Cryptanalysis of Key Exchange Protocol Based on Tensor Ergodic Problem

Chunsheng Gu

doi:10.1109/CC.2018.8485479

Cryptanalysis of Key Exchange Protocol Based on Tensor Ergodic Problem

2018-10-01

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DOI：10.1109/CC.2018.8485479

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Recently, Mao, Zhang, Wu et al. constructed two key exchange (KE) protocols based on tensor ergodic problem (TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they did not provide a rigorous security proof for their KE protocols. In this paper, applying the properties of ergodic matrix, we first present a polynomial time algorithm to solve the TEP problem using O(n(6)) arithmetic operations in the finite field, where n is the security parameter. Then, applying this polynomial time algorithm, we generate a common shared key for two TEP-based KE constructions, respectively. In addition, we also provide a polynomial time algorithm with O(n(6)) arithmetic operations that directly recovers the plaintext from a ciphertext for the KE-based encryption scheme. Thus, the TEP-based KE protocols and their corresponding encryption schemes are insecure.

Keyword:

key exchange

KE-based encryption

tensor decomposition

ergodic matrix

Cryptanalysis of Key Exchange Protocol Based on Tensor Ergodic Problem

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