This page is dedicated to the cryptographic sponge function family called Keccak, which has been selected by NIST to become the new SHA-3 standard. The draft of the standard (FIPS 202) is available for reading.

## Keccak in a nutshell

Keccak is a family of sponge functions. The *sponge function* is a generalization of the concept of cryptographic hash function with infinite output and can perform quasi all symmetric cryptographic functions, from hashing to pseudo-random number generation to authenticated encryption.

For a quick introduction, we propose a *pseudo-code* description of Keccak. The reference specification, analysis, reference and optimized code and test vectors for Keccak can be found in the file section.

As primitive used in the sponge construction, the Keccak instances call one of seven permutations named Keccak-*f*[*b*], with *b*=25, 50, 100, 200, 400, 800 or 1600. In the scope of the SHA-3 contest, we proposed the largest permutation, namely Keccak-*f*[1600], but smaller (or more “lightweight”) permutations can be used in constrained environments. Each permutation consists of the iteration of a simple round function, similar to a block cipher without a key schedule. The choice of operations is limited to bitwise XOR, AND and NOT and rotations. There is no need for table-lookups, arithmetic operations, or data-dependent rotations.

Keccak has a very different design philosophy from its predecessor RadioGatún. This is detailed in our paper presented at Dagstuhl in 2009.

## Strengths of Keccak

### Flexibility

Keccak inherits the flexibility of the sponge and duplex constructions.

- As a sponge function, Keccak has
**arbitrary output length**. This allows to simplify modes of use where dedicated constructions would be needed for fixed-output-length hash functions. It can be natively used for, e.g., hashing, full domain hashing, randomized hashing, stream encryption, MAC computation. In addition, the arbitrary output length makes it suitable for tree hashing. - As a duplex object, Keccak can be used in
**clean and efficient modes**as a reseedable pseudo-random bit generator and for authenticated encryption. Efficiency of duplexing comes from the**absence of output transformation**. - Keccak has a
**simple security claim**. One can target a given security strength level by means of choosing the appropriate capacity, i.e., for a given capacity*c*, Keccak is claimed to stand any attack up to complexity 2^{c/2}(unless easier generically). This is similar to the approach of*security strength*used in NIST's SP 800-57. - The security claim is
**disentangled from the output length**. There is a minimum output length as a consequence of the chosen security strength level (i.e., to avoid generic birthday attacks), but it is not the other way around, namely, it is not the output length that determines the security strength level. For an illustration with the classical security requirements of hashing (i.e., collision and (second) preimage resistance), we refer to our interactive page. - The instances proposed for SHA-3 make use of a
**single permutation**for all security strengths. This cuts down implementation costs compared to hash function families making use of two (or more) primitives, like the SHA-2 family. And with the same permutation, one can make**performance-security trade-offs**by way of choosing the suitable appropriate capacity-rate pair.

### Design and security

- Keccak has a
**thick safety margin**. In [Keccak reference, Section 5.4], we estimate that the Keccak sponge function should stand by its security claim even if the number of rounds is almost divided by two (i.e., from 24 down to 13 in the case of Keccak-*f*[1600]). - Keccak was scrutinized by
**third-party cryptanalysis**. For more details, we refer to the cryptanalysis page. - We showed that the Keccak-
*f*permutations have provable lower**bounds on the weight of differential trails**. - The design of the permutations follows the
**Matryoshka principle**, where the security properties of the seven permutations are linked. The cryptanalysis of the smaller permutations, starting from the “toy” Keccak-*f*[25], is meaningful to the larger permutations, and vice-versa. In particular, differential and linear trails in one Keccak-*f*instance extend to symmetric trails in larger instances. - The sponge and duplex constructions used by Keccak are
**provably secure against generic attacks**. This covers also the joint use of multiple Keccak instances with different rate/capacity parameters. - Unlike SHA-1 and SHA-2, Keccak does not have the length-extension weakness, hence
**does not need the HMAC nested construction**. Instead, MAC computation can be performed by simply prepending the message with the key. - From the mode down to the round function, our design choices are fairly different from those in the SHA-1 and SHA-2 hash functions or in the Advanced Encryption Standard (AES). Keccak therefore provides
**diversity with respect to existing standards**.

### Implementation

- Keccak excels in
**hardware performance**, with speed/area trade-offs, and outperforms SHA-2 by an order of magnitude. See for instance the works of Gürkaynak et al., Gaj et al., Latif et al., Kavun et al., Kaps et al. and Jungk presented at the Third SHA-3 Candidate Conference. - Keccak has overall
**good software performance**. It is faster than SHA-2 on modern PCs and shines when used in a mode exploiting parallelism. On AMD™ Bulldozer™, 128-bit and 256-bit security hashing tops at 4.8 and 5.9 cycles/byte, respectively. On Intel™ Sandy Bridge™, the same functions reach 5.4 and 6.9 cycles/byte. On constrained platforms, Keccak has moderate code size and RAM consumption requirements. - For modes involving a key, protecting the implementation against
**side-channel attacks**is wanted. The operations used in Keccak allow for**efficient countermeasures**against these attacks. Against cache-timing attacks, the most efficient implementations involve no table lookups. Against power analysis attacks and variants, countermeasures can take advantage of the quadratic round function.

