5 results sorted by ID
Several classes of minimal binary linear codes violating the Aschikhmin-Barg's bound
Enes Pasalic, René Rodríguez, Fengrong Zhang, Yongzhuang Wei
Minimal linear codes are a special class of codes which have important applications in secret sharing and secure two-party computation. These codes are characterized by the property that none of the codewords is covered by some other codeword. Denoting by $w_{min}$ and $w_{max}$ minimal and maximal weight of the codewords respectively, such codes are relatively easy to design when the ratio $w_{min}/w_{max} > 1/2$ (known as Aschikhmin-Barg's bound). On the other hand, there are few known...
Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions
Sihem Mesnager, Kwang Ho Kim, Myong Song Jo
To determine the dimension of null space of any given linearized
polynomial is one of vital problems in finite field theory, with
concern to design of modern symmetric cryptosystems. But, the known
general theory for this task is much far from giving the exact
dimension when applied to a specific linearized polynomial. The
first contribution of this paper is to give a better general method
to get more precise upper bound on the root number of any given
linearized polynomial. We anticipate...
Attacks against Filter Generators Exploiting Monomial Mappings
Anne Canteaut, Yann Rotella
Secret-key cryptography
Filter generators are vulnerable to several attacks which have led to well-known design criteria on the Boolean filtering function. However, Rønjom and Cid have observed that a change of the primitive root defining the LFSR leads to several equivalent generators. They usually offer different security levels since they involve filtering functions of the form F(x^k) where k is coprime to (2^n-1) and n denotes the LFSR length. It is proved here that this monomial equivalence does not affect the...
Structural Lattice Reduction: Generalized Worst-Case to Average-Case Reductions and Homomorphic Cryptosystems
Nicolas Gama, Malika Izabachene, Phong Q. Nguyen, Xiang Xie
In lattice cryptography, worst-case to average-case reductions rely on two problems: Ajtai's SIS and Regev's LWE,
which both refer to a very small class of random lattices related to the group $G=\mZ_q^n$.
We generalize worst-case to average-case reductions to all integer lattices of sufficiently large determinant,
by allowing $G$ to be any (sufficiently large) finite abelian group.
In particular, we obtain a partition of the set of full-rank integer lattices of large volume
such that...
Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property
Subhamoy Maitra
Secret-key cryptography
Constructing highly nonlinear balanced Boolean functions with very good
autocorrelation property is an interesting open question. In this direction
we use the measure $\Delta_f$ for a function $f$ proposed by Zhang and
Zheng (1995). We provide balanced functions $f$ with currently best known
nonlinearity and $\Delta_f$ values together. Our results for 15-variable
functions disprove the conjecture proposed by Zhang and Zheng (1995),
where our constructions are based on modifications...
Minimal linear codes are a special class of codes which have important applications in secret sharing and secure two-party computation. These codes are characterized by the property that none of the codewords is covered by some other codeword. Denoting by $w_{min}$ and $w_{max}$ minimal and maximal weight of the codewords respectively, such codes are relatively easy to design when the ratio $w_{min}/w_{max} > 1/2$ (known as Aschikhmin-Barg's bound). On the other hand, there are few known...
To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known general theory for this task is much far from giving the exact dimension when applied to a specific linearized polynomial. The first contribution of this paper is to give a better general method to get more precise upper bound on the root number of any given linearized polynomial. We anticipate...
Filter generators are vulnerable to several attacks which have led to well-known design criteria on the Boolean filtering function. However, Rønjom and Cid have observed that a change of the primitive root defining the LFSR leads to several equivalent generators. They usually offer different security levels since they involve filtering functions of the form F(x^k) where k is coprime to (2^n-1) and n denotes the LFSR length. It is proved here that this monomial equivalence does not affect the...
In lattice cryptography, worst-case to average-case reductions rely on two problems: Ajtai's SIS and Regev's LWE, which both refer to a very small class of random lattices related to the group $G=\mZ_q^n$. We generalize worst-case to average-case reductions to all integer lattices of sufficiently large determinant, by allowing $G$ to be any (sufficiently large) finite abelian group. In particular, we obtain a partition of the set of full-rank integer lattices of large volume such that...
Constructing highly nonlinear balanced Boolean functions with very good autocorrelation property is an interesting open question. In this direction we use the measure $\Delta_f$ for a function $f$ proposed by Zhang and Zheng (1995). We provide balanced functions $f$ with currently best known nonlinearity and $\Delta_f$ values together. Our results for 15-variable functions disprove the conjecture proposed by Zhang and Zheng (1995), where our constructions are based on modifications...