The Keccak sponge function family

Guido Bertoni1, Joan Daemen1, Michaël Peeters2 and Gilles Van Assche1

1STMicroelectronics

2NXP Semiconductors

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Yes, this is Keccak!

4 October 2013

SUMMARY: NIST's current proposal for SHA-3 is a subset of the Keccak family, and one can generate test vectors for that proposal using our reference code submitted to the contest.

In the end, it will be NIST's decision on what exactly will be standardized for SHA-3, but we would like, as the Keccak team, to take the opportunity to remind some facts about Keccak and give some opinion on the future SHA-3 standard.

First some reminders on Keccak

Keccak in the SHA-3 standard

NIST's current proposal for SHA-3, namely the one presented by John Kelsey at CHES 2013 in August, is a subset of the Keccak family. More concretely, one can generate the test vectors for that proposal using the Keccak reference code (version 3.0 and later, January 2011). This alone shows that the proposal cannot contain internal changes to the algorithm.

We did not suggest NIST to make any change to the Keccak components, namely the Keccak-f permutations, the sponge construction and the multi-rate padding, and we are not aware of any plans that NIST would do so. However, the future standard will not include the entire Keccak family but will select only specific instances of Keccak (i.e., with specific capacities), similarly to the block and key lengths of AES being a subset of those of Rijndael. Moreover, it will append some parameter-dependent suffix to the input prior to processing (see below) and fix the output length (for the SHA-2 drop-in replacements) or keep it variable (for the SHAKEs).

Here are further comments on these choices.

First, about suffixes (sometimes referred to as padding).

In Sakura, we propose to append some suffix to the input message, before applying Keccak. This is sometimes presented as a change in Keccak's padding rule because adding such a suffix can be implemented together with the padding, but technically this is still on top of the original multi-rate padding.

The suffixes serve two purposes. The first is domain separation between the different SHA-3 instances, to make them behave as independent functions (even if they share the same capacity). The second is to accomodate tree hashing in the future in such a way that domain separation is preserved.

The security is not reduced by adding these suffixes, as this is only restricting the input space compared to the original Keccak. If there is no security problem on Keccak(M), there is no security problem on Keccak(M|suffix), as the latter is included in the former.

Second, about the output length.

Variable output length hashing is an interesting feature for natively supporting a wide range of applications including full domain hashing, keystream generation and any protocol making use of a mask generating function. In its current proposal, NIST plans on standardizing two instances: SHAKE256 and SHAKE512, with capacity c=256 and c=512 and therefore security strength levels of 128 and 256 bits, respectively.

The traditional fixed output-length instances acting as SHA-2 drop-in replacement (SHA3-xxx) are obtained from truncating Keccak instances at the given output length.

Third, about the proposed instances and their capacities.

The capacity of the SHAKEs is given above and we now focus on the SHA-2 drop-in replacement instances with fixed output length n, with n in {224, 256, 384, 512}.

The SHA-3 requirements asked for a spectrum of resistance levels depending on the attack: n/2 for collision, n for first pre-image and n-k for second pre-image (with 2k the length of the first message). To meet the requirements and avoid being disqualified, we set c=2n so as to match the n-bit pre-image resistance level, and the requirements on other attacks followed automatically as they were lower. However, setting c=2n is also a waste of resources. For instance, Keccak[c=2n] before truncation provides n-bit collision resistance (in fact n-bit resistance against everything), but after truncation to n bits of output it drops to n/2-bit collision resistance.

Instead, adjusting the capacity to meet the security strength levels of [NIST SP 800-57] gives better security-performance trade-offs. In this approach, one aims at building a protocol or a system with one consistent security target, i.e., where components are chosen with matching security strength levels. The security strength level is defined by the resistance to the strongest possible attack, i.e., (internal) collisions so that, e.g., SHA-256 is at 128 bits for digital signatures and hash-only applications. Hence, setting c=n simply puts SHA3-n at the n/2-bit security level.

Among the Keccak family, NIST decided to propose instances with capacities of c=256 for n=224 or 256, and c=512 bits for n=384 or 512. This proposal is the result of discussions between the NIST hash team and us, when we visited them in February and afterwards via mail. It was then publically presented by John Kelsey at CT-RSA later in February and posted on the NIST hash-forum mailing list soon after. It was then presented at several occasions, including Eurocrypt 2013, CHES 2013 at UCSB, etc.

The corresponding two security strength levels are 128 bits, which is rock-solid, and an extremely high 256 bits (e.g., corresponding to RSA keys of 15360 bits [NIST SP 800-57]).

Comments on some of the criticism

Finally, we now comment on some criticism we saw in the discussions on the NIST hash-forum mailing list.

As explained in our new proposal, we think the SHA-3 standard should emphasize the SHAKE functions. The SHA-3 user would keep the choice between lean SHAKE256 with its rock-solid security strength level and the heavier SHAKE512 with its extremely high security strength level. In implementations, the bulk of the code or circuit is dedicated to the Keccak-f[1600] permutation and from our experience supporting multiple rates can be done at very small cost.

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