Denying Collision In The Second Round Of Keccak Hash Function By Camouflaging Free Bits

Keccak Hash Function is the winner of SHA3 competition. Hash function collision has become one of the fundamental problem in Keccak Hash Function. One of the attack which is based on collision has been proposed by Plasencia, et.al. They proposed the practical analysis of reduced round Keccak Hash Function, such that the collision will be found in the second round of Keccak-224. For preventing Keccak Hash Function against Plasencia attack, denying collision in the second round is necessary. Denying the collision of Keccak Hash Function has become one challenge. Since the attacker used free bit for finding the collision, then for preventing against the attack the free bit camouflaging should be conducted. Therefore, for denying the collision in the second round of Keccak Hash Function, free bit camouflaging is proposed. Free bits are used to find the original message that is caused by the collision. For denying the collision, the proposed method modifies the input message by using reverse interleaving scheme. This scheme introduces inverse double mirror image sequence of a message to prevent the attacker in obtaining the original free bits. Based on the experiment, it has been proven that using reverse interleaving, the attacker obtained the camouflaged free bit instead of the original one. The camouflaged free bit will increase the difficulty for finding the collision such that the collision could not be found in the second round. This condition will prevent the attacker for finding the original message. The larger the difference would increase the complexity of attack on Keccak Hash Function in obtaining the original message

Cryptographic Applications of the Duplex Construction

Assured security is the desirable feature of modern cryptography. Most of moderncryptography primitives have no provably secure constructions. Their safety is defined on the basis ofwell-known in the given time cryptanalytic attacks. The duplex construction equipped with one idealpermutation and appropriate security parameters is suitable for building provably secure cryptographicprimitives. The constructions can be used for unclassified information of different sensitivity levelsprotection. Some of them can secure classified information up to the TOP SECRET level. Theapplications based on the duplex construction can be used for key wrapping, authenticated encryptionand can work as a pseudo-random bit sequence generator. They are not covered by any knownintellectual property

TurboSHAKE

In a recent presentation, we promoted the use of 12-round instances of Keccak, collectively called “TurboSHAKE”, in post-quantum cryptographic schemes, but without defining them further. The goal of this note is to fill this gap: The definition of the TurboSHAKE family simply consists in exposing and generalizing the primitive already defined inside KangarooTwelve

Practical Complexity Cube Attacks on Round-Reduced Keccak Sponge Function

In this paper we mount the cube attack on the Keccak sponge function. The cube attack, formally introduced in 2008, is an algebraic technique applicable to cryptographic primitives whose output can be described as a low-degree polynomial in the input. Our results show that 5- and 6-round Keccak sponge function is vulnerable to this technique. All the presented attacks have practical complexities and were verified on a desktop PC

Preimage attacks on the round-reduced Keccak with the aid of differential cryptanalysis

In this paper we use differential cryptanalysis to attack the winner of the SHA-3 competition, namely Keccak hash function. Despite more than 6 years of intensive cryptanalysis there have been known only two preimage attacks which reach 3 (or slightly more) rounds. Our 3-round preimage attack improves the complexity of those two existing attacks and it is obtained with a different technique. We also show the partial preimage attack on the 4-round Keccak, exploiting two properties of the linear step of the Keccak-f permutation

On the Multi-output Filtering Model and Its Applications

In this paper, we propose a novel technique, called multi-output filtering model, to study the non-randomness property of a cryptographic algorithm such as message authentication codes and block ciphers. A multi-output filtering model consists of a linear feedback shift register (LFSR) and a multi-output filtering function. Our contribution in this paper is twofold. First, we propose an attack technique under IND-CPA using the multi-output filtering model. By introducing a distinguishing function, we theoretically determine the success rate of this attack. In particular, we construct a distinguishing function based on the distribution of the linear complexity of component sequences, and apply it on studying \T\u27s $f_1$ algorithm, \AES, \Kasumi and \Present. We demonstrate that the success rate of the attack on \Kasumi and \Present is non-negligible, but $f_1$ and \AES are resistant to this attack. Second, we study the distribution of the cryptographic properties of component functions of a random primitive in the multi-output filtering model. Our experiments show some non-randomness in the distribution of algebraic degree and nonlinearity for \Kasumi

