On the conjugacy problem in certain metabelian groups

We analyze the computational complexity of an algorithm to solve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most exponential. For a subfamily of groups, we prove that the conjugacy search problem is polynomial. We also show that for a different subfamily the conjugacy search problem reduces to the discrete logarithm problem

Cryptographic multilinear maps using pro-p groups

To any nilpotent group of class n, one can associate a non-interactive key exchange protocol between n+1 users. The multilinear commutator maps associated to nilpotent groups play a key role in this protocol. In the present paper, we discuss the security of this key exchange when applied to finite p-groups and explore some alternative platforms, such as pro-p groups.Comment: To appear in Advances in Mathematics of Communication

A closer look at the multilinear cryptography using nilpotent groups

In Kahrobaei et al. [Multilinear cryptography using nilpotent groups, Proceedings of Elementary Theory of Groups and Group Rings, and Related Topics conference. Conference held at Fairfield University and at the Graduate Center, CUNY, New York, NY, USA, November 1-2, 2018, De Gruyter, 2020, pp. 127-133] we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address some incorrect cryptanalysis which has been proposed in Roman'kov [Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system, Prikl. Diskretn. Mat. Suppl. (12), (2019), pp. 154-160]

Secure information transmission based on physical principles

Abstract. We employ physical properties of the real world to design a protocol for secure information transmission where one of the parties is able to transmit secret information to another party over an insecure channel, without any prior secret arrangements between the parties. The distinctive feature of this protocol, compared to all known public-key cryptographic protocols, is that neither party uses a one-way function. In particular, our protocol is secure against (passive) computationally unbounded adversary.

Cryptosystems using subgroup distortion

In this paper we propose cryptosystems based on subgroup distortion in hyperbolic groups. We also include concrete examples of hyperbolic groups as possible platforms

Adjoint-based history matching of structural models using production and time-lapse seismic data

In spite of large uncertainties in the actual reservoir structure, structural parameters of a reservoir model are usually fixed during history matching and only the flow properties of the model are allowed to vary. This often leads to unlikely or even unfeasible property updates and possibly to a poor predictive capability of the model. In those cases it may be expected that updating of the structural parameters will improve the quality of the history match. Preferably such structural updates should be implemented in the static (geological) model, and not just in the dynamic (flow) model. In this paper we use a gradient-based history matching method to update structural properties of the static model. We use an adjoint method to efficiently compute the derivatives of the data mismatch with respect to grid block porosities in the dynamic model and convert the corresponding volume changes to structural updates (layer thicknesses) in the static model. This method is suitable for structural updating of large scale reservoir models using production data and/or time-lapse seismics or other spatially distributed data. The method is tested on a 3D synthetic model, where time-lapse as well as production data have been used to update depth of the reservoir's bottom horizon. We obtained significant improvements in the history match quality and the predictive capability of the model.</p

Adjoint-based history matching of structural models using production and time-lapse seismic data

In spite of large uncertainties in the actual reservoir structure, structural parameters of a reservoir model are usually fixed during history matching and only the flow properties of the model are allowed to vary. This often leads to unlikely or even unfeasible property updates and possibly to a poor predictive capability of the model. In those cases it may be expected that updating of the structural parameters will improve the quality of the history match. Preferably such structural updates should be implemented in the static (geological) model, and not just in the dynamic (flow) model. In this paper we use a gradient-based history matching method to update structural properties of the static model. We use an adjoint method to efficiently compute the derivatives of the data mismatch with respect to grid block porosities in the dynamic model and convert the corresponding volume changes to structural updates (layer thicknesses) in the static model. This method is suitable for structural updating of large scale reservoir models using production data and/or time-lapse seismics or other spatially distributed data. The method is tested on a 3D synthetic model, where time-lapse as well as production data have been used to update depth of the reservoir's bottom horizon. We obtained significant improvements in the history match quality and the predictive capability of the model