Guido Bertoni^{3}, Joan Daemen^{1,2}, Michaël Peeters^{1}, Gilles Van Assche^{1} and Ronny Van Keer^{1}
^{1}STMicroelectronics - ^{2}Radboud University - ^{3}Security Pattern
Welcome to the web pages of the Keccak Team!
In these pages, you can find information about our different cryptographic schemes and constructions, their specifications, cryptanalysis on them, the ongoing contests and the related scientific papers.
At the rump session of FSE 2018 that took place last week in Brugge, Belgium, we announced the outcome of the Ketje cryptanalysis prize.
There were three submissions:
The first two submissions push the boundaries of cube attacks, or more generally, higher-order differential cryptanalysis of round-reduced Keccak-f. In Ketje, these attacks always target the initialization phase that applies Keccak-p[n_{r}=12] to the concatenation of a key and a nonce. The algebraic degree of Keccak-p[n_{r}], for a small number of rounds, is d=2^{nr}, so a straightforward higher-order differential attack would require a data complexity of 2^{d} chosen input blocks (e.g., for n_{r}=6 rounds, the degree is d=64 and the straightforward data complexity is 2^{64}). By applying some sophisticated tricks, one can peel off one or two rounds resulting in much lower data complexities. The first two submissions achieve this by exploiting specific propagation properties of the round function.
The third submission is the first to attack the encryption/decryption phase of Ketje Jr. In this phase, a known-plaintext attacker gets the value of the first r=16 bits of the state for every round of Keccak-f. Information-theoretically n=200/16=12.5 such blocks would be sufficient to break Ketje by state recovery, but the computational difficulty increases quickly with n. This submission investigates weakened versions of Ketje Jr with increased rates: r=32 and r=40 bits and break the security claim. The attacks confirm that the tweak between Ketje v1 and Ketje v2 results in an increase in safety margin.
These three attacks add to the already substantial amount of cryptanalysis of the Keccak-f permutation in a keyed setting. They enforce the positions of Ketje (and Keyak) as being among the most cryptanalyzed authenticated ciphers.
Given these nice results, we decided to award all three submissions. For practical reasons, the contestants of the first two entries got Belgian chocolates, while those of the latter received Belgian beer.
Everyone's a winner in this contest. Congratulations to all!
We are glad to announce the final version of the Farfalle construction and of the Kravatte pseudo-random function and encryption schemes.
First published in late 2016 on IACR ePrint, an update of our paper Farfalle: parallel permutation-based cryptography was accepted at the journal Transactions on Symmetric Cryptography (ToSC). We will present it at the yearly Fast Software Encryption (FSE) conference in Brugge, Belgium, in March 2018.
In the last couple of months, we applied some changes to both Farfalle and Kravatte^{1}. This was due to prompt third-party cryptanalysis by different researchers. First Ling Song and Jian Guo contacted us with a key recovery cube attack on the (full) previous version of Kravatte. Then a second team of cryptanalysts (who wish to stay anonymous at this point, as their paper is under submission) sent us the description of even more powerful attacks targeting the expansion layer specifically. Consequently, we modified Kravatte by taking 6 rounds for all four permutation instances. And to counteract the attacks of the second team, we made a more fundamental change by adopting a non-linear rolling function in the expansion layer. We realize that switching from a linear rolling function to a non-linear one is a change in philosophy, and we discuss it in the paper.
The optimized code in the KCP and the reference implementation in KeccakTools are in sync.
^{1}To distinguish the latest version of Kravatte from the previous one, we call it Kravatte Achouffe.
If SHA-2 is not broken, why would one switch to SHA-3 and not just stay with SHA-2? In this post, we highlight another argument why Keccak/SHA-3 is a better choice than SHA-2, namely openness, in analogy with open-source versus closed-source in software development and deployment.
Software has two sides: its executable and its source code. The former is used as a black box by the users, while the latter is of interest to developers who want to extend it, to understand its inner workings or to make sure there is no obvious malicious code. As an analogy, we see the specification of the cryptographic primitive, mode or algorithm in a (proposed) cryptographic standard as the counterpart of the software executable: It allows everyone to include the cryptographic object, as is, in his/her project. The counterpart of the source code in cryptography would be the design rationale, preliminary cryptanalysis and evidence of extensive third-party cryptanalysis: These are the elements that give insight into the inner workings and ultimately trust.
The transition of cryptography from a proprietary activity to a scientific one in the last 50 years can be seen as a move from closed-source to open-source in this analogy. Surprisingly, there are exceptions and we still see closed-source cryptography today.
The SHA-1 and SHA-2 NIST standard hash functions were designed behind closed doors at NSA. The standards were put forward in 1995 and 2001 respectively, without public scrutiny of any significance, despite the fact that at time of publication there was already a considerable cryptographic community doing active research on this subject. Even the 2015 update of FIPS 180, the standard that specifies SHA-2, does not contain, nor refer to, a design rationale.
In contrast, SHA-3 is the result of an open call of NIST to the cryptographic community for hash function proposals. There was no restriction on who could participate, so submissions were open in the broadest possible sense. Every submitted candidate algorithm had to contain a description, a design rationale and preliminary cryptanalysis. The authors of the 64 submissions included the majority of people active in open symmetric crypto research at the time. NIST solicited the symmetric crypto community for performing and publishing research in cryptanalysis, implementations, proofs and comparisons of the candidates and based its decision on the results. After a three-round process involving hundreds of people in the community for several years, NIST finally announced that Keccak was selected to become the SHA-3 standard.
