode of
RSA, so you will find e=3 in the wild.
e doesn't have to be prime and being prime is not sufficient either. e must
be relatively prime to L=LCM(p-1,q-1). This means that 3 doesn't always
work. In practice, the value 65537 is nice number because it "big enough" in
the Goldilocks sense, unlikely to be a factor of L, and is fast to compute
with if the binary exponentiation algorithm is used.
_____________________________________
Greg Stark
Ethentica, Inc.
[EMAIL PROTECTED]
_____________________________________
----- Original Message -----
From: "Deng Lor" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, February 16, 2001 2:41 AM
Subject: Re: What does the "e-value" do?
> Firstly i'd like to thank you for your help.
>
> I was always considering that e should be selected at random,
> so i'm really surprised at the answer.
>
> I'm eager to know why 65537 is selected as the e, and are there
> any fact proofing it is better than other primes seleted out
> randomly?
>
>
> ----- Original Message -----
> From: "Joseph Ashwood" <[EMAIL PROTECTED]>
> To: <[EMAIL PROTECTED]>
> Sent: Friday, February 16, 2001 3:02 AM
> Subject: Re: What does the "e-value" do?
>
>
> > First a bit of background. RSA is this:
> > p,q primes
> > N=pq
> > e=prime that is not a factor of p-1 or q-1 and not equal to p or q
> > d = e^-1 mod (p-1)(q-1)
> > public key = {e,N}
> > private key = {d, N}
> > Encryption = X = M^e mod N
> > Decryption = M = X^d mod N
> >
> > The e-value you see in the call is the value e above. The recommendation
> of
> > using 3 or 65537 is a speed decision, and I would definitely recommend
> 65537
> > over 3 for security reasons.
> > Joe
> >
> >
> > ______________________________________________________________________
> > OpenSSL Project http://www.openssl.org
> > User Support Mailing List [EMAIL PROTECTED]
> > Automated List Manager [EMAIL PROTECTED]
>
> ______________________________________________________________________
> OpenSSL Project http://www.openssl.org
> User Support Mailing List [EMAIL PROTECTED]
> Automated List Manager [EMAIL PROTECTED]
______________________________________________________________________
OpenSSL Project http://www.openssl.org
User Support Mailing List [EMAIL PROTECTED]
Automated List Manager [EMAIL PROTECTED]
