Cryptanalysis of the TRMC-4 Public Key Cryptosystem

Authors:
Xuyun Nie;Lei Hu;Jintai Ding;Jianyu Li;John Wagner
Affiliations:
State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45220, USA and Fachbereich Informatik, Technische Universität Darmstadt, Germany;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049, China;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45220, USA
Venue:
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Year:
2007

Citing 7
Cited 0

Public quadratic polynomial-tuples for efficient signature-verification and message-encryption

Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

SIAM Journal on Computing
Cryptoanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88

CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the TTM Cryptosystem

ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Building secure tame-like multivariate public-key cryptosystems: the new TTS

ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Cryptanalysis of the tractable rational map cryptosystem

PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Breaking a new instance of TTM cryptosystems

ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security

Quantified Score

Hi-index	0.00

Visualization

Abstract

In 2006, the inventors of TRMC public key cryptosystem proposed a new variant of TRMC, TRMC-4, which can resist the existing attack, in particular, the Joux et al attack. In this paper, we show that the new version is vulnerable to attack via the linearization equations (LE) method. For any given valid ciphertext and its corresponding TRMC-4 public key, we can derive the corresponding plaintext within 224$\mathbb{F}_{2^8}$-operations, after performing once for the public key a computation of complexity less than 234. Our results are confirmed by computer experiments.