Weak Keys Research Articles

ROTATIONAL CRYPTANALYSIS OF GOST WITH IDENTICAL S-BOXES

ABSTRACT Rotational cryptanalysis was introduced by Khovratovich and Nikoli ´c as a tool to analyse ARX-type cipher designs. GOST 28147-89 is a former Soviet Union cipher standard based on a Feistel construction with 32 rounds. Each round function adds the round key modulo 232, transforms the result with 4-to-4 bit S-boxes, and rotates the output. We apply the rotational cryptanalysis to a version of GOST using eight identical S-boxes, such as GOST-PS. We show the existence of (practical) rotational distinguisher in related key model for full GOST. Furthermore, there is a set of weak keys (rotationally symmetric keys) that enables rotational attacks in single-key model as well. Finally, we show a simple attack on the last round that uses the rotational distinguisher to reduce the complexity of the full GOST to 208 bits.

Square reflection cryptanalysis of 5-round Feistel networks with permutations

In this work, we introduce a new generic attack on 5-round Feistel networks whose round functions are random permutations, under the condition that the second and the fourth round keys are equal. The attack is a combination of the square attack technique with the reflection attack technique and exploits the unbalanced distribution of the fixed points of the inner rounds among all the keys. The data complexity of the attack is ⌈4mn⌉2n/2 chosen plaintexts where ⌈4mn⌉ is the smallest integer bigger than or equal to 4mn, m is the length of a round key and n is the block length of the Feistel network. We utilize Hellman tables to construct a tradeoff between the time complexity and the memory complexity of the attack which are 23m−2M−1 and 2M respectively where M is the tradeoff parameter. The number of weak keys is 2k−m where k is the key length. As a concrete example, we mount the attack on 5-round DEAL. Our attack has overall complexity of 265 and works on a key set of cardinality 272 for 128-bit key length.

Full analysis of PRINTcipher with respect to invariant subspace attack: efficient key recovery and countermeasures

In this paper we investigate the invariant property of PRINTcipher initially discovered by Leander et al. in their CRYPTO 2011 paper. We provide a complete study of the attack and show that there exist 64 families of weak keys for PRINTcipher---48 and as many as 115,669 for PRINTcipher---96. Moreover, we show that searching the weak key space may be substantially sped up by splitting the search process into two consecutive steps. We show that for many classes of weak keys, key recovery can be done with very small time complexity in the chosen/known plaintext scenario. In fact, at least $$2^{45}$$ 2 45 weak keys can be recovered in less than 10 s per key on a single PC. Still, effective countermeasures exist against the attack. On the methodological level, the method of finding all weak key families has value on its own. It is based on Mixed Integer Linear Programming and can be adapted to solving other interesting problems on similar ciphers.

An Effective and Secure Cipher Based on SDDO

To improve the efficiency of security of the information secure mechanism, an algorithm BMD-128 is proposed. This algorithm is built on the SDDO. Using this operator decreases significanthy the cost of hardware implementation. Besides, it also ensures both the high applicability in the transaction needing the change of session keys with high frequency and the ability against slide attack. Concurrently, this algorithm also eliminates the weak keys without the complex round key proceduce. The algorithm is evaluated regards to the standard NESSIE and the ability against the differential cryptanalysis. Concurrently, it is also compared the performance with the other famous ciphers when implementing on hardware FPGA.

Cryptographic Properties of BOMM

BOMM is a byte-oriented mixed type algorithm with memory,which is used to disorder a given byte sequence.It has been used as a main component in a new stream cipher called Loiss for having many good cryptographic properties.This paper builds an algebraic equation system with degree 5 for BOMM,and based on this equation system,discusses the complexity of algebraic attack on Loiss.In addition,the paper also discusses the statistic weakness of BOMM and gives an analysis of the security of Loiss under a specific class of weak keys.

On the security of the block cipher GOST suitable for the protection in U-business services

The paper revisits the security of the block cipher GOST, which is suitable for the protection in U-business services due to its simple design. Inspired from the reflection-meet-in-the-middle attack on GOST, we firstly find a large portion of weak keys on the full GOST: GOST has 2128 weak keys in which key recovery attack is mounted with a data complexity of 232 known plaintexts and a time complexity of 2125.5. Secondly, we present a differential fault attack on the full GOST, which required 64 fault injections to recover the entire key. This is the first known side-channel attack on GOST.

Study on the security of the extended version for the ISO/IEC international standardized block cipher SEED

ABSTRACTIn this paper, we analyze the block cipher SEED‐192, which is an extended version of the ISO/IEC block cipher SEED. According to the result of this paper, there exist weak keys in 8 out of the 20 rounds of SEED‐192 against related‐key differential attacks, and there exist weak keys in 16 out of the 20 rounds of SEED‐192 against related‐key rectangle/boomerang attacks. This is the first cryptanalytic result for the key schedule of SEED‐192. Copyright © 2012 John Wiley & Sons, Ltd.