## Latest news

### 14 May 2014 — The Keccak crunchy crypto contest re-opens

We are happy to announce that from today the Keccak Crunchy Crypto Collision and Pre-image Contest re-opens without limit of time.

There are two minor changes.

- We have simplified the rules for the prizes. For all open challenges the first submission now simply receives 10 € multiplied by the number of rounds
*n*. The challenges that have been closed remain closed._{r} - We allow for some more flexibility in choosing the reduced-round versions of Keccak-
*f*. Previously, the*n*-round reduced-round version was fixed to the first_{r}*n*consecutive rounds. The submitters can now choose to take the last_{r}*n*consecutive rounds (as in the draft of FIPS 202) or any other_{r}*n*rounds, as long as they are consecutive._{r}

We refer to Keccak Crunchy Crypto Collision and Pre-image Contest for more details.

### 6 May 2014 — Practical complexity cube attacks

Recently, Itai Dinur, Paweł Morawiecki, Josef Pieprzyk, Marian Srebrny and Michał Straus published new attacks on keyed instances of Keccak, i.e., when it is used as a stream cipher or to compute a message authentication code (MAC). The attacks are *cube attacks* that exploit the low algebraic degree of a primitive and have a data complexity of the order of 2^{n} if this degree is *n*. Since the round function has algebraic degree 2, the attacks can be applied on 5 or 6 rounds of Keccak-*f* with a practical complexity.

These attacks are the first ones with practical complexity to reach 6 rounds. Looking at more theoretical complexities, these attacks can most probably reach a few more rounds.

### 8 April 2014 — The FIPS 202 draft is available

Last Friday, NIST released the draft of the FIPS 202 standard. It proposes six instances: the four SHA-2 drop-in replacements with fixed output length SHA3-224 to SHA3-512, and the two future-oriented *extendable-output functions* SHAKE128 and SHAKE256.

The latest version of the Keccak Code Package is in line with the draft and contains test vectors for the six aforementioned instances.

### 8 February 2014 — KeccakTools moved to GitHub

Recently, we decided to move KeccakTools to GitHub. This allows easier updates as well as an easier integration of potential contributions from others.

As a reminder, KeccakTools is a set of documented C++ classes that can help analyze Keccak. It also contains the best differential and linear trails we found in the various Keccak-*f* instances.

### 4 October 2013 — Yes, this is Keccak!

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 is a
**family**of sponge function instances, encompassing capacity values ranging from 0 to 1599 bits. All these instances are well-defined and so are their security claim. Our SHA-3 submission highlighted instances with capacities*c*=448, 512, 768 and 1024 for strictly meeting NIST's SHA-3 requirements on the SHA-2 drop-in replacement instances, plus a capacity of 576 for a variable-output-length instance. Nevertheless, the capacity is an explicitly tunable parameter, in the line of what NIST suggested in their SHA-3 call, and we therefore proposed in our SHA-3 submission document that the**capacity would be user-selectable**. - The
**capacity**is a parameter of the sponge construction (and of Keccak) that determines a particular**security strength level**, in the line of the levels defined in [NIST SP 800-57]. Namely, for a capacity*c*, the security strength level is*c*/2 bits and the sponge function is claimed to resist against all attacks up to 2^{c/2}, unless easier with a random oracle. As we make a clear security claim for each possible value of the capacity, a user knows what the expect and a cryptanalyst knows her target. Conversely, we provide a tool that helps determine the minimum capacity and output length given collision and pre-image resistance requirements. **The core of Keccak**, namely the Keccak-*f*permutations,**has not changed**since round 2 of the SHA-3 competition. When Keccak was selected for the 2^{nd}round, we increased the number of rounds to have a better safety margin (from 18 to 24 rounds for Keccak-*f*[1600]). The round function has not changed since the original submission in 2008.- Keccak is the result of using the sponge construction on top of the Keccak-
*f*permutations and applying the multi-rate padding to the input. Using multi-rate padding causes each member of the Keccak family (and in particular for each value of the capacity) to act as an**independent function**. - As a native feature, Keccak provides
**variable output length**, that is, the user can dynamically ask for as many output bits as desired (e.g., as a mask generating function such as MGF1).

#### 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 2^{k} the length of the first message). To meet the requirements and avoid being disqualified, we set *c*=2*n* 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*=2*n* is also a waste of resources. For instance, Keccak[*c*=2*n*] 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.

