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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,...
Masks will Fall Off -- Higher-Order Optimal Distinguishers
security analysis cryptographic devices
2015/12/30
Higher-order side-channel attacks are able to break the security
of cryptographic implementations even if they are protected with
masking countermeasures. In this paper, we derive the best possible
...
Last fall degree, HFE, and Weil descent attacks on ECDLP
ECDLP Weil descent solving equations
2015/12/29
Weil descent methods have recently been applied to attack
the Hidden Field Equation (HFE) public key systems and solve the elliptic
curve discrete logarithm problem (ECDLP) in small characteristic.
...
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.
Indistinguishability Obfuscation vs. Auxiliary-Input Extractable Functions: One Must Fall
indistinguishability obfuscation knowledge of exponent
2014/3/7
We show that if there exist indistinguishability obfuscators for all circuits then there do not exist auxiliary-input extractable one-way functions. In particular, the knowledge of exponent assumption...