5 results sorted by ID
Possible spell-corrected query: subgroup of affine Cremona group
On Extremal Expanding Algebraic Graphs and post-quantum secure delivery of passwords, encryption maps and tools for multivariate digital signatures.
Vasyl Ustimenko
Cryptographic protocols
Expanding graphs are known due to their remarkable applications to Computer Science. We are looking for their applications to Post Quantum Cryptography. One of them is postquantum analog of Diffie-Hellman protocol in the area of intersection of Noncommutative and Multivariate Cryptographies .This graph based protocol allows correspondents to elaborate
collision cubic transformations of affine space Kn defined over finite commutative ring K. Security of this protocol rests on the...
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 Multivariate Algorithms of Digital Signatures on Secure El Gamal Type Mode.
Vasyl Ustimenko
Cryptographic protocols
The intersection of Non-commutative and Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K with the unit. We consider special subsemigroups (platforms) in a semigroup of all endomorphisms of K[x_1, x_2, …, x_n].
Efficiently computed homomorphisms between such platforms can be used in Post Quantum key exchange protocols when correspondents elaborate common...
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...
On semigroups of multiplicative Cremona transformations and new solutions of Post Quantum Cryptography.
Vasyl Ustimenko
Cryptographic protocols
Noncommutative cryptography is based on the applications of algebraic structures like noncommutative groups, semigroups and noncommutative rings. Its intersection with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K. We consider special semigroups of transformations of the variety (K*)^n, K=F_q or K=Z_m defined via multiplications of variables.
Efficiently...
Expanding graphs are known due to their remarkable applications to Computer Science. We are looking for their applications to Post Quantum Cryptography. One of them is postquantum analog of Diffie-Hellman protocol in the area of intersection of Noncommutative and Multivariate Cryptographies .This graph based protocol allows correspondents to elaborate collision cubic transformations of affine space Kn defined over finite commutative ring K. Security of this protocol rests on the...
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...
The intersection of Non-commutative and Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K with the unit. We consider special subsemigroups (platforms) in a semigroup of all endomorphisms of K[x_1, x_2, …, x_n]. Efficiently computed homomorphisms between such platforms can be used in Post Quantum key exchange protocols when correspondents elaborate common...
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...
Noncommutative cryptography is based on the applications of algebraic structures like noncommutative groups, semigroups and noncommutative rings. Its intersection with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K. We consider special semigroups of transformations of the variety (K*)^n, K=F_q or K=Z_m defined via multiplications of variables. Efficiently...
