Thursday, December 8, 2011

The price to pay for perfect-forward secrecy

[EDIT: Updated results for GnuTLS 3.2 and to adhere to ECRYPT recommendations for key equivalence]

Ok, the question seems to be what is perfect forward secrecy? Perfect forward secrecy (PFS) is a property of a cryptographic protocol, such as SSL (or better TLS). That property ensures that once the cryptographic keys of a participant are leaked the secrecy of past sessions remains. For example if the amazon.com private key is leaked your previous transactions with this site remain secure. That is a very interesting protocol property, but is actually only effective if the web site wouldn't store any of the sensitive transaction data. In this post we ignore any issues due to storage and focus on the protocol property. So does TLS have this property? That is a yes and a no.

TLS provides the option to use ciphersuites offering perfect forward secrecy. Those are the ciphersuites that use ephemeral Diffie-Hellman and elliptic curve Diffie-Hellman authentication. However those come at a cost very few web sites are willing to pay for. They involve expensive calculations that put some burden on the server and delay the transaction for few milliseconds. Why would a server bother to protect your data anyway? And that seems to be the current attitude. Most servers totally prohibit the usage of ciphersuites that offer PFS. Try for example to connect to amazon.com using:
$ ./gnutls-cli www.amazon.com --priority NORMAL:-KX-ALL:+DHE-RSA:+ECDHE-RSA
Resolving 'www.amazon.com'...
Connecting to '72.21.214.128:443'...
*** Fatal error: A TLS fatal alert has been received.
*** Received alert [40]: Handshake failed

So let's try to evaluate the cost of PFS versus the plain RSA ciphersuites that do not offer PFS, using a simple approach initially. For that we use Diffie-Hellman group parameters of 1024 bits, a 192-bit elliptic curve and a 1024-bit RSA key and a modified gnutls-cli for its benchmark-tls option.


Key exchangeParametersTransactions/sec
DHE-RSA1024-bit RSA key,
1024-bit DH parameters
345.53
ECDHE-RSA1024-bit RSA key,
192-bit ECDH parameters
604.92
ECDHE-ECDSA192-bit ECDSA key,
192-bit ECDH parameters
595.84
RSA1024-bit RSA key994.59

In this test the ciphersuites DHE-RSA, ECDHE-RSA and ECDHE-ECDSA provide perfect forward secrecy, and use a signed ephemeral (Diffie-Hellman) key exchange. The signature in the key exchange is an RSA or ECDSA one, determined by the ciphersuite and the certificate. The plain RSA ciphersuite doesn't offer PFS and utilizes RSA's encryption capability (instead of signing). We can see that the non-PFS ciphersuite is a clear winner with 3x factor from DHE_RSA ciphersuite. The elliptic curve equivalents of DHE also fail to reach plain RSA's performance.

However, our security levels are not consistent. An elliptic curve of 192-bits provides 96-bits of security  according to ECRYPT (don't confuse the bits of an algorithm such as RSA with the bits of the security level, a security level of 96-bits is a good level of security for today's standards). That means it is equivalent to roughly 1776-bits RSA and DH parameters. So let's do the same experiment with more consistent parameters.


Key exchangeParametersTransactions/sec
DHE-RSA1776-bit RSA key,
1776-bit DH parameters
98.26
ECDHE-RSA1776-bit RSA key,
192-bit ECDH parameters
352.41
ECDHE-ECDSA192-bit ECDSA key,
192-bit ECDH parameters
595.84
RSA1776-bit RSA key460.08

So it is obvious that increasing the security level to 96-bits degrades performance for all ciphersuites (except ECDHE-ECDSA which already offered that level of security). The Diffie-Hellman key exchange is very slow over a 1776-bit group, and in addition it includes an RSA signature of 1776-bits. The Elliptic curve equivalent (ECDHE-RSA) is much more efficient, even though it also includes a 1776-bit RSA signature. The clear winner though is the ECDHE-ECDSA variant which uses an ECDSA public key and outperforms even plain RSA.

Nevertheless, if we restrict to RSA keys that are supported by almost every implementation, the winner is plain RSA, with a small but not insignificant difference from the second.


[Note that in previous to 3.2 versions of GnuTLS ECDHE-ECDSA was slower than plain RSA. The re-implementation of the ECC subsystem in nettle library provided a significant boost in ECC operations.]

So although I'd suggest ciphersuites offering PFS for almost everything, in practice, when ECDSA keys are not option, they degrade performance, and this should not be underestimated. When it is desired to have PFS, then its shortcomings have to be evaluated against the benefits.

On the other hand if a decent security level is required (such as the 96-bit one used in our example), we see that the switch from plain RSA to ECDHE-ECDSA provides both efficiency and forward secrecy.

So given the fact that any web server may at some point be compromised, my suggestion would be, that if you value the exchanged data in the transactions, only PFS ciphersuites should be used. Otherwise, using the plain RSA ciphersuite may still suit better.

PS. Note that protecting the server's private key on the disk using PIN or passwords is futile as the key resides unencrypted in the server's memory.

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