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Title:
An improved method for predicting truncated multiple recursive generators with unknown parameters
Authors: Han-Bing Yu, Qun-Xiong Zheng, Yi-Jian Liu, Jing-Guo Bi, Yu-Fei Duan, Jing-Wen Xue, You Wu, Yue Cao, Rong Cheng, Lin Wang, Bai-Shun Sun
Abstract:Multiple recursive generators are an important class of pseudorandom number generators which are widely used in cryptography. The predictability of truncated sequences that predict the whole sequences by the truncated high-order bits of the sequences is not only a crucial aspect of evaluating the security of pseudorandom number generators but also serves an important role in the design of pseudorandom number generators. This paper improves the work of Sun et al on the predictability of truncated multiple recursive generators with unknown parameters. Given a few truncated digits of high-order bits output by a multiple recursive generator, we adopt the resultant, the Chinese Remainder Theorem and the idea of recovering p-adic coordinates of the coefficients layer by layer, and Kannan’s embedding technique to recover the modulus, the coefficients and the initial state, respectively. Experimental results show that our new method is superior to that of the work of Sun et al, no matter in terms of the running time or the number of truncated digits required.
ePrint: https://eprint.iacr.org/2022/1134
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