Weak Keys in RSA over The Work of Blomer & May

In this paper we generalize the idea given by Weger and Maitra & Sarkar. This generalization is coming from the concept of x9.31-1997 standard for public key cryptography, Section 4:1:2, i.e., there are a number of recommendations for the generalization of the primes of an RSA modulus. Among them, the ratio of the primes shall not be close to the ratio of small integers. Also we try to improve the range of weak keys of RSA cryptosystem for the Generalized Wiener's attack given by Blomer & May. We have shown that the range of weak keys can be extended by more than 8 times than the range given by Blomer & May. Further we have shown that for |ap - bq| ≤ N(superscript (α/2)) where 0 ＜α≤ 1, if e satisfies an equation ex + y = m∅(N), for m ＞ 0. Then N can be factored in( O poly(logN)) times when 0 ＜ x ≤ 1/6√∅ (N)/e N(superscript (1/2 -α/4)) and |y|≤ |ap - bq|/∅(N)N(superscript (1/4) ex.

Weak key analysis for chaotic cipher based on randomness properties

Weak key analysis is a key issue in the design of chaotic ciphers. While most of the existing research focusing on the degradation of the chaotic sequences which causes weak keys, we point out that the parameters for which the chaotic sequences do not degrade are still possible to be weak keys. In this paper, we propose a new approach based on the rigorous statistical test to improve the weak key analysis. The weak keys of a specific chaotic cipher are investigated by using our method and a large number of new weak keys are detected. These results verify that our method is more effective. On the other hand, although statistical tests are now widely adopted to test the chaos-based bit sequences, there are few reports of analysis results on the weak keys or weak sequences of chaotic cipher. Thus our work may be helpful for current research on statistical tests of chaotic cipher.

A Single-Key Attack on the Full GOST Block Cipher

The GOST block cipher is the Russian encryption standard published in 1989. In spite of considerable cryptanalytic efforts over the past 20 years, a key recovery attack on the full GOST block cipher without any key conditions (e.g., weak keys and related keys) has not been published yet. In this paper, we show the first single-key attack, which works for all key classes, on the full GOST block cipher. To begin, we develop a new attack framework called Reflection-Meet-in-the-Middle Attack. This approach combines techniques of the reflection attack and the meet-in-the-middle (MITM) attack. Then we apply it to the GOST block cipher employing bijective S-boxes. In order to construct the full-round attack, we use additional novel techniques which are the effective MITM techniques using equivalent keys on a small number of rounds. As a result, a key can be recovered with a time complexity of 2225 encryptions and 232 known plaintexts. Moreover, we show that our attack is applicable to the full GOST block cipher using any S-boxes, including non-bijective S-boxes.

A family of weak keys in HFE and the corresponding practical key-recovery

The HFE (hidden field equations) cryptosystem is one of the most interesting public-key multivariate schemes. It has been proposed more than 10 years ago by Patarin and seems to withstand the attacks that break many other multivariate schemes, since only subexponential ones have been proposed. The public key is a system of quadratic equations in many variables. These equations are generated from the composition of the secret elements: two linear mappings and a polynomial of small degree over an extension field. In this paper we show that there exist weak keys in HFE when the coefficients of the internal polynomial are defined in the ground field. In this case, we reduce the secret key recovery problem to an instance of the Isomorphism of Polynomials (IP) Problem between the equations of the public key and themselves. Even though the hardness of recovering the secret-key of schemes such as SFLASH or relies on the hardness of the IP Problem, this is normally not the case for HFE, since the internal polynomial is kept secret. However, when a weak key is used, we show how to recover all the components of the secret key in practical time, given a solution to an instance of the IP Problem. This breaks in particular a variant of HFE proposed by Patarin to reduce the size of the public key and called the “subfield variant”. Recovering the secret key takes a few minutes.

An Improved Image Encryption Algorithm Based on a New Two-Dimensional Map

The paper analyzes a symmetric image encryption scheme based on a new chaotic two-dimensional map. The map can encrypt image. The numbers of the left-map and the right-map are used as the secret keys of encryption. A diffusion mechanism was used to diffuse the pixels of image. But it isn’t enough safe. Firstly there are a lot of week keys and duplicate keys. Secondly the diffusion mechanism is too simple to ensure the information security. The paper designs a new method of keys generation. The keys are non-zero and random. It has a large keys space and avoids the duplicate keys. Then it takes parts of keys as the parameters of a classic chaotic map. The process is the new diffusion mechanism. It solves the problem of weak keys. Simulation results show the effectiveness of the method.

