Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
System architecture directions for networked sensors
ASPLOS IX Proceedings of the ninth international conference on Architectural support for programming languages and operating systems
The Design of Rijndael
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
IEEE Transactions on Computers
FLASH, a Fast Multivariate Signature Algorithm
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
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
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
C*-+ and HM: Variations Around Two Schemes of T. Matsumoto and H. Imai
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: 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
Attacking the Affine Parts of SFLASH
Proceedings of the 8th IMA International Conference on Cryptography and Coding
Solving Underdefined Systems of Multivariate Quadratic Equations
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
A Fast and Secure Implementation of Sflash
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Generic Attacks and the Security of Quartz
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
The nesC language: A holistic approach to networked embedded systems
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Equivalent keys in HFE, c*, and variations
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Similar keys of multivariate quadratic public key cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
Tractable rational map signature
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Cryptanalysis of the tractable rational map cryptosystem
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Rainbow, a new multivariable polynomial signature scheme
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Public key cryptography in sensor networks—revisited
ESAS'04 Proceedings of the First European conference on Security in Ad-hoc and Sensor Networks
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
On the differential security of multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
High-Speed hardware implementation of rainbow signature on FPGAs
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
Applicability of public key infrastructures in wireless sensor networks
EuroPKI'07 Proceedings of the 4th European conference on Public Key Infrastructure: theory and practice
Efficient implementations of MQPKS on constrained devices
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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Multivariate (or $\mathcal{MQ}$) public-key cryptosystems (PKC) are alternatives to traditional PKCs based on large algebraic structures (e.g., RSA and ECC); they usually execute much faster than traditional PKCs on the same hardware. However, one major challenge in implementing multivariates in embedded systems is that the key size can be prohibitively large for applications with stringent resource constraints such as low-cost smart cards, sensor networks (e.g., Berkeley motes), and radio-frequency identification (RFID). In this paper, we investigate strategies for shortening the key of a multivariate PKC. We apply these strategies to the Tame Transformation Signatures (TTS) as an example and quantify the improvement in key size and running speed, both theoretically and via implementation. We also investigate ways to save die space and energy consumption in hardware, reporting on our ASIC implementation of TTS on a TSMC 0.25μm process. Even without any key shortening, the current consumption of TTS is only 21 μA for computing a signature, using 22,000 gate equivalents and 16,000 100-kHz cycles (160 ms). With circulant-matrix key shortening, the numbers go down to 17,000 gates and 4,400 cycles (44 ms). We therefore conclude: besides representing a future-proofing investment against the emerging quantum computers, multivariates can be immediately useful in niches.