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Register a new userCryptanalysis of group-based key agreement protocols using subgroup distance functions
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Added by
Boaz Tsaban
Publication date
2010
fields
Informatics Engineering
and research's language is
English
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We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. This approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the Shpilrain-Ushakov protocol, which is based on Thompsons group F.
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Key-agreement protocols whose security is proven in the random oracle model are an important alternative to protocols based on public-key cryptography. In the random oracle model, the parties and the eavesdropper have access to a shared random function (an oracle), but the parties are limited in the number of queries they can make to the oracle. The random oracle serves as an abstraction for black-box access to a symmetric cryptographic primitive, such as a collision resistant hash. Unfortunately, as shown by Impagliazzo and Rudich [STOC 89] and Barak and Mahmoody [Crypto 09], such protocols can only guarantee limited secrecy: the key of any $ell$-query protocol can be revealed by an $O(ell^2)$-query adversary. This quadratic gap between the query complexity of the honest parties and the eavesdropper matches the gap obtained by the Merkles Puzzles protocol of Merkle [CACM 78]. In this work we tackle a new aspect of key-agreement protocols in the random oracle model: their communication complexity. In Merkles Puzzles, to obtain secrecy against an eavesdropper that makes roughly $ell^2$ queries, the honest parties need to exchange $Omega(ell)$ bits. We show that for protocols with certain natural properties, ones that Merkles Puzzle has, such high communication is unavoidable. Specifically, this is the case if the honest parties queries are uniformly random, or alternatively if the protocol uses non-adaptive queries and has only two rounds. Our proof for the first setting uses a novel reduction from the set-disjointness problem in two-party communication complexity. For the second setting we prove the lower bound directly, using information-theoretic arguments.
Wireless Body Sensor Network (WBSN) is a developing technology with constraints in energy consumption, coverage radius, communication reliability. Also, communications between nodes contain very sensitive personal information in which sometimes due to the presence of hostile environments, there are a wide range of security risks. As such, designing authenticated key agreement (AKA) protocols is an important challenge in these networks. Recently, Li et al. proposed a lightweight scheme using the hash and XOR functions which is much more efficient compared with similar schemes based on elliptic curve. However, the investigations revealed that the claim concerning the unlinkability between the sessions of a sensor node is NOT true. The present paper considers the security issues of the scheme proposed by Li et al. and some of its new extensions in order to propose a new AKA scheme with anonymity and unlinkability of the sensor node sessions. The results of theoretical analysis compared with similar schemes indicate that the proposed scheme reduces average energy consumption and average computation time by 61 percent while reduces the average communication cost by 41 percent. Further, it has been shown by formal and informal analysis that, Besides the two anonymity and unlinkability features, the other main features of the security in the proposed scheme are comparable and similar to the recent similar schemes.
There are several methods to measure computing power. On the other hand, Bit Length (BL) can be considered a metric to measure the strength of an asymmetric encryption method. We review here ways to determine the security, given an span of time, of a factoring-based encryption method, such as RSA, by establishing a relation between the processing power needed to break a given encryption and the given bit length used in the encryption. This relation would help us provide an estimation of the time span that an encryption method for a given BL will be secure from attacks.
Recently, an image encryption algorithm using block-based scrambling and image filtering has been proposed by Hua et al. In this paper, we analyze the security problems of the encryption algorithm in detail and break the encryption by a codebook attack. We construct an linear relation between plain-images and cipher-images by differential cryptanalysis. With this linear relation, we build a codebook containing $(M times N + 1)$ pairs of plain-images and cipher-images, where $Mtimes N$ is the size of images. The proposed codebook attack indicates that the encryption scheme is insecure. To resist the codebook attack, an improved algorithm is proposed. Experimental results show that the improved algorithm not only inherits the merits of the original scheme, but also has stronger security against the differential cryptanalysis.
We present an attack against a code-based signature scheme based on the Lyubashevsky protocol that was recently proposed by Song, Huang, Mu, Wu and Wang (SHMWW). The private key in the SHMWW scheme contains columns coming in part from an identity matrix and in part from a random matrix. The existence of two types of columns leads to a strong bias in the distribution of set bits in produced signatures. Our attack exploits such a bias to recover the private key from a bunch of collected signatures. We provide a theoretical analysis of the attack along with experimental evaluations, and we show that as few as 10 signatures are enough to be collected for successfully recovering the private key. As for previous attempts of adapting Lyubashevskys protocol to the case of code-based cryptography, the SHMWW scheme is thus proved unable to provide acceptable security. This confirms that devising secure code-based signature schemes with efficiency comparable to that of other post-quantum solutions (e.g., based on lattices) is still a challenging task.
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