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Possible spell-corrected query: computational same homomorphism
On the cryptosystems based on two Eulerian transfor-mations defined over the commutative rings $Z_{2^s}, s>1$.
Vasyl Ustimenko
Cryptographic protocols
We suggest the family of ciphers s^E^n, n=2,3,.... with the space of plaintexts (Z*_{2^s})^n, s >1 such that the encryption map is the composition of kind G=G_1A_1G_2A_2 where A_i are the affine transformations from AGL_n(Z_{2^s}) preserving the variety (Z*_{2^s)}^n , Eulerian endomorphism G_i , i=1,2 of K[x_1, x_2,...., x_n] moves x_i to monomial term ϻ(x_1)^{d(1)}(x_2)^{d(2)}...(x_n)^{d(n)} , ϻϵ Z*_{2^s} and act on (Z*_{2^s})^n as bijective transformations.
The cipher is...
On effective computations in special subsemigroups of polynomial transformations and protocol based multivariate cryptosystems
Vasyl Ustimenko
Foundations
Large semigroups and groups of transformations of finite affine space of dimension n with the option of computability of the composition of n arbitrarily chosen elements in polynomial time are described in the paper. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of...
On Noncommutative Cryptography and homomorphism of stable cubical multivariate transformation groups of infinite dimensional affine spaces
V. Ustimenko, M. Klisowski
Cryptographic protocols
Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups and non-commutative rings. Its inter-section with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined overfinite commutative rings. Efficiently computed homomorphisms between stable subsemigroups of affine Cremona semigroups can be used in tame homomorphisms protocols schemes and...
We suggest the family of ciphers s^E^n, n=2,3,.... with the space of plaintexts (Z*_{2^s})^n, s >1 such that the encryption map is the composition of kind G=G_1A_1G_2A_2 where A_i are the affine transformations from AGL_n(Z_{2^s}) preserving the variety (Z*_{2^s)}^n , Eulerian endomorphism G_i , i=1,2 of K[x_1, x_2,...., x_n] moves x_i to monomial term ϻ(x_1)^{d(1)}(x_2)^{d(2)}...(x_n)^{d(n)} , ϻϵ Z*_{2^s} and act on (Z*_{2^s})^n as bijective transformations. The cipher is...
Large semigroups and groups of transformations of finite affine space of dimension n with the option of computability of the composition of n arbitrarily chosen elements in polynomial time are described in the paper. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of...
Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups and non-commutative rings. Its inter-section with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined overfinite commutative rings. Efficiently computed homomorphisms between stable subsemigroups of affine Cremona semigroups can be used in tame homomorphisms protocols schemes and...
