Pub. online:6 May 2020Type:Research ArticleOpen Access
Volume 31, Issue 2 (2020), pp. 277–298
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.
Pub. online:1 Jan 2017Type:Research ArticleOpen Access
Volume 28, Issue 3 (2017), pp. 517–524
In this paper we consider an improved version of earlier published asymmetric encryption protocol based on matrix power function (MPF). Recently, a linear algebra attack on earlier version of this protocol was found. This attack allows an attacker to break suggested protocol in polynomial time.
Here we show that the improved version of our encryption protocol is not vulnerable to the declared linear attack, while retaining its effective realization in embedded systems.
Pub. online:1 Jan 2014Type:Research ArticleOpen Access
Volume 25, Issue 2 (2014), pp. 283–298
New asymmetric cipher based on matrix power function is presented. Cipher belongs to the class of recently intensively evolving non-commuting cryptography due to expectation of its resistance to potential quantum cryptanalysis.
The algebraic structures for proposed cipher construction are defined. Security analysis was performed and security parameters are defined. On the base of this research the secure parameters values are determined. The comparison of efficiency of microprocessor realization of proposed algorithm with different security parameters values is presented.
Pub. online:1 Jan 2010Type:Research ArticleOpen Access
Volume 21, Issue 2 (2010), pp. 215–228
The asymmetric cipher protocol, based on decomposition problem in matrix semiring ℳ over semiring of natural numbers 𝒩 is presented. The security of presented cipher protocol is based on matrix decomposition problem (MDP), which is linked to the problem of solution of multivariate polynomial system of equations. Compromitation of proposed scheme relies on the solution of system of multivariate polynomial system of equations over the semiring of natural numbers 𝒩. The security parameters are defined, security analysis and implementation is presented.
Pub. online:1 Jan 2007Type:Research ArticleOpen Access
Volume 18, Issue 1 (2007), pp. 115–124
The key agreement protocol based on infinite non-commutative group presentation and representation levels is proposed.
Two simultaneous problems in group representation level are used: the conjugator search problem (CSP) and modified discrete logarithm problem (DLP). The modified DLP in our approach is a matrix DLP and is different from that's used in other publications. The algorithm construction does not allow to perform a crypto-analysis by replacing the existing CSP solution to the decomposition problem (DP) solution.
The group presentation level serves for two commuting subgroups and invertible group's word image matrix construction. The group representation level allows reliable factors disguising in the initial word. The word equivalence problem (WEP) solution is transformed from the group presentation level to the group representation level. Hence there are not necessary to solve WEP in the group presentation level and hence there are no restrictions on the group complexity in this sense. The construction of irreducible representation of group is required. The presented protocol is a modernization of protocol declared in (Sakalauskas et al., 2005).
Pub. online:1 Jan 2005Type:Research ArticleOpen Access
Volume 16, Issue 3 (2005), pp. 383–394
A modernization of signature scheme published in (Sakalauskas, 2004) is presented. This scheme differs from the prototype by its structure and uses a more general algebraic systems. It has a higher security and shorter key length and is also more computationally effective.
The introduced new algebraic structures, semiring and semimodule, are mutually compatible algebraic systems. The semiring is a set of operators acting in a semimodule as endomorphisms. There is postulated that action operation has a one-way function (OWF) property. The compatibility of both algebraic structures' means that the action operation has right and left distributivity property with respect to the additive operation defined in semimodule and semiring.
Two other essential OWFs are defined. The latter are based on known constructions and have a greater complexity than other recognized hard problems such as conjugator search problem in noncommutative groups, for example.
Pub. online:1 Jan 2004Type:Research ArticleOpen Access
Volume 15, Issue 2 (2004), pp. 251–270
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.
Volume 30, Issue 2 (2019), pp. 327–348
In our previous paper we presented an offline e-cash system with observers. We have shown that the proposed system satisfies basic requirements for e-cash schemes. We also covered such security issues as chosen message attack resistance and forgery of protocols data. However, in that paper we focused more on the system itself, rather than its analysis.
Hence, here we present cryptanalysis of our system. We aim to prove that existential forgery of data is not possible due to complexity of the discrete logarithm problem. Furthermore, we perform the analysis of trustworthiness of the system using the so-called BAN logic. Also, we consider effectivity of the proposed e-cash system in observers with limited computational resources.