Comment by crote
4 days ago
As I understand it, a big issue is that they are really hard to implement correctly. This means that backdoors and weaknesses might not exist in the theoretical algorithm, but still be common in real-world implementations.
On the other hand, Curve25519 is designed from the ground up to be hard to implement incorrectly: there are very few footguns, gotchas, and edge cases. This means that real-world implementations are likely to be correct implementations of the theoretical algorithm.
This means that, even if P-224/P-256/P-384 are on paper exactly as secure as Curve25519, they could still end up being significantly weaker in practice.
I tried to defend a similar argument in a private forum today and basically got my ass handed to me. In practice, not only would modern P-curve implementations not be "significantly weaker" than Curve25519 (we've had good complete addition formulas for them for a long time, along with widespread hardware support), but Curve25519 causes as many (probably more) problems than it solves --- cofactor problems being more common in modern practice than point validation mistakes.
In TLS, Curve25519 vs. the P-curves are a total non-issue, because TLS isn't generally deployed anymore in ways that even admit point validation vulnerabilities (even if implementations still had them). That bit, I already knew, but I'd assumed ad-hoc non-TLS implementations, by random people who don't know what point validation is, might tip the scales. Turns out guess not.
Again, by way of bona fides: I woke up this morning in your camp, regarding Curve25519. But that won't be the camp I go to bed in.
I agree that Curve25519 and other "safer" algorithms are far from immune to side channel attacks in their implementation. For example, [1] is a single trace EM side channel key recovery attack against Curve25519 implemented in MbedTLS on an ARM Cortex-M4. This implementation had the benefit of a constant-time Montgomery ladder algorithm that NIST P curve implementations have traditionally not had a similar approach for, but nonetheless failed due to a conditional swap instruction that leaked secret state via EM.
The question is generally, could a standard in 2025 build upon decades of research and implementation failures to specify side channel resistant algorithms to address conditional jumps, processor optimisations for math functions, etc which might leak secret state via timing, power or EM signals. See for example section VI of [1] which proposed a new side channel countermeasure that ended up being implemented in MbedTLS to mitigate the conditional swap instruction leak. Could such countermeasures be added to the standard in the first instance, rather than left to implementers to figure out based on their review of IACR papers?
One could argue that standards are simply following interests of standards proposers and organisations who might not care about cryptography implementations on smart cards, TPMs, etc, or side channel attacks between different containers on the same host. Instead, perhaps standards proposers and organisations only care about side channel resistance across remote networks with high noise floors for timing signals, where attacks such as [2] (300ns timing signal) are not considered feasible. If this is the case, I would argue that the standards should still state their security model more clearly, for example:
* Is the standard assuming the implementation has a noise floor of 300ns for timing signals, 1ms, etc? Are there any particular cryptographic primitives that implementers must use to avoid particular types of side channel attack (particularly timing)?
* Implementation fingerprinting resistance/avoidance: how many choices can an implementation make that may allow a cryptosystem party to be deanonymised by the specific version of a crypto library in use?[3] Does the standard provide any guarantee for fingerprinting resistance/avoidance?
[1] Template Attacks against ECC: practical implementation against Curve25519, https://cea.hal.science/cea-03157323/document
[2] CVE-2024-13176 openssl Timing side-channel in ECDSA signature computation, https://openssl-library.org/news/vulnerabilities/index.html#...
[3] Table 2, pyecsca: Reverse engineering black-box ellipticcurve cryptography via side-channel analysis, https://tches.iacr.org/index.php/TCHES/article/view/11796/11...
> As I understand it, a big issue is that they are really hard to implement correctly.
Any reference for the "really hard" part? That is a very interesting subject and I can't imagine it's independent of the environment and development stack being used.
I'd welcome any standard that's "really hard to implement correctly" as a testbed for improving our compilers and other tools.
I posted above, but most of the 'really hard' bits come from the unreasonable complexity of actual computing vs the more manageable complexity of computing-with-idealized-software.
That is, an algorithm and compiler and tool safety smoke test and improvement thereby is good. But you also need to think hard about what happens when someone induces an RF pulse at specific timings targeted at a certain part of a circuit board, say, when you're trying to harden these algorithmic implementations. Lots of things that compiler architects typically say is "not my problem".