Key Agreement Protocol (KAP) Using Conjugacy and Discrete Logarithm Problems in Group Representation Level

doi:10.15388/Informatica.2007.167

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Authenticated Key Agreement Protocol Based on Provable Secure Cryptographic Functions

Ausrys Kilciauskas Gintaras Butkus Eligijus Sakalauskas

https://doi.org/10.15388/20-INFOR415

Pub. online: 6 May 2020 Type: Research Article

Open Access

Journal: Informatica Volume 31, Issue 2 (2020), pp. 277–298

Abstract

The vulnerable part of communications between user and server is the poor authentication level at the user’s side. For example, in e-banking systems for user authentication are used passwords that can be lost or swindled by a person maliciously impersonating bank.

To increase the security of e-banking system users should be supplied by the elements of public key infrastructure (PKI) but not necessary to the extent of standard requirements which are too complicated for ordinary users.

In this paper, we propose two versions of authenticated key agreement protocol (AKAP) which can be simply realized on the user’s side. AKAP is a collection of cryptographic functions having provable security properties.

It is proved that AKAP1 is secure against active adversary under discrete logarithm assumption when formulated certain conditions hold. AKAP2 provides user’s anonymity against eavesdropping adversary. The partial security of AKAP2 is investigated which relies on the security of asymmetric encryption function.

New Digital Signature Scheme in Gaussian Monoid

Eligijus Sakalauskas

https://doi.org/10.15388/Informatica.2004.058

Pub. online: 1 Jan 2004 Type: Research Article

Journal: Informatica Volume 15, Issue 2 (2004), pp. 251–270

Abstract

A new digital signature scheme in non‐commutative Gaussian monoid is presented. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. Monoid action level is defined as monoid element (word) action on module element as an operator. A module is a set of functions (elements) with special properties and could be treated as some generalization of vector space.

Signature scheme is based on the one‐way functions (OWF) design using: three recognized hard problems in monoid presentation level, one postulated hard problem in monoid action level and one provable hard problem in module action level.

For signature creation and verification the word equivalence problem is solved in monoid action level thus avoiding solving it in monoid presentation level. Then the three recognized hard problems in monoid presentation level can be essentially as hard as possible to increase signature security. Thus they do not influence on the word problem complexity and, consequently, on the complexity of signature realization.

The investigation of signature scheme security against four kind of attacks is presented. It is shown that the signature has a provable security property with respect to the list of attacks presented here, which are postulated to be complete.

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INFORMATICA

Online ISSN: 1822-8844
Print ISSN: 0868-4952

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