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The problem of information leak due to parasitic loop currents and voltages in the KLJN secure key exchange scheme

Melhem Mutaz Y., Kish Laszlo B.

Metrology and Measurement Systems

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2019

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Vol. 26, nr 1

37--40

EN

The Kirchhoff-law-Johnson-noise (KLJN) secure key exchange scheme offers unconditional security, however it can approach the perfect security limit only in the case when the practical system’s parameters approach the ideal behavior of its core circuitry. In the case of non-ideal features, non-zero information leak is present. The study of such leaks is important for a proper design of practical KLJN systems and their privacy amplifications in order to eliminate these problems.

2

Systemy uwierzytelniania pozapasmowego

Bilski T.

Studia Informatica

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2014

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Vol. 35, nr 3

39--51

PL

Standardowe kanały komunikacyjne oparte na falach elektromagnetycznych nie mogą być uznawane za zaufane i autentyczne. Docierające do odbiorcy fale elektromagnetyczne mogą pochodzić ze źródeł, których istnienie może być ukryte przed odbiorcą. W ogólnym przypadku użytkownik odbierający takie sygnały nie jest w stanie określić ich pochodzenia i nie ma pewności co do tego, czy sygnały te pochodzą od określonego (zaufanego) nadawcy. Brak tej pewności może prowadzić do naruszeń bezpieczeństwa, takich jak podszywanie się czy podsłuch. Tak więc pojawia się potrzeba uwierzytelnienia urządzenia bezprzewodowego bez użycia zwykłego kanału komunikacyjnego opartego na falach radiowych. Artykuł stanowi przegląd metod uwierzytelniania pozapasmowego. Uwzględniono zarówno prace teoretyczne, standardy, jak i rozwiązania komercyjne

EN

Standard communication channels based on radio waves may not be considered safe. Signals that user receives may come from different places, which may be hidden. User is not able to determine the source of the signals. This may be used by illegitimate users to spoof or to sniff wireless channel. In order to authenticate the sender’s wireless device one has to use additional out-of-band channel. The paper is a survey of out-of-band authentication methods and systems. Standards, theoretical works as well as commercial solutions have been presented.

3

On the key exchange and multivariate encryption with nonlinear polynomial maps of stable degree

Ustimenko V., Wroblewska A.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2013

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Vol. 13, no. 1

63--80

EN

We say that the sequence gn, n≥3, n→∞ of polynomial transformation bijective mapsof free module Kgn over commutative ring K is a sequence of stable degree if the order of gn is growing with n and the degree of each nonidentical polynomial map of kind gkn is an independent constant c. Transformation b = τgnkτ−1, where τ is the affine bijection, n is large and k is relatively small, can be used as a base of group theoretical Diffie-Hellman key exchange algorithm for the Cremona group C(Kn) of all regular automorphisms of Kn. The specific feature of this method is that the order of the base may be unknown for the adversary because of the complexity of its computation. The exchange can be implemented by tools of Computer Algebra (symbolic computations). The adversary can not use the degree of right handside in bx = d to evaluate unknown x in this form for the discrete logarithm problem. In the paper we introduce the explicit constructions of sequences of elements of stable degree for the cases c = 3 and c = n+2/4 for each commutative ring K containing at least 3 regular elements and discuss the implementation of related key exchange and multivariate map algorithms.

4

On the key exchange with new cubical maps based on graphs

Romańczuk U., Ustimenko V.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2011

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Vol. 11, no. 4

11--19

EN

Families of edge transitive algebraic graphs Fn(K), over the commutative ring K were used for the graph based cryptographic algorithms. We introduce a key exchange protocol defined in terms of bipartite graph An(K), n ≥ 2 with point set Pn and line set Ln isomorphic to n-dimensional free module Kn. Graphs A(n, K) are not vertex and edge transitive. There is a well defined projective limit lim A(n, K) = A(K), n → ∞ which is an infinite bipatrtite graph with point set P = lim Pn and line set L = limLn. Let K be a commutative ring contain at least 3 regular elements (not zero divisors). For each pair of (n, d), n ≥ 2, n ≥ 1 and sequence of elements α1, α2, …, α2d, such that α1, αi+αi+1, i = 1, 2, …, 2d, i = 1, 2, … 2d-1 and α2d+α1 are regular elements of the ring K. We define polynomial automorphism hn = hn (d, α1, α2, …, α2d) of variety Ln (or Pn). The existence of projective limit lim An(K) guarantees the existence of projective limit h = h(d, α1, α2, …, α2d) = lim hn, n → ∞ which is cubical automorphism of infinite dimensional varieties L (or P). We state that the order of h is an infinity. There is a constant n0 such that hn, n ≥ n0 is a cubical map. Obviously the order of hn is growing with the growth of n and the degree of polynomial map (hn)k from the Cremona group of all polynomial automorphisms of free module Kn with operation of composition is bounded by 3. Let τ be affine automorphism of Kn i.e. the element of Cremona group of degree 1. We suggest symbolic Diffie Hellman key exchange with the use of cyclic subgroup of Cremona group generated by τ-1hnτ. In the case of K = Fp, p is prime, the order of hn is the power of p. So the order is growing with the growth of p. We use computer simulation to evaluate the orders in some cases of K = Zm, where m is a composite integer.