A chosen key attack against the secret S-boxes of GOST

I am making this work from August 1998 available for historical reasons. It has been cited as an ``unpublished manuscript\u27\u27 more than two dozen times over the years -- even though it has not been publicly available anywhere for almost 20 years. The short memo describes a simple non-intrusive reverse engineering technique against Russian GOST chips. The technique is based on a slide attack. This may be historically interesting since slide attacks had not been ``invented yet\u27\u27, at least in formal sense. The brief original abstract: We show that a simple ``black box\u27\u27 chosen-key attack against GOST can recover secret S-boxes with approximately $2^{32}$ encryptions

Security Evaluation of GOST 28147-89 In View Of International Standardisation

GOST 28147-89 is is a well-known 256-bit block cipher which is a plausible alternative for AES-256 and triple DES, which however has a much lower implementation cost. GOST is implemented in standard crypto libraries such as OpenSSL and Crypto++ and is increasingly popular and used also outside its country of origin and on the Internet. In 2010 GOST was submitted to ISO, to become a worldwide industrial encryption standard. Until 2011 researchers unanimously agreed that GOST could or should be very secure, which was summarized in 2010 in these words: despite considerable cryptanalytic efforts spent in the past 20 years, GOST is still not broken . Unhappily, it was recently discovered that GOST can be broken and is a deeply flawed cipher. There is a very considerable amount of recent not yet published work on cryptanalysis of GOST known to us. One simple attack was already presented in February at FSE 2011. In this short paper we describe another attack, to illustrate the fact that there is now plethora of attacks on GOST, which require much less memory, and don\u27t even require the reflection property to hold, without which the recent attack from FSE 2011 wouldn\u27t work. We are also aware of many substantially faster attacks and of numerous special even weaker cases. These will be published in appropriate peer-reviewed cryptography conferences but we must warn the ISO committees right now. More generally, our ambition is to do more than just to point out that a major encryption standard is flawed. We would like to present and suggest a new general paradigm for effective symmetric cryptanalysis of so called Algebraic Complexity Reduction which in our opinion is going to structure and stimulate substantial amounts of academic research on symmetric cryptanalysis for many years to come. In this paper we will explain the main ideas behind it and explain also the precise concept of Black-box Algebraic Complexity Reduction . This new paradigm builds on many already known attacks on symmetric ciphers, such as fixed point, slide, involution, cycling, reflection and other self-similarity attacks but the exact attacks we obtain, could never be developed previously, because only in the recent 5 years it became possible to show the existence of an appropriate last step for many such attacks, which is a low data complexity software algebraic attack. This methodology leads to a large number of new attacks on GOST, way more complex, better and more efficient than at FSE 2011. One example of such an attack is given in the present paper

Differential Cryptanalysis of GOST

GOST 28147-89 is a well-known block cipher and the official encryption standard of the Russian Federation. A 256-bit block cipher considered as an alternative for AES-256 and triple DES, having an amazingly low implementation cost and thus increasingly popular and used. Until 2010 researchers unanimously agreed that: despite considerable cryptanalytic efforts spent in the past 20 years, GOST is still not broken and in 2010 it was submitted to ISO 18033 to become a worldwide industrial encryption standard. In 2011 it was suddenly discovered that GOST is insecure on more than one account. There is an amazing variety of recent attacks on GOST. We have reflection attacks, attacks with double reflection, and various attacks which does not use reflections. All these methods follow a certain general framework called Algebraic Complexity Reduction , a new general umbrella paradigm. The final key recovery step is in most cases a software algebraic attack and sometimes a Meet-In-The-Middle attack. In this paper we show that GOST is NOT SECURE even against (advanced forms of) differential cryptanalysis (DC). Previously Russian researchers postulated that GOST will be secure against DC for as few as 7 rounds out of 32 and Japanese researchers were already able to break about 13 rounds. In this paper we show a first advanced differential attack faster than brute force on full 32-round GOST. This paper is just a sketch and a proof of concept. More results of this kind will be published soon

Efficient Slide Attacks

The slide attack, presented in 1999 by Biryukov and Wagner, has already become a classical tool in cryptanalysis of block ciphers. While it was used to mount practical attacks on a few cryptosystems, its practical applicability is limited, as typically, its time complexity is lower bounded by $2^n$ (where $n$ is the block size). There are only a few known scenarios in which the slide attack performs better than the $2^n$ bound. In this paper we concentrate on {\it efficient} slide attacks, whose time complexity is less than $2^n$. We present a number of new attacks that apply in scenarios in which previously known slide attacks are either inapplicable, or require at least $2^n$ operations. In particular, we present the first known slide attack on a Feistel construction with a {\it 3-round} self-similarity, and an attack with practical time complexity of $2^{40}$ on a 128-bit key variant of the GOST block cipher with {\it unknown} S-boxes. The best previously known attack on the same variant, with {\it known} S-boxes (by Courtois, 2014), has time complexity of $2^{91}$

Practical-Time Related-Key Attack on GOST with Secret S-boxes

The block cipher GOST 28147-89 was the Russian Federation encryption standard for over 20 years, and is still one of its two standard block ciphers. GOST is a 32-round Feistel construction, whose security benefits from the fact that the S-boxes used in the design are kept secret. In the last 10 years, several attacks on the full 32-round GOST were presented. However, they all assume that the S-boxes are known. When the S-boxes are secret, all published attacks either target a small number of rounds, or apply for small sets of weak keys. In this paper we present the first practical-time attack on GOST with secret S-boxes. The attack works in the related-key model and is faster than all previous attacks in this model which assume that the S-boxes are known. The complexity of the attack is less than $2^{27}$ encryptions. It was fully verified, and runs in a few seconds on a PC. The attack is based on a novel type of related-key differentials of GOST, inspired by local collisions. Our new technique may be applicable to certain GOST-based hash functions as well. To demonstrate this, we show how to find a collision on a Davies-Meyer construction based on GOST with an arbitrary initial value, in less than $2^{10}$ hash function evaluations

