Real-world measurements of structured-lattices and supersingular isogenies in TLS (30 Oct 2019)

This is the third in a series of posts about running experiments on post-quantum confidentiality in TLS. The first detailed experiments that measured the estimated network overhead of three families of post-quantum key exchanges. The second detailed the choices behind a specific structured-lattice scheme. This one gives details of a full, end-to-end measurement of that scheme and a supersingular isogeny scheme, SIKE/p434. This was done in collaboration with Cloudflare, who integrated Microsoft's SIKE code into BoringSSL for the tests, and ran the server-side of the experiment.


Google Chrome installs, on Dev and Canary channels, and on all platforms except iOS, were randomly assigned to one of three groups: control (30%), CECPQ2 (30%), or CECPQ2b (30%). (A random ten percent of installs did not take part in the experiment so the numbers only add up to 90.) CECPQ2 is the hybrid X25519+structured-lattice scheme previously described. CECPQ2b is the name that we gave to the combination of X25519 and the SIKE/p434 scheme.

Because optimised assembly implementations are labour-intensive to write, they were only available/written for AArch64 and x86-64. Because SIKE is computationally expensive, it wasn’t feasible to enable it without an assembly implementation, thus only AArch64 and x86-64 clients were included in the experiment and ARMv7 and x86 clients did not contribute to the results even if they were assigned to one of the experiment groups.

Cloudflare servers were updated to include support for both CECPQ2 and CECPQ2b, and to support an empty TLS extension that indicated that they were part of the experiment. Depending on the experiment group, Chrome would either offer CECPQ2, CECPQ2b, or just non-post-quantum options, in its TLS 1.3 handshake, along with the signaling extension to indicate which clients were part of the control group. Measurements were taken of how long TLS handshakes took to complete using Chrome’s metrics system. Chrome knew which servers were part of the experiment because they echoed the signaling extension, thus all three groups were measuring handshake duration against the same set of servers.

After this phase of the trial was complete, client-side measurements were disabled and Chrome Canary was switched to a mode where it randomly picked one of CECPQ2, CECPQ2b, or neither to offer. This enabled some additional, server-side measurements to ensure that nothing unexpected was occuring.

(Cloudflare has a significantly more detailed write up of this experiment.)


We’re aware of a couple of biases and these need to be kept in mind when looking at the results. Firstly, since ARMv7 and x86 platforms were excluded, the population was significantly biased towards more powerful CPUs. This will make supersingular isogenies look better. Also, we’ve seen from past experiments that Canary and Dev Chrome users tend to have worse networks than the Chrome user population as a whole, and this too will tend to advantage supersingular isogenies since they require less network traffic.


Here are histograms of client-side results, first from Windows (representing desktops/laptops) and from Android (representing mobile devices):

1 10 100 1000 10000 TLS handshake time (ms) TLS handshake latency (Windows) Control Control CECPQ2 CECPQ2 CECPQ2b CECPQ2b 1 10 100 1000 10000 TLS handshake time (ms) TLS handshake latency (Android) Control Control CECPQ2 CECPQ2 CECPQ2b CECPQ2b

From the histograms we can see that the CECPQ2b (SIKE) group shifts visibly to the right (i.e. slower) in both cases. (On Android, a similar but smaller shift is seen for CECPQ2.) Despite the advantages of removing the slower clients and experimenting with worse-than-usual networks, the computational demands of SIKE out-weigh the reduced network traffic. Only for the slowest 5% of connections are the smaller messages of SIKE a net advantage.

Cloudflare have a much more detailed analysis of the server-side results, which are very similar.


While there may be cases where the smaller messages of SIKE are a decisive advantage, that doesn’t appear to be the case for TLS, where the computational advantages of structured lattices make them a more attractive choice for post-quantum confidentiality.