Tunnels in Hash Functions: MD5 Collisions Within a Minute

In this paper we introduce a new idea of tunneling of hash functions. In some sense tunnels replace multi-message modification methods and exponentially accelerate collision search. We describe several tunnels in hash function MD5. Using it we find a MD5 collision roughly in one minute on a standard notebook PC (Intel Pentium, 1.6 GHz). The method works for any initializing value. Tunneling is a general idea, which can be used for finding collisions of other hash functions, such as SHA-1, 2. We show several capabilities of tunnels. A program, which source code is available on a project homepage, experimentally verified the method. Revised version of this paper contains the appendix with the description of more tunnels. These tunnels further decrease the average time of MD5 collision to 31 seconds. On PC Intel Pentium 4 (3,2 GHz) it is 17 seconds in average

Huge Multicollisions and Multipreimages of Hash Functions BLENDER-n

In this paper we present a multicollision and multipreimage attack on the hash function Blender-n [1] for all output sizes n = 224, 256, 384 and 512. The complexity and memory requirements for finding 2^{2n} multipreimages (multicollisions) of Blender-n is roughly 10 times more than finding a collision for n/2-bit random hash function. All previous attacks were based on the trick by Joux [2] using many messages. Our attacks are based on one message with several fixpoints. The state register has eight words. By properly choosing message words we force half of the register to go to the original state. Then we will find a collision in the rest with complexity 2^{n/4}. The collision creates a fix point in the sequence of states of the state register. We use 10 such fix points. Previously known attacks [4, 5] on Blender-n have the complexity at least 2^{n/2}. Our 2^{2n}-multicollision and multipreimage attacks have a complexity 10*2^{n/4}

Finding MD5 Collisions – a Toy For a Notebook

One of the major cryptographic break-through of the recent years was a discovery of collisions for a set of hash functions (MD4, MD5, HAVAL-128, RIPEMD) by the Chinese cryptographers in August 2004 [1]. Their authors (Wang et al.) kept the algorithm secret, however. We have found a way to generate the first message block of the collision about 1000 - 2000 times faster than the Chinese team - that corresponds to reaching the first colliding block in 2 minutes using a common notebook. The same computation phase took the Chinese team about an hour using an IBM P690 supercomputer. On the other hand, the Chinese team was 2 - 80 times faster when computing the second message block of their collisions. Therefore, our and the Chinese methods probably differs in both parts of the computation. Overall, our method is about 3 - 6 times faster. More specifically, finding the first (complete) collision took 8 hours using a notebook PC (Intel Pentium 1.6 GHz). That should be a warning towards persisting usage of MD5. Note that our method works for any initialization vector. In the appendix, we show new examples of collisions for a standard and chosen initialization vectors

Fast Diffusion Block for Secret Key Cryptography

We present a diffusion block (DB), which is extraordinarily fast. After one round, it reaches complete diffusion, which means only 16 memory reads and 15 XOR operations. It uses only the most common operations available in any microprocessor. The diffusion and speed are based on a large key, about 64 kB for encryption and 34 kB for decryption, expanded from the classical key size of 128, 256, or more bits. The basic block length is 128 bits and could be expanded to 192, 256, or more. DB uses the same core idea as uses AES, DES, and others, which has been studied for more than 50 years by many cryptanalysts

Attack on Private Signature Keys of the OpenPGP Format, PGP(TM) Programs and Other Applications Compatible with OpenPGP

The article describes an attack on OpenPGP format, which leads to disclosure of the private signature keys of the DSA and RSA algorithms. The OpenPGP format is used in a number of applications including PGP, GNU Privacy Guard and other programs specified on the list of products compatible with OpenPGP, which is available at http://www.pgpi.org/products. Therefore all these applications must undergo the same revision as the actual program PGP. The success of the attack was practically verified and demonstrated on the PGP program, version 7.0.3 with a combination of AES and DH/DSS algorithms. As the private signature key is the basic information of the whole system which is kept secret, it is encrypted using the strong cipher. However, it shows that this protection is illusory, as the attacker has neither to attack this cipher nor user´s secret passphrase. A modification of the private key file in a certain manner and subsequent capturing of one signed message is sufficient for successful attack. Insufficient protection of the integrity of the public as well as private parts of signature keys in the OpenPGP format is analyzed in DSA and RSA algorithms and on the basis of this, a procedure of attacks is shown on both private signature keys. The attacks apply to all lengths of parameters (modules, keys) of RSA and DSA. In the end the cryptographic measures for correction of the OpenPGP format as well as PGP format are proposed

