Score:1

Crypto

What is the security strength of XMSS according to NIST PQC categories?

Raoul722

4/21/23, 4:11 PM

In the context of the NIST PQC standardization process, NIST has defined the following five security categories:

Any attack that breaks the relevant security definition must require computational resources comparable to or greater than those required for key search on a block cipher with a 128-bit key (e.g. AES128)
Any attack that breaks the relevant security definition must require computational resources comparable to or greater than those required for collision search on a 256-bit hash function (e.g. SHA256/ SHA3-256)
Any attack that breaks the relevant security definition must require computational resources comparable to or greater than those required for key search on a block cipher with a 192-bit key (e.g. AES192)
Any attack that breaks the relevant security definition must require computational resources comparable to or greater than those required for collision search on a 384-bit hash function (e.g. SHA384/ SHA3-384)
Any attack that breaks the relevant security definition must require computational resources comparable to or greater than those required for key search on a block cipher with a 256-bit key (e.g. AES 256)

In which category does XMSS fall when instantiated with SHA256 or SHAKE256?

0 + 0

post-quantum-cryptography

hash-signature

kelalaka

4/21/23, 4:41 PM

[The security of the stateful HBS schemes in this publication depends only on the security of the underlying hash functions—in particular, the infeasibility of finding a preimage or a second preimage—and it is believed that the security of hash functions will not be broken by the development of large-scale quantum computers`](https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-208.pdf)

Score:3

Crypto

poncho

4/21/23, 7:02 PM

In which category does XMSS fall when instantiated with SHA256 or SHAKE256?

Well, XMSS is as strong as the second preimage resistance of the underlying hash function - with either SHA256 or SHAKE256, a second preimage can't be found (to the best of our knowledge, of course) any easier than finding an AES-256 key; hence it is NIST level 5.

For the IETF-defined parameter sets, XMSS uses SHAKE-128 for 256 bit hashes, which reduces the security level significantly (if not practically). On the other hand, the parameter sets defined in NIST SP 800-208 all use SHAKE-256, so the above logic applies.

0 + 0

poncho

4/21/23, 9:33 PM

@kelalaka: I hadn't realized that the IETF RFC8391 and NIST SP 800-208 differed...

kelalaka

4/21/23, 9:40 PM

Does XMMS have real-life usage? Do you know anything about it? Note: the permutation property was good to include in the answer.

poncho

4/21/23, 10:00 PM

@kelalaka: I do believe that XM*S*S is used on occasion to authenticate software updates (which is the ideal use case for it - we have tight control of the signer, we don't have to sign that many times, and we don't care if the signatures are largish...)

kelalaka

4/21/23, 10:04 PM

Tight control, could you expand it a little?

poncho

4/21/23, 10:07 PM

@kelalaka: well, with stateful hashes (such as XMSS), you have to be careful about remembering state (essentially, how many signatures you've generated so far) - if you sign two different things with the same state, well, bad things happen. A centralized signer for software updates can presumably be careful about that (and make sure that, say, a database backup and restore doesn't back up the state) - with other scenarios, we can't state this with such confidence.

kelalaka

4/21/23, 10:10 PM

Ah, I see, the tight control of the usage. Thanks.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: What is the security strength of XMSS according to NIST PQC categories?

TH: ความแข็งแกร่งด้านความปลอดภัยของ XMSS ตามหมวดหมู่ NIST PQC คืออะไร

RO: Care este puterea de securitate a XMSS conform categoriilor NIST PQC?

RU: Каков уровень безопасности XMSS в соответствии с категориями NIST PQC?

VI: Độ mạnh bảo mật của XMSS theo danh mục PQC của NIST là gì?

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