Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field . In certain cases those polynomials could be defined over both a ground and an extension field. If the polynomials have the degree two, we talk about multivariate quadratics. Solving systems of multivariate polynomial equations is proven to be NP-complete. That's why those schemes are often considered to be good candidates for post-quantum cryptography. Multivariate cryptography has been very productive in terms of design and cryptanalysis. Overall, the situation is now more stable and the strongest schemes have withstood the test of time. It is commonly admitted that Multivariate cryptography turned out to be more successful as an approach to build s
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| - Multivariate cryptography (en)
- Cryptographie multivariée (fr)
- Многомерная криптография (ru)
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| - La cryptographie multivariée regroupe un ensemble de techniques cryptographiques à clé publique reposant sur l'utilisation de polynômes multivariés à coefficients dans un corps fini. Il s'agit d'une des directions de recherches considérées pour développer la cryptographie post-quantique. Pour l'essentiel, la sécurité des constructions issues de cette direction de recherche découle du fait que la résolution de systèmes d'équations polynomiales est un problème NP-difficile en général. (fr)
- Многомерная криптография или многомерная криптография открытого ключа — это общий термин, описывающий асимметричные криптографические схемы, построенные на решениях уравнений, основанных на многомерных полиномах над конечным полем . Безопасность многомерной криптографии основывается на предположении, что решения системы квадратичных многочленов над конечным полем , в общем случае, является NP-полной задачей в сильном смысле или просто NP-полной. Вот почему эти схемы часто считаются хорошими кандидатами для постквантовой криптографии. (ru)
- Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field . In certain cases those polynomials could be defined over both a ground and an extension field. If the polynomials have the degree two, we talk about multivariate quadratics. Solving systems of multivariate polynomial equations is proven to be NP-complete. That's why those schemes are often considered to be good candidates for post-quantum cryptography. Multivariate cryptography has been very productive in terms of design and cryptanalysis. Overall, the situation is now more stable and the strongest schemes have withstood the test of time. It is commonly admitted that Multivariate cryptography turned out to be more successful as an approach to build s (en)
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| - Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field . In certain cases those polynomials could be defined over both a ground and an extension field. If the polynomials have the degree two, we talk about multivariate quadratics. Solving systems of multivariate polynomial equations is proven to be NP-complete. That's why those schemes are often considered to be good candidates for post-quantum cryptography. Multivariate cryptography has been very productive in terms of design and cryptanalysis. Overall, the situation is now more stable and the strongest schemes have withstood the test of time. It is commonly admitted that Multivariate cryptography turned out to be more successful as an approach to build signature schemes primarily because multivariate schemes provide the shortest signature among post-quantum algorithms. (en)
- La cryptographie multivariée regroupe un ensemble de techniques cryptographiques à clé publique reposant sur l'utilisation de polynômes multivariés à coefficients dans un corps fini. Il s'agit d'une des directions de recherches considérées pour développer la cryptographie post-quantique. Pour l'essentiel, la sécurité des constructions issues de cette direction de recherche découle du fait que la résolution de systèmes d'équations polynomiales est un problème NP-difficile en général. (fr)
- Многомерная криптография или многомерная криптография открытого ключа — это общий термин, описывающий асимметричные криптографические схемы, построенные на решениях уравнений, основанных на многомерных полиномах над конечным полем . Безопасность многомерной криптографии основывается на предположении, что решения системы квадратичных многочленов над конечным полем , в общем случае, является NP-полной задачей в сильном смысле или просто NP-полной. Вот почему эти схемы часто считаются хорошими кандидатами для постквантовой криптографии. (ru)
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