The open effort of the symmetric crypto community did not stop there. Since then, Keccak has remained under public scrutiny and new papers appear regularly. Paper after paper confirms the large safety margin of Keccak. What is important, is that these papers reach a high degree of sophistication as research can start from the preliminary cryptanalysis that we provided in our SHA-3 submission document.
It is true that cryptanalysis of MD5, SHA-1 and SHA-2 has also reached a high degree of sophistication. However, this took longer to develop due to the absence of rationale and preliminary cryptanalysis, but also due to the adoption of the ARX design methodology.
SHA-2 is essentially a security patch of SHA-1 while SHA-3 is its open-source alternative, much in the same way that Triple-DES is a security patch for DES and AES the open-source alternative. In retrospect, even if Triple-DES is not broken, would you still recommend not to switch to AES?
If SHA-2 is not broken, why would one switch to SHA-3 and not just stay with SHA-2? There are several arguments why Keccak/SHA-3 is a better choice than SHA-2. In this post, we come back on a particular design choice of Keccak and explain why Keccak is not ARX, unlike SHA-2.
We specified Keccak at the bit-level using only transpositions, bit-level additions and multiplications (in GF(2)). We arranged these operations to allow efficient software implementations using fixed sequences of bitwise Boolean instructions and (cyclic) shifts. In contrast, many designers specify their primitives directly in pseudocode similarly including bitwise Boolean instructions and (cyclic) shifts, but on top of that also additions. These additions are modulo 2^{n} with n a popular CPU word length such as 8, 32 or 64. Such primitives are dubbed ARX that stands for “addition, rotation and exclusive-or (XOR)”. The ARX approach is widespread and adopted by popular designs MD4, MD5, SHA-1, SHA-2, Salsa, ChaCha, Blake(2) and Skein.
So why isn't Keccak following the ARX road? We give some arguments in the following paragraphs.
One of the main selling points of ARX is its efficiency in software: Addition, rotation and XOR usually only take a single CPU cycle. For addition, this is not trivial because the carry bits may need to propagate from the least to the most significant bit of a word. Processor vendors have gone through huge efforts to make additions fast, and ARX primitives take advantage of this in a smart way. When trying to speed up ARX primitives by using dedicated hardware, not so much can be gained, unlike in bit-oriented primitives as Keccak. Furthermore, the designer of an adder must choose between complexity (area, consumption) or gate delay (latency): It is either compact or fast, but not at the same time. A bitwise Boolean XOR (or AND, OR, NOT) does not have this trade-off: It simply take a single XOR per bit and has a gate delay of a single binary XOR (or AND, OR, NOT) circuit. So the inherent computational cost of additions is a factor 3 to 5 higher than that of bitwise Boolean operations.
But even software ARX gets into trouble when protection against power or electromagnetic analysis is a threat. Effective protection at primitive level requires masking, namely, where each sensitive variable is represented as the sum of two (or more) shares and where the operations are performed on the shares separately. For bitwise Boolean operations and (cyclic) shifts, this sum must be understood bitwise (XOR), and for addition the sum must be modulo 2^{n}. The trouble is that ARX primitives require many computationally intensive conversions between the two types of masking.
The cryptographic strength of ARX comes from the fact that addition is not associative with rotation or XOR. However, it is very hard to estimate the security of such primitives. We give some examples to illustrate this. For MD5, it took almost 15 years to be broken while the collision attacks that have finally been found can be mounted almost by hand. For SHA-1, it took 10 years to convert the theoretical attacks of around 2006 into a real collision. More recently, at the FSE 2017 conference in Tokyo, some attacks on Salsa and ChaCha were presented, which in retrospect look trivial but that remained undiscovered for many years.
Nowadays, when a new cryptographic primitive is published, one expects arguments on why it would provide resistance against differential and linear cryptanalysis. Evaluating this resistance implies investigating propagation of difference patterns and linear masks through the round function. In ARX designs, the mere description of such difference propagation is complicated, and the study of linear mask propagation has only barely started, more than 25 years after the publication of MD5.
A probable reason for this is that (crypt)analyzing ARX, despite its merits, is relatively unrewarding in terms of scientific publications: It does not lend itself to a clean mathematical description and usually amounts to hard and ad-hoc programming work. A substantial part of the cryptographic community is therefore reluctant to spend their time trying to cryptanalyze ARX designs. We feel that the cryptanalysis of more structured designs such as Rijndael/AES or Keccak/SHA-3 leads to publications that provide more insight.
But if ARX is really so bad, why are there so many primitives from prominent cryptographers using it? Actually, the most recent hash function in Ronald L. Rivest's MD series, the SHA-3 candidate MD6, made use of only bitwise Boolean instructions and shifts. More recently, a large team including Salsa and ChaCha designer Daniel J. Bernstein published the non-ARX permutation Gimli. Gimli in turn refers to NORX for its design approach, a CAESAR candidate proposed by a team including Jean-Philippe Aumasson and whose name stems from a rather explicit “NO(T A)RX”. Actually, they are moving in the direction where Keccak and its predecessors (e.g., RadioGatún, Noekeon, BaseKing) always were.
So, maybe better skip ARX?
We congratulate Yao Sun^{1} and Ting Li^{1} for solving the 3-round pre-image challenge on Keccak[r=240, c=160].
The previous pre-image challenge on the 400-bit version was solved on 2 rounds by Paweł Morawiecki in 2011. This present challenge was solved by combining brute-force and algebraic techniques. It took 5 days with eight GPU cards (nvidia 1080Ti).