Introduction

The following are observations from when I started testing my own pure-Rust crypto library, including its dependencies, for constant-time execution. Starting with a short introduction to dudect and how it can be used to test code for timing-based side-channel vulnerabilities. Then discussing the process of discovering a short-circuit that resulted in variable-time execution, in dalek-cryptography’s subtle library and how this seems to relate to Rust codegen option opt-level .

DISCLAIMER: The tests and analysis presented in this post were not done by a professional - take everything with a grain of salt.

dudect

Excerpts from the original papers abstract:

“[…] a tool to assess whether a piece of code runs in constant time or not on a given platform. We base our approach on leakage detection techniques, resulting in a very compact, easy to use and easy to maintain tool.”

“Contrary to others, our solution requires no modeling of hardware behavior. Our solution can be used in black-box testing, yet benefits from implementation details if available. We show the effectiveness of our approach by detecting several variable-time cryptographic implementations.”

dudect uses Welch’s t-tests to detect variances in execution time, which is used to detect leakage in code that is supposed to be constant-time.

Welch’s t-tests

“In statistics, Welch’s t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means.”

(Wiki source)

In terms of dudect, Welch’s t-test is used to test the hypothesis that two input-classes produce two sets of timing measurements, that have equal means.

Threshold

The threshold is the maximum t-value that is considered acceptable. The paper suggests that:

“A t value larger than 4.5 provides strong statistical evidence that the distributions are different”

When calculating the t-value, two means are subtracted: M1 - M2 . Measurements can report negative t-values, this is however of little concern to us since this will just indicate that M1 < M2 . Therefore, t-values should be within the acceptable threshold when t > -4.5 or t < 4.5 (see also this question).

Note: Throughout the rest of this post I’ll also use the term “ max t ”, which will refer to the same statistical t-value discussed here.

Number of samples

Based on what is tested, it should be assessed how many samples are to be generated. In some cases, a larger number of samples are required to detect any timing difference, as the author of the paper describes here:

“Once we have around 20k measurements, the timing leak starts to be detectable, and we can conclude that the implementation is not constant time”

Inputs for measuring

When testing functions such as constant-time comparisons, it’s often sufficient to use random input-pairs. Though, in some cases when looking for timing difference it might yield better results, or even be required to detect leakage, to use specially crafted test vectors.

Implementations such as Poly1305 will only be variable-time for some inputs. Poly1305 implementations that use big-num libraries are most likely not constant-time, where variable-time execution could arise from the internal operations (multiplication, modulo, etc):

“For example, if the multiplication is performed as a separate operation from the modulus, the result will sometimes be under 2^256 and sometimes be above 2^256.”

RFC 8439

Creating tailored test vectors would involve identifying on which inputs such behavior occurs. Perhaps a good place to start would be using Google Wycheproof test vectors for ChaCha20Poly1305 with dudect, which include some edge-cases for Poly1305.

This paper describes some specially crafted test vectors for leakage detection in RSA implementations, using Welch’s t-tests.

The length of the input should also be considered. Testing a constant-time comparison function using arrays with a single element won’t yield any results at all. However, measuring, for example, two arrays of length 128 where the first element differs, would have a much better chance of revealing differences in timing.

Testing orion

All the tests can be examined in the repository orion-dudect. To run dudect tests, I use the wonderful dudect-bencher crate.

The parts of orion that are currently tested for constant-time execution, are as follows:

The constant-time comparison function secure_cmp , that is provided as a wrapper around subtle’s ct_eq .

, that is provided as a wrapper around subtle’s . The macro that implements PartialEq , in constant-time, for all newtypes.

, in constant-time, for all newtypes. The Poly1305 implementation.

Testing specifics:

The number of samples generated (ie. number of input-pairs) was 1e6.

dudect-bencher input-pairs were either both random or one random and one all 0’s.

A threshold of 4.5.

Testing was done with Rust 1.34 and latest nightly.

and latest nightly. Crate versions: orion 0.13.4 , subtle 2.0.0 , dudect-bencher 0.3.0 and orion-dudect at commit 9dcb019.

Short-circuit in dalek-cryptography’s subtle library

secure_cmp was the first interface I tested and the test-runner for that is shown below, where u and v are a single input-pair.

// Run timing for (class, (u, v)) in classes.into_iter().zip(inputs.into_iter()) { runner.run_one(class, || secure_cmp(&u[..], &v[..])); }

The first results I got were:

running 1 bench bench test_secure_cmp seeded with [0xe3fcea9a, 0x2a24a9d8, 0x336618e6, 0x625fc346] bench test_secure_cmp ... : n == +0.690M, max t = +704.74089, max tau = +0.84869, (5/tau)^2 = 34

I spent two days inspecting the code in both subtle, dudect-bencher and orion, but couldn’t find anything amiss. The fourth day, I realized I had only been testing in debug-mode. Running the tests in release gave:

running 1 bench bench test_secure_cmp seeded with [0x760ce3a5, 0x97c6bd44, 0x6baee54f, 0xcbd63a51] bench test_secure_cmp ... : n == +0.228M, max t = -1.32524, max tau = -0.00277, (5/tau)^2 = 3246511