Towards formal analysis of wireless LAN security with MIS protocol

In 2004, the MIS and MISAUTH protocols (shortly MISP) were proposed for secure and fast connection in Wireless LAN (WLAN). Since then, several studies were conducted to evaluate MISP. However, because of the lack of formal security analysis, the security measures provided by them cannot be trusted to be precise and reasonable. Motivated by this, we formally analyse MISP based on both BAN-logic and the Automated Validation of Internet Security Protocols and Applications (AVISPAS) tool. This analysis clearly shows that MISP suffers from weak Session Key (SK) while being vulnerable to Denial of Service (DoS) attack. We discuss these weaknesses and related attacks in detail, and also provide considerable comments for implementation of MISP.

Generalized Classes of Weak Keys on RC4 Using Predictive State

Conventional class of weak keys on RC4 stream cipher is defined as a specific case that combinations of the first three bytes of secret key satisfy two relational equations. This paper expands and generalizes the classes of weak keys using generalized relational equations and special classes of the internal state (called predictive state). We derive the probability that generalized classes of weak keys leak the information of bytes of the secret key. Furthermore, we enumerate the generalized classes of weak keys and show that most of them leak more information of the secret key than Roos' one.

Cryptanalysis on a parallel keyed hash function based on chaotic neural network

In this paper, we analyze the security of a parallel keyed hash function based on chaotic neural network proposed by Xiao et al. recently. Weak keys and forgery attacks against Xiao et al.’s scheme are demonstrated. Both theoretical analysis and experimental results show that the parallel keyed hash function is not security. Besides, some improvement measures are presented to enhance the security of the parallel keyed hash function.

Several short periodic trajectories of TD-ERCS and their stabilities

TD-ERCS is a class of chaotic system designed for chaos encryption.Though it has good encryption properties such as being chaotic in all fields for encryption,Tangent-Delay Ellipse Reflecting Cavity map System(TD-ERCS)is comprises of quite a lot of short cycling trajectories,which may lead to weak keys.Power spectrum analysis and Lyapunov calculation of the periodic trajectories indicated that the periodic trajectories were stable under tangent-delay operation m=0 and instable under tangent-delay operation m≥1.And the instability was independent of parameter μ,TD-ERCS tended from order to chaos under tangent-delay operation.The results show that TD-ERCS does not have weak keys caused by the stable short-period Trajectories.

Fast certificate-based authentication scheme in multi-operator maintained wireless mesh networks

In this paper, we consider QoS aware mesh networks that are maintained by multiple operators and they cooperate in the provision of networking services to the mesh clients. In order to support mobile users and seamless handover between the access points, the authentication delay has to be reduced. Many proposed fast authentication schemes rely on trust models that are not appropriate in a multi-operator environment. In this paper, we propose two certificate-based authentication schemes such that the authentication is performed locally between the access point and the mesh client. We assume that the access point is always a constrained device, and we propose different mechanisms for mesh clients with different computational performance. For constrained devices, we propose a mechanism where weak keys are used for digital signatures to decrease the latency of the authentication. The authenticity of the weak keys are provided by short-term certificates issued by the owner of the key. The short-term certificate has the digital signature generated by the owner’s long-term key. We prove formally that the use of our weak key mechanism on the mesh client side is as secure as the use of some stronger keys. We perform a detailed performance evaluation on our proof-of-concept implementation, and we also compare our solution to the current standard methods.

Cryptanalysis on a parallel keyed hash function based on chaotic maps

This Letter analyzes the security of a novel parallel keyed hash function based on chaotic maps, proposed by Xiao et al. to improve the efficiency in parallel computing environment. We show how to devise forgery attacks on Xiao's scheme with differential cryptanalysis and give the experiment results of two kinds of forgery attacks firstly. Furthermore, we discuss the problem of weak keys in the scheme and demonstrate how to utilize weak keys to construct collision.

Some remarks on the TKIP key mixing function of IEEE 802.11i

Temporal key integrity protocol (TKIP) is a sub-protocol of IEEE 802.11i. TKIP remedies some security flaws in wired equivalent privacy (WEP) protocol. TKIP adds four new algorithms to WEP: a message integrity code (MIC) called Michael, an initialization vector (IV) sequencing discipline, a key mixing function and a re-keying mechanism. The key mixing function, also called temporal key hash, de-correlates the IVs from weak keys. Some cryptographic properties of the substitution box (S-box) used in the key mixing function are investigated in this paper, such as regularity, avalanche effect, differ uniform and linear structure. Moen et al pointed out that there existed a temporal key recovery attack in TKIP key mixing function. In this paper a method is proposed to defend against the attack, and the resulting effect on performance is discussed.

Cryptanalysis of RSA for a special case with d >e

In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N0.258 ⩽ e ⩽ N0.854, d > e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee’s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.