Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Security of Hidden Field Equations (HFE)
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Multivariate Public Key Cryptosystems (Advances in Information Security)
Multivariate Public Key Cryptosystems (Advances in Information Security)
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Inverting HFE is quasipolynomial
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Square-Vinegar Signature Scheme
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Square, a New Multivariate Encryption Scheme
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
SSE Implementation of Multivariate PKCs on Modern x86 CPUs
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Cryptanalysis of multivariate and odd-characteristic HFE variants
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Inverting HFE systems is quasi-polynomial for all fields
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Ring signature scheme based on multivariate public key cryptosystems
Computers & Mathematics with Applications
Secure variants of the square encryption scheme
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Feasibility of position-based multivariate cryptosystems for WSN
International Journal of Internet Technology and Secured Transactions
Performance analysis of multivariate cryptosystem schemes for wireless sensor network
Computers and Electrical Engineering
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In this paper, we study how the algebraic attack on the HFE multivariate public key cryptosystem works if we build an HFE cryptosystem on a finite field whose characteristic is not two. Using some very basic algebraic geometry we argue that when the characteristic is not two the algebraic attack should not be polynomial in the range of the parameters which are used in practical applications. We further support our claims with extensive experiments using the Magma implementation of F4, which is currently the best publicly available implementation of the Gröbner basis algorithm. We present a new variant of the HFE cryptosystems, where we project the public key of HFE to a space of one dimension lower. This protects the system from the Kipnis-Shamir attack and makes the decryption process avoid multiple candidates for the plaintext. We propose an example for a practical application on GF(11) and suggest a test challenge on GF(7).