After having a look through all the code again, I noticed debug_assert! statements in subtle (a debug_assert! call is not included in release builds), which used the || short-circuit operator:

debug_assert!(input == 0u8 || input == 1u8); debug_assert!(source.0 == 0u8 || source.0 == 1u8);

After changing these to strict evaluations ( | ), the max t values reported decreased to about 20.

debug_assert!((input == 0u8) | (input == 1u8)); debug_assert!((source.0 == 0u8) | (source.0 == 1u8));

This was still outside of the threshold, but to make sure using strict evaluations actually was the solution, I extracted the secure_cmp test, into a separate one that tested subtle’s ct_eq . This resulted in max t values of ~2, within the threshold.

debug_assert! and assert!

I had assumed that since debug_assert! is left out in release builds, using the short-circuit evaluation in an assert! statement (an assert! call is included in release builds), the same timing results would be reported in debug and release mode.

I ran tests, with all the short-circuiting debug_assert! s being changed to assert! s, assuming that the variable-time execution would persist in release builds as well. These were the results that were reported:

running 1 bench bench test_secure_cmp seeded with [0xc1df4b3f, 0x7e07c3db, 0xbe9f442f, 0x7dc6dfd4] bench test_secure_cmp ... : n == +0.048M, max t = +1.54205, max tau = +0.00702, (5/tau)^2 = 506736

My assumption was, that the compiler was using the information about input and source.0 to optimize the code, resulting in variable-time execution. Seeing these results I assume this is not entirely the case, which led me to think that perhaps it is some of the debug information, that is included in debug builds. To tests this, I specified profile attributes in orion-dudect:

[profile.release] debug = false debug-assertions = false [profile.dev] debug = false debug-assertions = false

Toggling any of these on and off individually made no difference. One difference between release and debug are the codegen options passed to LLVM. debug uses opt-level = 0 by default and release uses opt-level = 3 . Testing release with opt-level = 3/2/1 made no difference, but with opt-level = 0 , still using assert! , reported:

running 1 bench bench test_secure_cmp seeded with [0x3aaf907c, 0xcc37be69, 0x30af1b90, 0xd613fd43] bench test_secure_cmp ... : n == +0.556M, max t = +1428.01869, max tau = +1.91513, (5/tau)^2 = 6

Replacing the assert! s with strict evaluations had the same result on timing, as when testing debug_assert! s. This had made me spend some time trying to figure out what exact codegen parameters are used with LLVM, when setting opt-level = 1 , to identify the parameters that made the compiler ignore the short-circuit evaluations. I haven’t been able to find information on what parameters are passed and could therefore not proceed with this. The only thing I could take away from this was that with an opt-level = 0 , the compiler uses results of short-circuit evaluations in assert-statements.

Result and constant-time evaluations

The max t values for secure_cmp were still outside of threshold after applying strict evaluations to subtle’s debug_assert! s.

When toggling the opt-level , as with subtle, the same behavior was observed - only opt-level = 0 in both debug and release mode resulted in max t values outside of the threshold.

secure_cmp currently returns a Result , like so:

if a.ct_eq(b).into() { Ok(true) } else { Err(errors::UnknownCryptoError) }

Testing secure_cmp with is_ok() and is_err() , instead of not using the Result , gave the following:

running 1 bench bench test_secure_cmp seeded with 0xcf4880125e45af1b bench test_secure_cmp ... : n == +0.563M, max t = -63.07522, max tau = -0.08409, (5/tau)^2 = 3535

Again, toggling the opt-level s showed the exact same results as before. Changing secure_cmp to return only a bool , directly from .into() , showed the exact same results as when testing subtle’s ct_eq separately.

Perhaps the compiler can somehow use the information, arising from subtle’s From<> for bool conversion, when calling .into() combined with an Ok(true) return? I honestly have no idea as to what the cause of this is. The only thing I could take away from this was that using Result in code that is expected to run in constant-time, using opt-level = 0 , can result in variable-time execution.

Summary

A short summary of my overall takeaway:

All Rust code should be tested in both debug and release mode.

Testing Rust code for constant-time execution should be done with all opt-level values.

values. Rust code that is expected to run in constant-time must never be compiled with opt-level = 0 .

be compiled with . assert! and debug_assert! should be avoided, with opt-level = 0 , in code that needs to execute in constant time.

and should be avoided, with , in code that needs to execute in constant time. Result return-types should be avoided, with opt-level = 0 , in code that needs to execute in constant time.

As the introduction mentioned: all of the above are merely observations, and not very detailed ones. Furthermore, the tests are based on only one measurement tool. Testing for constant-time execution should preferably combine uses of both dudect, ctgrind and other relevant ones.

There’s also a new tool in Rust called SideFuzz, which currently combines differential fuzzing, genetic algorithms and dudect for leakage detection. I’m quite excited to try it out and see how it develops.

Found a mistake?

Please reach out.