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On the security of a realization of cryptosystem $MST3$

In: Tatra Mountains Mathematical Publications, vol. 41, no. 3
Spyros S. Magliveras - Pavol Svaba - Tran Van Trung - Pavol Zajac
Detaily:
Rok, strany: 2008, 65 - 78
O článku:
A new type of public key cryptosystem, called $MST3$, has been recently developed on the basis of logarithmic signatures and covers of finite groups. The Suzuki 2-groups have been suggested for a possible realization of the generic version of $MST3$. On one hand, due to their structure, the Suzuki 2-groups allow one to study the security of the system, on the other hand they possess a simple presentation allowing for an efficient implementation of the system. In this paper we present a detailed study of the security of this realization of $MST3$. We prove a new general lower bound for the work effort required to determine the secret key in terms of the size of the underlying groups. This bound has size $q=2m$, where $q$ is the order of the finite field $\mathbb{F}q$, on which the Suzuki 2-group $A(m,θ)$ is defined. Further, by exploiting properties of the group operation in the Suzuki 2-groups, as well as a special property of canonical transversal logarithmic signatures for elementary abelian 2-groups, we show that canonical transversal logarithmic signatures are unfit to use in this realization of $MST3$.
Ako citovať:
ISO 690:
Magliveras, S., Svaba, P., Trung, T., Zajac, P. 2008. On the security of a realization of cryptosystem $MST3$. In Tatra Mountains Mathematical Publications, vol. 41, no.3, pp. 65-78. 1210-3195.

APA:
Magliveras, S., Svaba, P., Trung, T., Zajac, P. (2008). On the security of a realization of cryptosystem $MST3$. Tatra Mountains Mathematical Publications, 41(3), 65-78. 1210-3195.