Cryptanalysis of Dedicated Cryptographic Hash Functions

In this thesis we study the security of a number of dedicated cryptographic hash functions against cryptanalytic attacks. We begin with an introduction to what cryptographic hash functions are and what they are used for. This is followed by strict definitions of the security properties often required from cryptographic hash functions. FSB hashes are a class of hash functions derived from a coding theory problem. We attack FSB by modeling the compression function of the hash by a matrix in GF(2). We show that collisions and preimages can easily be found in FSB with the proposed security parameters. We describe a meet-in-the-middle attack against the FORK-256 hash function. The attack requires 2^112.8 operations to find a collision, which is a 38000-fold improvement over the expected 2^128 operations. We then present a method for finding slid pairs for the compression function of SHA-1; pairs of inputs and messages that produce closely related outputs in the compression function. We also cryptanalyse two block ciphers based on the compression function of MD5, MDC-MD5 and the Kaliski-Robshaw "Crab" encryption algorithm. VSH is a hash function based on problems in number theory that are believed to be hard. The original proposal only claims collision resistance; we demonstrate that VSH does not meet the other hash function requirements of preimage resistance, one-wayness, and collision resistance of truncated variants. To explore more general cryptanalytic attacks, we discuss the d-Monomial test, a statistical test that has been found to be effective in distinguishing iterated Boolean circuits from real random functions. The test is applied to the SHA and MD5 hash functions. We present a new hash function proposal, LASH, and its initial cryptanalysis.The LASH design is based on a simple underlying primitive, and some of its security can be shown to be related to lattice problems

Cryptanalysis of Dedicated Cryptographic Hash Functions

In this thesis we study the security of a number of dedicated cryptographic hash functions against cryptanalytic attacks. We begin with an introduction to what cryptographic hash functions are and what they are used for. This is followed by strict definitions of the security properties often required from cryptographic hash functions. FSB hashes are a class of hash functions derived from a coding theory problem. We attack FSB by modeling the compression function of the hash by a matrix in GF(2). We show that collisions and preimages can easily be found in FSB with the proposed security parameters. We describe a meet-in-the-middle attack against the FORK-256 hash function. The attack requires 2^112.8 operations to find a collision, which is a 38000-fold improvement over the expected 2^128 operations. We then present a method for finding slid pairs for the compression function of SHA-1; pairs of inputs and messages that produce closely related outputs in the compression function. We also cryptanalyse two block ciphers based on the compression function of MD5, MDC-MD5 and the Kaliski-Robshaw "Crab" encryption algorithm. VSH is a hash function based on problems in number theory that are believed to be hard. The original proposal only claims collision resistance; we demonstrate that VSH does not meet the other hash function requirements of preimage resistance, one-wayness, and collision resistance of truncated variants. To explore more general cryptanalytic attacks, we discuss the d-Monomial test, a statistical test that has been found to be effective in distinguishing iterated Boolean circuits from real random functions. The test is applied to the SHA and MD5 hash functions. We present a new hash function proposal, LASH, and its initial cryptanalysis.The LASH design is based on a simple underlying primitive, and some of its security can be shown to be related to lattice problems

Algebraic Complexity Reduction and Cryptanalysis of GOST

GOST 28147-89 is a well-known Russian government encryption standard. Its large key size of 256 bits at a particularly low implementation cost make that it is widely implemented and used, in OpenSSL and elsewhere. In 2010 GOST was submitted to ISO to become an international standard. GOST was analysed by Schneier, Biham, Biryukov, Dunkelman, Wagner, various Australian, Japanese, and Russian scientists, and all researchers seemed to agree that it looks quite secure. Though the internal structure of GOST seems quite weak compared to DES, and in particular the diffusion is not quite as good, it is always stipulated that this should be compensated by a large number of 32 rounds and by the additional non-linearity and diffusion provided by modular additions. At Crypto 2008 the hash function based on this cipher was broken. Yet as far as traditional encryption applications with keys generated at random are concerned, until 2011 no cryptographically significant attack on GOST was found. In this paper we present several new attacks on full 32-rounds GOST. Our methodology is derived from the idea of conditional algebraic attacks on block ciphers which can be defined as attacks in which the problem of key recovery is written as a problem of solving a large system of algebraic equations, and where the attacker makes some clever assumptions on the cipher which lead to an important simplification in the algebraic description of the problem, which makes it solvable in practice if the assumptions hold. Our methods work by black box reduction and allow to literally break the cipher apart into smaller pieces and reduce breaking GOST to a low data complexity software/algebraic/MITM attack on 8 or less rounds. Overall we obtain some 60 distinct attacks faster than brute force on the full 32-round GOST and we provide five nearly practical attacks on two major 128-bit variants of GOST (cf. Table 6). Our single key attacks are summarized in Table 3 p.53 and Table 7 p.153 and attacks with multiple keys in Table 4 page 128

A Salad of Block Ciphers

This book is a survey on the state of the art in block cipher design and analysis. It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months. However, it is also in a self-contained, useable, and relatively polished state, and for this reason I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much. At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people