Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Algebraic Methods for Constructing Asymmetric Cryptosystems
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
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
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
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
Cache attacks and countermeasures: the case of AES
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
How far can we go on the x64 processors?
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Rainbow, a new multivariable polynomial signature scheme
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Inoculating multivariate schemes against differential attacks
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
QUAD: a practical stream cipher with provable security
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and lIC-Derivatives
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
SSE Implementation of Multivariate PKCs on Modern x86 CPUs
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Dial C for cipher: le chiffrement était presque parfait
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
KFC - The Krazy Feistel Cipher
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
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This work investigates several methods to achieve efficient software implementations of systems of multivariate quadratic equations. Such systems of equations appear in several multivariate cryptosystems such as the signature schemes SFLASH, Rainbow, the encryption scheme PMI+, or the stream cipher QUAD. We describe various implementation strategies. These strategies were combined to implement the public computations of three asymmetric schemes as well as the stream cipher QUAD. We conducted extensive benchmarks on our implementations which are exposed in the final section of this paper. The obtained figures support the claim that when some care is taken, multivariate schemes can be efficiently implemented in software.