This website contains information about the LowMC cryptanalysis challenge.

LowMC

LowMC (ePrint, Springer) is a very parameterizable block cipher design, where the block size, the key size, and various other internals can be chosen freely by the user. The design is a partial substitution-permutation network, meaning that the nonlinear layers in each round do not cover the full state. This construction approach has shown to be beneficial for use cases like MPC, where the number of nonlinear gates has to be kept low.

Another use case where this design is efficient is a novel post-quantum signature scheme named Picnic (ePrint, ACM), which is currently a round-2 candidate in the NIST PQ competition. In Picnic, the number of multiplications of the underlying primitive has a direct impact on the resulting signature size.

From a cryptanalytic point of view, this scenario is interesting because a potential attacker is only ever able to have access to a single (plaintext, ciphertext) pair. The purpose of this cryptanalysis challenge is therefore to gain a deeper knowledge about the security of LowMC in this setting.

Instances

We consider different instances of LowMC, where n denotes the block size (and the key size) and s denotes the number of S-boxes in each round. Specifically, we make a distinction between partial S-box layers and full S-box layers:

• n = 128, s = 1
• n = 128, s = 10
• n = 129, s = 43 (full S-box layer)
• n = 192, s = 1
• n = 192, s = 10
• n = 192, s = 64 (full S-box layer)
• n = 256, s = 1
• n = 256, s = 10
• n = 255, s = 85 (full S-box layer)

The Cryptanalysis Challenge

Sponsoring: Currently USD 50k from Microsoft and EUR 50k from iov42

The goal of all attacks here is to recover the secret key. We have following challenges and prices in mind for the versions with full S-box layers:

• Submitters of the fastest attack on 2 rounds win EUR 2k.
• Submitters of the fastest attack on 3 rounds win EUR 3k.
• Submitters of the fastest attack on 4 rounds win EUR 4k.

For the versions with partial S-box layers, let again denote by n the block size (and key size) and by s the number of S-boxes. Using this notation, we have following prices in mind for the possible instances from above:

• Submitters of the fastest attack on floor(n/s)*0.8 rounds win EUR 2k.
• Submitters of the fastest attack on floor(n/s)*1.0 rounds win EUR 3k.
• Submitters of the fastest attack on floor(n/s)*1.2 rounds win EUR 4k.

By the fastest attack we mean the biggest gain in efficiency over exhaustive search. Note that we always use a data complexity of 1 for these attacks, which means that no more than a single (plaintext, ciphertext) pair is allowed. The claimed security level is always n bits.

Additionally, we also offer a bonus prize for finding an interesting property of LowMC or for showing a new technique (we will consider weak-key attacks, but not related-key attacks). The winner of this side challenge gets EUR 4k.

In total, EUR 22k may be earned in this current round.

Schedule and Rules

Tentative schedule:

• The first quick round is until August 10 2020 (one week before Crypto 2020), and winners will be announced after that
• The second round is until December 1 (one week before Asiacrypt 2020)
• Potentially, a third round will be held until June 1 2021.
• Overall duration is around 2 years (money not spent remains in the pot and is part of the following rounds)

Rules:

• Results with the fastest attacks are better (date of submission does not count)
• If two attacks are equally efficient or very similar, the one submitted earlier wins
• Verifiability is important
• Submissions will be published
• Brute force-like approaches with minor gains will not be considered

Further Material

The baseline document with some attack approaches can be found here.

You can find reference implementations of LowMC and scripts to generate all needed values (e.g., matrices, constants) in the original LowMC repository. Our implementation of the decoding attack on LowMC is available here.

Current Results

The first result is a 2-round attack and an attack on floor(n/s)*0.8 rounds, both with lowest complexities. The attack was found by Subhadeep Banik (EPFL), Khashayar Barooti (EPFL), F. Betül Durak (Bosch Research), and Serge Vaudenay (EPFL), and is further described here.

News and Updates

5 January 2021

Congratulations to the second winners, who are Subhadeep Banik (EPFL) and Serge Vaudenay (EPFL)! In their paper, they describe new and faster attacks on 2 rounds (full S-box layers) and floor(n/s)*0.8 rounds (partial S-box layers).

18 August 2020

The second round is announced. More details about this can be found in our Crypto 2020 rump session slides.

17 August 2020

Congratulations to the first winners, who are Subhadeep Banik (EPFL), Khashayar Barooti (EPFL), F. Betül Durak (Bosch Research), and Serge Vaudenay (EPFL)! In their paper, they describe a 2-round attack and an attack on floor(n/s)*0.8 rounds, both with lowest complexities. The price they claim is EUR 4k.

2 June 2020

iov42 has joined our sponsors with EUR 50k!

15 May 2020

Corrected some mistakes in the reference implementations regarding the plaintext output and a missing matrix multiplication. Thanks to Vukasin Karadzic (TU Darmstadt) for pointing this out.

13 May 2020

Challenge started!

Contact

You’ve solved a challenge or have any other questions? Let us know by writing an email to lowmc-challenge@iaik.tugraz.at!