*“128 bits of security are not enough in particular in the light of multi-target pre-image attacks.”*We addressed this specifically in a message to the NIST SHA-3 mailing list, we explained why this fear is unfounded and why the 128 bits of security do not degrade for multi-target pre-image attacks. And anyway the SHA-3 proposal includes functions with 256-bit security, which the user is free to choose as well.*“SHA3-256 does not provide 256-bit pre-image resistance.”*With*c*=256, this is correct indeed. We proposed to reduce the capacity of SHA3-256 to 256 bits to follow our security-strength oriented approach, which better addresses actual user requirements than the traditional way of inferring resistance of hash functions from the output length. Nevertheless, to avoid confusion for people expecting 256-bit resistance from SHA3-256, we made a 2^{nd}proposal that sets*c*=512 for all SHA-2 drop-in replacement instances, hence providing the traditional 256-bit pre-image resistance.*“There is no instance providing 512-bit pre-image resistance.”*Again, this is correct. The answer is similar to the previous point, except that our new proposal does not extend to capacities higher than*c*=512 bits, simply because claiming or relying on security strength levels above 256 bits is meaningless. Setting*c*=1024 would induce a significant performance loss, and there are no standard public-key parameters matching 512 bits of security. Also we believe that this security level was more a side-effect and not a security target in itself. All conventional hash functions that would aim at 256-bit collision resistance would automatically provide 512-bit preimage resistance. Keccak however is a different cryptographic object and SHA3-512 can safely provide a security strength of 256 bits against all attacks without the need to boost the security level beyond any meaning.*“Claiming a higher security level provides a safety margin.”*In the Keccak design philosophy, safety margin comes from the number of rounds in Keccak-*f*, whereas the security level comes from the selected capacity. We have designed Keccak so as to have a strong safety margin for all possible capacities. At this moment, this safety margin is very comfortable (4 to 5 rounds out of 24 are broken). Of course, the user can still increase the capacity to get a security level that is higher than the one he targets, and hence somehow artificially increase the safety margin. But, there is simply no need to do so. We also refer to Martin Schläffer's excellent summary, posted on the NIST hash-forum mailing list on October 1st, 2013 at 10:16 GMT+2 (thanks Martin!).

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.

#### References

Recommended reading from third parties:

- Jeff Trombly's excellent comments
- Martin's mail (the NIST hash-forum mailing list on October 1st, 2013 at 10:16 GMT+2)

Other references:

- NIST SHA-3 pages and the hash-forum mailing list
- Bruce Schneier on the subject (no, there was no “internal changes to the algorithm”)
- Slashdot thread on the subject (although, no, NIST didn't “cripple SHA-3”)
- CDT post (with many factual errors)
- And of course our pages on Keccak and on sponge functions

### 2 October 2013 — A concrete proposal

*This article is a copy of a message we posted on the NIST hash-forum mailing list on September 30, 2013.*

SUMMARY: In the SHA-3 standard, we propose to set the capacity of all four SHA-2 drop-in replacements to 512 bits, and to make SHAKE256 and SHAKE512 the primary choice.

Technically, we think that NIST's current proposal is fine. As said in our previous post, we have proposed to reduce the capacities of the SHA-3 hash functions at numerous occasions, including during our last visit to NIST in February. Nevertheless, in the light of the current discussions and to improve public acceptance, we think it would be indeed better to change plans. For us, the best option would be the following (taking inspiration from different other proposals).

- Set the capacity of the SHA-2 drop-in replacements (i.e., SHA3-224 to SHA3-512) to
*c*=512. This guarantees the same claimed security properties as for the corresponding SHA-2 instances up to the 256-bit security level. (In particular, the pre-image resistance of SHA3-256 would be raised to 256 bits.) - Keep the SHAKEs as they are (i.e., SHAKE256 with
*c*=256 and SHAKE512 with*c*=512) and make them the primary choice for new applications of hash functions, for replacing mask generating functions (MGFs) and for those who wish to follow the security strength levels approach of [NIST SP 800-57].

For the SHAKEs, we think it would be good to include in the standard a short procedure for replacing a hash function or MGF based on SHA-1 or SHA-2. For instance, if there is only one to be replaced, here is a sketch.

- Choose between SHAKE256 and SHAKE512. If the user can determine the required security level and it is 128 bits or smaller, choose SHAKE256. Otherwise (or if unsure), choose SHAKE512.
- Let the output length be determined by the application.

We have seen proposals for keeping instances with *c*=1024 in SHA-3. We think that claiming or relying on security strength levels above 256 bits is meaningless and that *c*=1024 would induce a significant performance loss, which should be avoided.

This proposal means that SHA-3 standard will offer drop-in primitives with the same security level as SHA-2 (modulo the comment on *c*=1024), but also gives protocol and product designers the possibility to use SHAKE256, which is more efficient and is **in practice** not less secure than SHAKE512 or the drop-ins.

## Contact Information

Email: `keccak`

*-at-*`noekeon`

*-dot-*`org`