Security of the SHA-3 candidates Keccak and Blue Midnight Wish: Zero-sum property

The SHA-3 competition for the new cryptographic standard was initiated by National Institute of Standards and Technology (NIST) in 2007. In the following years, the event grew to one of the top areas currently being researched by the CS and cryptographic communities. The first objective of this thesis is to overview, analyse, and critique the SHA-3 competition. The second one is to perform an in-depth study of the security of two candidate hash functions, the finalist Keccak and the second round candidate Blue Midnight Wish. The study shall primarily focus on zero-sum distinguishers. First we attempt to attack reduced versions of these hash functions and see if any vulnerabilities can be detected. This is followed by attacks on their full versions. In the process, a novel approach is utilized in the search of zero-sum distinguishers by employing SAT solvers. We conclude that while such complex attacks can theoretically uncover undesired properties of the two hash functions presented, such attacks are still far from being fully realized due to current limitations in computing power

Practical consequences of the aberration of narrow-pipe hash designs from ideal random functions

In a recent note to the NIST hash-forum list, the following observation was presented: narrow-pipe hash functions differ significantly from ideal random functions $H:\{0,1\}^{N} \rightarrow \{0,1\}^n$ that map bit strings from a big domain where $N=n+m,\ m\geq n$($n=256$or$n=512$). Namely, for an ideal random function with a big domain space$\{0,1\}^{N}$and a finite co-domain space$Y=\{0,1\}^n$, for every element$y \in Y$, the probability$Pr\{H^{-1}(y) = \varnothing\} \approx e^{-2^{m}} \approx 0$where$H^{-1}(y) \subseteq \{0,1\}^{N}$and$H^{-1}(y) = \{x \ |\ H(x)=y \}$(in words - the probability that elements of$Y$are ``unreachable\u27\u27 is negligible). However, for the narrow-pipe hash functions, for certain values of$N$(the values that are causing the last padded block that is processed by the compression function of these functions to have no message bits), there exists a huge non-empty subset$Y_\varnothing \subseteq Y$with a volume$|Y_\varnothing|\approx e^{-1}|Y|\approx 0.36 |Y|$for which it is true that for every$y \in Y_\varnothing,\ H^{-1}(y) = \varnothing$. In this paper we extend the same finding to SHA-2 and show consequences of this abberation when narrow-pipe hash functions are employed in HMAC and in two widely used protocols: 1. The pseudo-random function defined in SSL/TLS 1.2 and 2. The Password-based Key Derivation Function No.1, i.e. PBKDF1

Generic Collision Attacks on Narrow-pipe Hash Functions Faster than Birthday Paradox, Applicable to MDx, SHA-1, SHA-2, and SHA-3 Narrow-pipe Candidates

In this note we show a consequence of the recent observation that narrow-pipe hash designs manifest an abberation from ideal random functions for finding collisions for those functions with complexities much lower than the so called generic birthday paradox lower bound. The problem is generic for narrow-pipe designs including classic Merkle-Damgard designs but also recent narrow-pipe SHA-3 candidates. Our finding does not reduces the generic collision security of n/2 bits that narrow-pipe functions are declaring, but it clearly shows that narrow-pipe designs have a property when we count the calls to the hash function as a whole, the birthday paradox bound of 2^{n/2} calls to the hash function is clearly broken. This is yet another property in a series of similar non-ideal random properties (like HMAC or PRF constructions) that narrow-pipe hash function manifest and that are described in [1] and [2]

Generic Related-key Attacks for HMAC

In this article we describe new generic distinguishing and forgery attacks in the related-key scenario (using only a single related-key) for the HMAC construction. When HMAC uses a k-bit key, outputs an n-bit MAC, and is instantiated with an l-bit inner iterative hash function processing m-bit message blocks where m=k, our distinguishing-R attack requires about 2^{n/2} queries which improves over the currently best known generic attack complexity 2^{l/2} as soon as l>n. This means that contrary to the general belief, using wide-pipe hash functions as internal primitive will not increase the overall security of HMAC in the related-key model when the key size is equal to the message block size. We also present generic related-key distinguishing-H, internal state recovery and forgery attacks. Our method is new and elegant, and uses a simple cycle-size detection criterion. The issue in the HMAC construction (not present in the NMAC construction) comes from the non-independence of the two inner hash layers and we provide a simple patch in order to avoid this generic attack. Our work finally shows that the choice of the opad and ipad constants value in HMAC is important