Preimage Attacks on the Round-reduced Keccak with Cross-linear Structures

In this paper, based on the work pioneered by Aumasson and Meier, Dinur et al., and Guo et al., we construct some new delicate structures from the roundreduced versions of Keccakhash function family. The new constructed structures are called cross-linear structures, because linear polynomials appear across in different equations of these structures. And we apply cross-linear structures to do preimage attacks on some instances of the round-reduced Keccak. There are three main contributions in this paper. First, we construct a kind of cross-linear structures by setting the statuses carefully. With these cross-linear structures, guessing the value of one linear polynomial could lead to three linear equations (including the guessed one). Second, for some special cases, e.g. the 3-round Keccakchallenge instance Keccak[r=240, c=160, nr=3], a more special kind of cross-linear structures is constructed, and these structures can be used to obtain seven linear equations (including the guessed) if the values of two linear polynomials are guessed. Third, as applications of the cross-linear structures, we practically found a preimage for the 3-round KeccakChallenge instance Keccak[r=240, c=160, nr=3]. Besides, by constructing similar cross-linear structures, the complexity of the preimage attack on 3-round Keccak-256/SHA3-256/SHAKE256 can be lowered to 2150/2151/2153 operations, while the previous best known result on Keccak-256 is 2192

Internal Differential Boomerangs: Practical Analysis of the Round-Reduced Keccak-f Permutation

We introduce internal differential boomerang distinguisher as a combination of internal differentials and classical boomerang distinguishers. The new boomerangs can be successful against cryptographic primitives having high-probability round-reduced internal differential characteristics. The internal differential technique, which follow the evolution of differences between parts of the state, is particularly meaningful for highly symmetric functions like the inner permutation Keccak-f of the hash functions defined in the future SHA-3 standard. We find internal differential and standard characteristics for three to four rounds of Keccak-f, and with the use of the new technique, enhanced with a strong message modification, show practical distinguishers for this permutation. Namely, we need $2^{12}$ queries to distinguish 7 rounds of the permutation starting from the first round, and approximately $2^{18}$ queries to distinguish 8 rounds starting from the fourth round. Due to the exceptionally low complexities, all of our results have been completely verified with a computer implementation of the analysis

Linear Structures: Applications to Cryptanalysis of Round-Reduced Keccak

In this paper, we analyze the security of round-reduced versions of the Keccak hash function family. Based on the work pioneered by Aumasson and Meier, and Dinur et al., we formalize and develop a technique named linear structure, which allows linearization of the underlying permutation of Keccak for up to 3 rounds with large number of variable spaces. As a direct application, it extends the best zero-sum distinguishers by 2 rounds without increasing the complexities. We also apply linear structures to preimage attacks against Keccak. By carefully studying the properties of the underlying Sbox, we show bilinear structures and find ways to convert the information on the output bits to linear functions on input bits. These findings, combined with linear structures, lead us to preimage attacks against up to 4-round Keccak with reduced complexities. An interesting feature of such preimage attacks is low complexities for small variants. As extreme examples, we can now find preimages of 3-round SHAKE128 with complexity 1, as well as the first practical solutions to two 3-round instances of Keccak challenge. Both zero-sum distinguishers and preimage attacks are verified by implementations. It is noted that the attacks here are still far from threatening the security of the full 24-round Keccak

Differential Fault Analysis of SHA-3 under Relaxed Fault Models

Keccak-based algorithms such as Secure Hash Algorithm-3 (SHA-3) will be widely used in crypto systems, and evaluating their security against different kinds of attacks is vitally important. This paper presents an efficient differential fault analysis (DFA) method on all four modes of SHA-3 to recover an entire internal state, which leads to message recovery in the regular hashing mode and key retrieval in the message authentication code (MAC) mode. We adopt relaxed fault models in this paper, assuming the attacker can inject random single-byte faults into the penultimate round input of SHA-3. We also propose algorithms to find the lower bound on the number of fault injections needed to recover an entire internal state for the proposed attacks. Results show that on average the attacker needs about 120 random faults to recover an internal state, while he needs 17 faults at best if he has control of the faults injected. The proposed attack method is further extended for systems with input messages longer than the bitrate