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

An Improved Differential Attack on Full GOST (extended version)

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 it is becoming increasingly popular. 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 can be broken and it is insecure on more than one account. There is a substantial variety of recent innovative attacks on GOST. We have reflection attacks, attacks with double, triple and even quadruple reflections, a large variety of self-similarity and black-box reduction attacks, some of which do not use any reflections whatsoever and few other. The final key recovery step in various attacks is in many cases a software algebraic attack or/and a Meet-In-The-Middle attack. In differential attacks key bits are guessed and confirmed by the differential properties and there have already been quite a few papers about advanced differential attacks on GOST. There is also several even more advanced “combination” attacks which combine the complexity reduction approach based on high-level self-similarity of with various advanced differential properties with 2,3 or 4 points. In this paper we consider some recent differential attacks on GOST and show how to further improve them. We present a single-key attack against full 32-round 256-bit GOST with time complexity of 2^179 which is substantially faster than any previous single key attack on GOST

On the Existence of Non-Linear Invariants and Algebraic Polynomial Constructive Approach to Backdoors in Block Ciphers

In this paper we study cryptanalysis with non-linear polynomials cf. Eurocrypt’95 (adapted to Feistel ciphers at Crypto 2004). Previously researchers had serious difficulties in making such attacks work. Even though this is less general than a general space partitioning attack (FSE’97), a polynomial algebraic approach has enormous advantages. Properties are more intelligible and algebraic computational methods can be applied in order to discover or construct the suitable properties. In this paper we show how round invariants can be found for more or less any block cipher, by solving a certain surprisingly simple single algebraic equation (or two). Then if our equation has solutions, which is far from being obvious, it will guarantee that some polynomial invariant will work for an arbitrarily large number of encryption rounds. This paper is a proof of concept showing that it IS possible, for at least one specific quite complex real-life cipher to construct in a systematic way, a non-linear component and a variety of non-linear polynomial invariants holding with probability 1 for any number of rounds and any key/IV. Thus we are able to weaken a block cipher in a permanent and pervasive way. An example of a layered attack with two stages is also shown. Moreover we show that sometimes our equation reduces to zero, and this leads to yet stronger invariants, which work for any Boolean function including the original historical one used in 1970-1990

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