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On Generalized First Fall Degree Assumptions
Elliptic curves Discrete logarithm problem Index calculus
2015/12/31
The first fall degree assumption provides a complexity approximation of Gr¨obner basis algorithms
when the degree of regularity of a polynomial system cannot be precisely evaluated. Most importantly,...
Complexity of ECDLP under the First Fall Degree Assumption
ECDLP First fall degree assumption polynomial time algorithm
2015/12/22
Semaev [14] shows that under the first fall degree assumption, the complexity
of ECDLP over F2n , where n is the input size, is O(2n
1/2+o(1) ). In his manuscript,
the cost for solving equations sy...
Polynomial time reduction from 3SAT to solving low first fall degree multivariable cubic equations system
multivariable cubic equations system Polynomial
2015/12/22
Recently, there are many researches [5] [3] [7] [4] that, under the first fall
degree assumption, the complexity of ECDLP over Fpn where p is small prime and the
extension degree n is input size, is...
On the First Fall Degree of Summation Polynomials
discrete logarithm problem elliptic curve cryptosystem
2015/12/21
We improve on the first fall degree bound of polynomial
systems that arise from a Weil descent along Semaev’s summation polynomials.