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On the families of stable multivariate transformations of large order and their cryptographical applications

In: Tatra Mountains Mathematical Publications, vol. 70, no. 3
Vasyl Ustimenko
Detaily:
Rok, strany: 2017, 107 - 117
Kľúčové slová:
Multivariate cryptography, stable transformations, key exchange protocols, shifted multivariate ElGamal algorithm, desynchronisation diagram
O článku:
Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces $K^n$ over general commutative ring $K$ of with $n$ increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind $g^k$ and $g^{-1}$ given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.
Ako citovať:
ISO 690:
Ustimenko, V. 2017. On the families of stable multivariate transformations of large order and their cryptographical applications. In Tatra Mountains Mathematical Publications, vol. 70, no.3, pp. 107-117. 1210-3195.

APA:
Ustimenko, V. (2017). On the families of stable multivariate transformations of large order and their cryptographical applications. Tatra Mountains Mathematical Publications, 70(3), 107-117. 1210-3195.