Expected coverage rate for the Hellman matrices

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Gharavi Naser Hosein; Mirqadri Abdorasool; ABDOLLAHI AZGOMI MOHAMMAD; Mousavi Sayyed Ahmad

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Journal: SIGNAL AND DATA PROCESSING Year:2018 | Volume:15 | Issue:3 (37) Page(s): 47-58

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Title

Expected coverage rate for the Hellman matrices

Author(s)

Gharavi Naser Hosein | Mirqadri Abdorasool | ABDOLLAHI AZGOMI MOHAMMAD | Mousavi Sayyed Ahmad | Issue Writer Certificate

Keywords

Time-Memory Trade-offQ1

one way functionQ1

Hellman matrixQ1

Expected coverage rateQ1

Abstract

Hellman’ s Time-Memory Trade-off is a probabilistic method for inverting one-way functions, using pre-computed data. Hellman introduced this method in 1980 and obtained a lower bound for the success probability of his algorithm. After that, all further analyses of researchers are based on this lower bound. In this paper, we first studied the Expected coverage rate (ECR) of the Hellman matrices, which are constructed by a single chain. We showed that the ECR of such matrices is maximum and equal to 0. 85. In this process, we find out that there exists a gap between the Hellman’ s lower bound and experimental coverage rate of a Hellman matrix. Specifically, this gap is larger, when considering the Hellman matrices constructed with one single chain. So, we are investigated to obtain an accurate formula for the ECR of a Hellman matrix. Subsequently, we presented a new formula that estimate the ECR of a Hellman matrix more accurately than the Hellman’ s lower bound. We showed that the given formula is closely match experimental data. In the last, we introduced a new method to construct matrices which have much more ECR than Hellman matrices. In fact, each matrix in this new method is constructed with one single chain, which is non-repeating trajectory from a random point. So, this approach result in a number of matrices that each one contains a chain with variable length. The main advantage of this method is that we have more probability of success than Hellman method, however online time and memory requirements are increased. We have also verified theory of this new method with experimental results.

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APA: Copy

Gharavi, Naser Hosein, Mirqadri, Abdorasool, ABDOLLAHI AZGOMI, MOHAMMAD, & Mousavi, Sayyed Ahmad. (2018). Expected coverage rate for the Hellman matrices. SIGNAL AND DATA PROCESSING, 15(3 (37) ), 47-58. SID. https://sid.ir/paper/160856/en

Vancouver: Copy

Gharavi Naser Hosein, Mirqadri Abdorasool, ABDOLLAHI AZGOMI MOHAMMAD, Mousavi Sayyed Ahmad. Expected coverage rate for the Hellman matrices. SIGNAL AND DATA PROCESSING[Internet]. 2018;15(3 (37) ):47-58. Available from: https://sid.ir/paper/160856/en

IEEE: Copy

Naser Hosein Gharavi, Abdorasool Mirqadri, MOHAMMAD ABDOLLAHI AZGOMI, and Sayyed Ahmad Mousavi, “Expected coverage rate for the Hellman matrices,” SIGNAL AND DATA PROCESSING, vol. 15, no. 3 (37) , pp. 47–58, 2018, [Online]. Available: https://sid.ir/paper/160856/en

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