Similar Keys of Multivariate Quadratic Public Key Cryptosystems

Most multivariate schemes have potentially much higher performance than other public key cryptosystems[15] [4] [1] [2]. Wolf and Preneel [16] show multivariate quadratic public key schemes have many equivalent keys and provide some transformations to identify the keys. In this paper, we propose the idea of similar keys of MQ-based public key cryptosystems(PKCs) and provide a method to reduce the size of private key in MQ-based PKCs to 50% ~ 70% of its original size. And our method is generic for most MQ-based PKCs except for UOV-like and STS-like schemes. Moreover, our method remains the equivalent security and efficiency with original MQ-based PKCs.

[1]  Lih-Chung Wang,et al.  Revision of Tractable Rational Map Cryptosystem , 2004, IACR Cryptol. ePrint Arch..

[2]  David Naccache,et al.  Topics in Cryptology — CT-RSA 2001 , 2001, Lecture Notes in Computer Science.

[3]  Jongin Lim,et al.  Information Security and Cryptology - ICISC 2003 , 2003, Lecture Notes in Computer Science.

[4]  Feipei Lai,et al.  Tractable Rational Map Signature , 2005, Public Key Cryptography.

[5]  Feipei Lai,et al.  An implementation of public key cryptosystem TTM with linear time complexity for decryption , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  Bo-Yin Yang,et al.  TTS: High-Speed Signatures on a Low-Cost Smart Card , 2004, CHES.

[8]  Serge Vaudenay.  Public Key Cryptography - PKC 2005, 8th International Workshop on Theory and Practice in Public Key Cryptography, Les Diablerets, Switzerland, January 23-26, 2005, Proceedings , 2005, Public Key Cryptography.

[9]  Ueli Maurer,et al.  Advances in Cryptology — EUROCRYPT ’96 , 2001, Lecture Notes in Computer Science.

[10]  Jacques Patarin,et al.  Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms , 1996, EUROCRYPT.

[11]  Hideki Imai,et al.  Public Quadratic Polynominal-Tuples for Efficient Signature-Verification and Message-Encryption , 1988, EUROCRYPT.

[12]  Louis Goubin,et al.  QUARTZ, 128-Bit Long Digital Signatures , 2001, CT-RSA.

[13]  Bart Preneel,et al.  Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations , 2005, IACR Cryptol. ePrint Arch..

[14]  Louis Goubin,et al.  SFLASHv3, a fast asymmetric signature scheme , 2003, IACR Cryptol. ePrint Arch..

[15]  Marc Joye,et al.  Cryptographic Hardware and Embedded Systems - CHES 2004 , 2004, Lecture Notes in Computer Science.

[16]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[17]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[18]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[19]  Niklaus Wirth,et al.  Advances in Cryptology — EUROCRYPT ’88 , 2000, Lecture Notes in Computer Science.

[20]  Louis Goubin,et al.  Unbalanced Oil and Vinegar Signature Schemes , 1999, EUROCRYPT.

[21]  Bart Preneel,et al.  Large Superfluous Keys in Multivariate Quadratic Asymmetric Systems , 2005, Public Key Cryptography.

[22]  Bo-Yin Yang,et al.  A More Secure and Efficacious TTS Signature Scheme , 2003, ICISC.