Design and Analysis of Cryptographic Hash Functions

Wydział Matematyki i InformatykiKryptograficzne funkcje haszujące stanowią element składowy wielu algorytmów kryptograficznych. Przykładowymi zastosowaniami kryptograficznych funkcji haszujących są podpisy cyfrowe oraz kody uwierzytelniania wiadomości. Ich własności kryptograficzne mają znaczący wpływ na poziom bezpieczeństwa systemów kryptograficznych wykorzystujących haszowanie. W dysertacji analizowane są kryptograficzne funkcje haszujące oraz omówione główne zasady tworzenia bezpiecznych kryptograficznych funkcji haszujących. Analizujemy bezpieczeństwo dedykowanych funkcji haszujących (BMW, Shabal, SIMD, BLAKE2, Skein) oraz funkcji haszujących zbudowanych z szyfrów blokowych (Crypton, Hierocrypt-3, IDEA, SAFER++, Square). Głównymi metodami kryptoanalizy użytymi są skrócona analiza różnicowa, analiza rotacyjna i przesuwna. Uzyskane wyniki pokazują słabości analizowanych konstrukcji.Cryptographic Hash Functions (CHFs) are building blocks of many cryptographic algorithms. For instance, they are indispensable tools for efficient digital signature and authentication tags. Their security properties have tremendous impact on the security level of systems, which use cryptographic hashing. This thesis analyzes CHFs and studies the design principles for construction of secure and efficient CHFs. The dissertation investigates security of both dedicated hash functions (BMW, Shabal, SIMD, BLAKE2, Skein) and hash functions based on block ciphers (Crypton, Hierocrypt-3, IDEA, SAFER++, Square). The main cryptographic tools applied are truncated differentials, rotational and shift analysis. The findings show weaknesses in the designs

Improved (Pseudo) Preimage Attacks on Reduced-Round GOST and Grøstl-256 and Studies on Several Truncation Patterns for AES-like Compression Functions (Full Version)

In this paper, we present improved preimage attacks on the reduced-round \texttt{GOST} hash function family, which serves as the new Russian hash standard, with the aid of techniques such as the rebound attack, the Meet-in-the-Middle preimage attack and the multicollisions. Firstly, the preimage attack on 5-round \texttt{GOST-256} is proposed which is the first preimage attack for \texttt{GOST-256} at the hash function level. Then we extend the (previous) attacks on 5-round \texttt{GOST-256} and 6-round \texttt{GOST-512} to 6.5 and 7.5 rounds respectively by exploiting the involution property of the \texttt{GOST} transposition operation. Secondly, inspired by the preimage attack on \texttt{GOST-256}, we also study the impacts of four representative truncation patterns on the resistance of the Meet-in-the-Middle preimage attack against \texttt{AES}-like compression functions, and propose two stronger truncation patterns which make it more difficult to launch this type of attack. Based on our investigations, we are able to slightly improve the previous pseudo preimage attacks on reduced-round \texttt{Grøstl-256}

Toha Key Hardened Function

TOHA is Key Hardened Function designed in the general spirit of sequential memory- hard function which based on secure cryptographic hash function, the idea behind its design is to make it harder for an attacker to perform some generic attacks and to make it costly as well, TOHA can be used for deriving keys from a master password or generating keys with length of 256-bit to be used in other algorithm schemes, general approach is to use a password and a salt like a normal scheme plus other parameters, and you can think of the salt as an index into a large set of keys derived from the same password, and of course you don’t need to hide the salt to operate

On the Security of Iterated Hashing based on Forgery-resistant Compression Functions

In this paper we re-examine the security notions suggested for hash functions, with an emphasis on the delicate notion of second preimage resistance. We start by showing that, in the random oracle model, both Merkle-Damgaard and HAIFA achieve second preimage resistance beyond the birthday bound, and actually up to the level of known generic attacks, hence demonstrating the optimality of HAIFA in this respect. We then try to distill a more elementary requirement out of the compression function to get some insight on the properties it should have to guarantee the second preimage resistance of its iteration. We show that if the (keyed) compression function is a secure FIL-MAC then the Merkle-Damgaard mode of iteration (or HAIFA) still maintains the same level of second preimage resistance. We conclude by showing that this ``new\u27\u27 assumption (or security notion) implies the recently introduced Preimage-Awareness while ensuring all other classical security notions for hash functions

Analysis Design & Applications of Cryptographic Building Blocks

This thesis deals with the basic design and rigorous analysis of cryptographic schemes and primitives, especially of authenticated encryption schemes, hash functions, and password-hashing schemes. In the last decade, security issues such as the PS3 jailbreak demonstrate that common security notions are rather restrictive, and it seems that they do not model the real world adequately. As a result, in the first part of this work, we introduce a less restrictive security model that is closer to reality. In this model it turned out that existing (on-line) authenticated encryption schemes cannot longer beconsidered secure, i.e. they can guarantee neither data privacy nor data integrity. Therefore, we present two novel authenticated encryption scheme, namely COFFE and McOE, which are not only secure in the standard model but also reasonably secure in our generalized security model, i.e. both preserve full data inegrity. In addition, McOE preserves a resonable level of data privacy. The second part of this thesis starts with proposing the hash function Twister-Pi, a revised version of the accepted SHA-3 candidate Twister. We not only fixed all known security issues of Twister, but also increased the overall soundness of our hash-function design. Furthermore, we present some fundamental groundwork in the area of password-hashing schemes. This research was mainly inspired by the medial omnipresence of password-leakage incidences. We show that the password-hashing scheme scrypt is vulnerable against cache-timing attacks due to the existence of a password-dependent memory-access pattern. Finally, we introduce Catena the first password-hashing scheme that is both memory-consuming and resistant against cache-timing attacks