Time-Area Optimized Public-Key Engines: MQ-Cryptosystems as Replacement for Elliptic Curves?

In this paper ways to efficiently implement public-key schemes based on ultivariate uadratic polynomials ($\mathcal{MQ}$-schemes for short) are investigated. In particular, they are claimed to resist quantum computer attacks. It is shown that such schemes can have a much better time-area product than elliptic curve cryptosystems. For instance, an optimised FPGA implementation of amended TTS is estimated to be over 50 times more efficient with respect to this parameter. Moreover, a general framework for implementing small-field $\mathcal{MQ}$-schemes in hardware is proposed which includes a systolic architecture performing Gaussian elimination over composite binary fields.

[1]  Tatsuaki Okamoto,et al.  Public Key Cryptography - PKC 2007, 10th International Conference on Practice and Theory in Public-Key Cryptography, Beijing, China, April 16-20, 2007, Proceedings , 2007, Public Key Cryptography.

[2]  Andrey Bogdanov,et al.  Fast Multivariate Signature Generation in Hardware: The Case of Rainbow , 2008, 2008 16th International Symposium on Field-Programmable Custom Computing Machines.

[3]  Olivier Billet,et al.  Cryptanalysis of Rainbow , 2006, SCN.

[4]  Information Security and Privacy , 1996, Lecture Notes in Computer Science.

[5]  Bo-Yin Yang,et al.  l-Invertible Cycles for Multivariate Quadratic (MQ) Public Key Cryptography , 2007, Public Key Cryptography.

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

[7]  Chin-Liang Wang,et al.  A Systolic Architecture for Computing Inverses and Divisions in Finite Fields GF(2^m) , 1993, IEEE Trans. Computers.

[8]  Patrice Quinton,et al.  Systolic Gaussian Elimination over GF(p) with Partial Pivoting , 1989, IEEE Trans. Computers.

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

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

[11]  M. Anwar Hasan,et al.  High-Performance Architecture of Elliptic Curve Scalar Multiplication , 2008, IEEE Transactions on Computers.

[12]  Andrey Bogdanov,et al.  SMITH - A Parallel Hardware Architecture for Fast Gaussian Elimination over GF(2) , 2006 .

[13]  Bo-Yin Yang,et al.  Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS , 2005, ACISP.

[14]  Jean-Jacques Quisquater,et al.  High-speed hardware implementations of Elliptic Curve Cryptography: A survey , 2007, J. Syst. Archit..

[15]  Andrey Bogdanov,et al.  A Parallel Hardware Architecture for fast Gaussian Elimination over GF(2) , 2006, 2006 14th Annual IEEE Symposium on Field-Programmable Custom Computing Machines.

[16]  Louis Goubin,et al.  Unbalanced Oil and Vinegar Signature Schemes -extended Version , 1999 .

[17]  Tarek A. El-Ghazawi,et al.  Low latency elliptic curve cryptography accelerators for NIST curves over binary fields , 2005, Proceedings. 2005 IEEE International Conference on Field-Programmable Technology, 2005..

[18]  Jintai Ding,et al.  Rainbow, a New Multivariable Polynomial Signature Scheme , 2005, ACNS.

[19]  Chen-Mou Cheng,et al.  Implementing Minimized Multivariate PKC on Low-Resource Embedded Systems , 2006, SPC.

[20]  Lei Hu,et al.  Note on Design Criteria for Rainbow-Type Multivariates , 2006, IACR Cryptol. ePrint Arch..

[21]  Frank Stajano.  Security in Pervasive Computing , 2003, SPC.