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Register a new userA mathematical problem for security analysis of hash functions and pseudorandom generators
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Added by
Koji Nuida
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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In this paper, we specify a class of mathematical problems, which we refer to as Function Density Problems (FDPs, in short), and point out novel connections of FDPs to the following two cryptographic topics; theoretical security evaluations of keyless hash functions (such as SHA-1), and constructions of provably secure pseudorandom generators (PRGs) with some enhanced security property introduced by Dubrov and Ishai [STOC 2006]. Our argument aims at proposing new theoretical frameworks for these topics (especially for the former) based on FDPs, rather than providing some concrete and practical results on the topics. We also give some examples of mathematical discussions on FDPs, which would be of independent interest from mathematical viewpoints. Finally, we discuss possible directions of future research on other cryptographic applications of FDPs and on mathematical studies on FDPs themselves.
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Local pseudorandom generators are a class of fundamental cryptographic primitives having very broad applications in theoretical cryptography. Following Couteau et al.s work in ASIACRYPT 2018, this paper further studies the concrete security of one important class of local pseudorandom generators, i.e., Goldreichs pseudorandom generators. Our first attack is of the guess-and-determine type. Our result significantly improves the state-of-the-art algorithm proposed by Couteau et al., in terms of both asymptotic and concrete complexity, and breaks all the challenge parameters they proposed. For instance, for a parameter set suggested for 128 bits of security, we could solve the instance faster by a factor of about $2^{61}$, thereby destroying the claimed security completely. Our second attack further exploits the extremely sparse structure of the predicate $P_5$ and combines ideas from iterative decoding. This novel attack, named guess-and-decode, substantially improves the guess-and-determine approaches for cryptographic-relevant parameters. All the challenge parameter sets proposed in Couteau et al.s work in ASIACRYPT 2018 aiming for 80-bit (128-bit) security levels can be solved in about $2^{58}$ ($2^{78}$) operations. We suggest new parameters for achieving 80-bit (128-bit) security with respect to our attacks. We also extend the attack to other promising predicates and investigate their resistance.
Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to $oplus$-linear hash functions and for certain multiplicative homomorphic hash schemes.
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.
Discussions about the choice of a tree hash mode of operation for a standardization have recently been undertaken. It appears that a single tree mode cannot address adequately all possible uses and specifications of a system. In this paper, we review the tree modes which have been proposed, we discuss their problems and propose remedies. We make the reasonable assumption that communicating systems have different specifications and that software applications are of different types (securing stored content or live-streamed content). Finally, we propose new modes of operation that address the resource usage problem for the three most representative categories of devices and we analyse their asymptotic behavior.
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process is illustrated using the pseudorandom number generator in Mathematica. This methodology may be useful to add to the current family of test procedures in real applications to finite sampling data.
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