A Note on Linear Approximations of BLUE MIDNIGHT WISH Cryptographic Hash Function

Abstract. BLUE MIDNIGHT WISH hash function is the fastest among 14 algorithms in the second round of SHA-3 competition [1]. At the beginning of this round authors were invited to add some tweaks before September 15th 2009. In this paper we discuss the tweaked version (BMW). The BMW algorithm [3] is of the type AXR, since it uses only operations ADD (sub), XOR and ROT (shift). If we substitute the operation ADD with operation XOR, we get a BMWlin, which is an affine transformation. In this paper we consider only a BMWlin function and its building blocks. These affine transformations can be represented as a linear matrix and a constant vector. We found that all matrices of main blocks of BMWlin have a full rank, or they have a rank very close to full rank. The structure of matrices was examined. Matrices of elementary blocks have an expected non-random structure, while main blocks have a random structure. We will also show matrices for different values of security parameter ExpandRounds1 (values between 0 and 16). We observed that increasing the number of rounds ExpandRounds1 tends to increase randomness as was intended by designers. These observations hold for both BMW256lin and BMW512lin. In this analysis we did not find any useful property, which would help in cryptanalysis, nor did we find any weaknesses of BMW. The study of all building blocks will follow

Side Channel Attacks on CBC Encrypted Messages in the PKCS#7 Format

Vaudenay has shown in [5] that a CBC encryption mode ([2], [9]) combined with the PKCS#5 padding [3] scheme allows an attacker to invert the underlying block cipher, provided she has access to a valid-padding oracle which for each input ciphertext tells her whether the corresponding plaintext has a valid padding or not. Having on mind the countermeasures against this attack, different padding schemes have been studied in [1]. The best one is referred to as the ABYT-PAD. It is designed for byte-oriented messages. It removes the valid-padding oracle, thereby defeating Vaudenay\u27s attack, since all deciphered plaintexts are valid in this padding scheme. In this paper, we try to combine the well-known cryptographic message syntax standard PKCS#7 [8] with the use of ABYT-PAD instead of PKCS#5. Let us assume that we have access to a PKCS#7CONF oracle that tells us for a given ciphertext (encapsulated in the PKCS#7 structure) whether the deciphered plaintext is correct or not according to the PKCS#7 (v1.6) syntax. This is probably a very natural assumption, because applications usually have to reflect this situation in its behavior. It could be a message for the user, an API error message, an entry in the log file, different timing behavior, etc. We show that access to such an oracle again enables an attacker to invert the underlying block cipher. The attack requires single captured ciphertext and approximately 128 oracle calls per one ciphertext byte. It shows that we cannot hope to fully solve problems with side channel attacks on the CBC encryption mode by using a “magic” padding method or an obscure message-encoding format. Strong cryptographic integrity checks of ciphertexts should be incorporated instead

Strengthened Encryption in the CBC Mode

Vaudenay [1] has presented an attack on the CBC mode of block ciphers, which uses padding according to the PKCS#5 standard. One of the countermeasures, which he has assumed, consisted of the encryption of the message M´= M || padding || hash(M || padding) instead of the original M. This can increase the length of the message by several blocks compared with the present padding. Moreover, Wagner [1] showed a security weakness in this proposal. The next correction, which Vaudenay proposed ( A Fix Which May Work ) has a general character and doesn\u27t solve practical problems with the real cryptographic interfaces used in contemporary applications. In this article we propose three variants of the CBC mode. From the external point of view they behave the same as the present CBC mode with the PKCS#5 padding, but they prevent Vaudenay\u27s attack

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]

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