scholarly journals Evaluation of effectiveness of chosen-plaintext attacks on the Rao-Nam cryptosystem over a finite Abelian group

Radiotekhnika ◽  
2021 ◽  
pp. 22-31
Author(s):  
A.N. Alekseychuk ◽  
O.S. Shevchuk
Keyword(s):  
Abelian Group ◽  
Simple Structure ◽  
Finite Abelian Group ◽  
Secret Key ◽  
Random Choice ◽  
Worst Case ◽  
Encryption Schemes ◽  
Symmetric Version ◽  
Equiprobable Scheme ◽  
Selection Of

The Rao-Nam cryptosystem is a symmetric version of the McEliece code-based cryptosystem proposed to get rid of the shortcomings inherent in the first symmetric code-based encryption schemes. Almost immediately after the publication of this cryptosystem, attacks on it based on selected plaintexts appeared, which led to the emergence of various improvements and modifications of the original cryptosystem. The secret key in the traditional Rao-Nam scheme is a certain Boolean matrix and a set of binary vectors used to generate distortions during encryption. Such vectors must have different syndromes, that is, be different modulo of the code generated by the rows of the specified matrix. The original work of Rao and Nam considered two methods of forming the set of these vectors, the first of which consists in using predetermined vectors of sufficiently large weight, and the second is random selection of these vectors according to the equiprobable scheme. It is known that the first option does not provide the proper security of the Rao – Nam cryptosystem (due to the small number and simple structure of these vectors), but the second option is more meaningful and requires additional research. The purpose of this paper is to obtain estimates of the effectiveness (time complexity for a given upper bound of the error probability) of attacks on a cryptosystem, which generalizes the traditional Rao – Nam scheme to the case of a finite Abelian group (note that the need to study such versions of the Rao – Nam cryptosystem is due to their consideration in recent publications). Two attacks, based on selected plaintext, are presented. The first of them is not mentioned in the works known to the authors of this article and, under certain well-defined conditions, it allows recovering the secret key of the cryptosystem with quadratic complexity. The second attack is a generalized and simplified version of the well-known Struik-van Tilburg attack. It is shown that the complexity of this attack depends on the power of the stabilizer of the set of vectors, which forms the second part of the key, in the translation group of the Abelian group, over which the Rao – Nam cryptosystem is considered. In this paper, a bound is obtained for the probability of triviality of the stabilizer under the condition of random choice of this set. From the obtained bound, it follows that Struik-van Tilburg attack is, on average, noticeably more efficient than the worst case considered earlier.

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

Representation of zero-sum invariants by sets of zero-sum sequences over a finite abelian group

2021 ◽  
Author(s):  
Weidong Gao ◽  
Siao Hong ◽  
Wanzhen Hui ◽  
Xue Li ◽  
Qiuyu Yin ◽  
...  
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Zero Sum

scholarly journals Selection of Optimal Magnets for Traction Motors to Prevent Demagnetization

Machines ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 124
Author(s):  
Dantam Rao ◽  
Madhan Bagianathan
Keyword(s):  
Flux Density ◽  
Electric Vehicles ◽  
Parallel Line ◽  
Low Grade ◽  
Lower Grade ◽  
Worst Case ◽  
Traction Motors ◽  
Knee Point ◽  
Point Of Intersection ◽  
Selection Of

Currently, permanent-magnet-type traction motors drive most electric vehicles. However, the potential demagnetization of magnets in these motors limits the performance of an electric vehicle. It is well known that during severe duty, the magnets are demagnetized if they operate beyond a ‘knee point’ in the B(H) curve. We show herein that the classic knee point definition can degrade a magnet by up to 4 grades. To prevent consequent excessive loss in performance, this paper defines the knee point k as the point of intersection of the B(H) curve and a parallel line that limits the reduction in its residual flux density to 1%. We show that operating above such a knee point will not be demagnetizing the magnets. It will also prevent a magnet from degenerating to a lower grade. The flux density at such a knee point, termed demag flux density, characterizes the onset of demagnetization. It rightly reflects the value of a magnet, so can be used as a basis to price the magnets. Including such knee points in the purchase specifications also helps avoid the penalty of getting the performance of a low-grade magnet out of a high-grade magnet. It also facilitates an accurate demagnetization analysis of traction motors in the worst-case conditions.

Stable cohomotopy and cobordism of abelian groups

1981 ◽  
Vol 90 (2) ◽  
pp. 273-278 ◽  
Author(s):  
C. T. Stretch
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Formal Group ◽  
Characteristic Class ◽  
Burnside Ring ◽  
Classifying Space ◽  
Formal Group Law ◽  
Stable Cohomotopy ◽  
Group Law

The object of this paper is to prove that for a finite abelian group G the natural map is injective, where Â(G) is the completion of the Burnside ring of G and σ0(BG) is the stable cohomotopy of the classifying space BG of G. The map â is detected by means of an M U* exponential characteristic class for permutation representations constructed in (11). The result is a generalization of a theorem of Laitinen (4) which treats elementary abelian groups using ordinary cohomology. One interesting feature of the present proof is that it makes explicit use of the universality of the formal group law of M U*. It also involves a computation of M U*(BG) in terms of the formal group law. This may be of independent interest. Since writing the paper the author has discovered that M U*(BG) has previously been calculated by Land-weber(5).

An improved query for the hidden subbroup problem

2014 ◽  
Vol 14 (5&6) ◽  
pp. 467-492
Author(s):  
Asif Shakeel
Keyword(s):  
Abelian Group ◽  
Standard Method ◽  
Finite Abelian Group ◽  
Quantum Algorithms ◽  
Success Probability ◽  
Hidden Subgroup Problem ◽  
Subgroup Identification ◽  
Subgroup Problem ◽  
Query Algorithms

The Hidden Subgroup Problem (HSP) is at the forefront of problems in quantum algorithms. In this paper, we introduce a new query, the \textit{character} query, generalizing the well-known phase kickback trick that was first used successfully to efficiently solve Deutsch's problem. An equal superposition query with $\vert 0 \rangle$ in the response register is typically used in the ``standard method" of single-query algorithms for the HSP. The proposed character query improves over this query by maximizing the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.

Generalization of Roos bias in RC4 and some results on key-keystream relations

2018 ◽  
Vol 12 (1) ◽  
pp. 43-56
Author(s):  
Sabyasachi Dey ◽  
Santanu Sarkar
Keyword(s):  
Large Scale ◽  
Simple Structure ◽  
Secret Key ◽  
Visual Patterns

AbstractRC4 has attracted many cryptologists due to its simple structure. In [9], Paterson, Poettering and Schuldt reported the results of a large scale computation of RC4 biases. Among the biases reported by them, we try to theoretically analyze a few which show very interesting visual patterns. We first study the bias which relates the key stream byte{z_{i}}with{i-k[0]}, where{k[0]}is the first byte of the secret key. We then present a generalization of the Roos bias. In 1995, Roos observed the bias of initial bytes{S[i]}of the permutation after KSA towards{f_{i}=\sum_{r=1}^{i}r+\sum_{r=0}^{i}K[r]}. Here we study the probability of{S[i]}equaling{f_{y}=\sum_{r=1}^{y}r+\sum_{r=0}^{y}K[r]}for{i\neq y}. Our generalization provides a complete correlation between{z_{i}}and{i-f_{y}}. We also analyze the key-keystream relation{z_{i}=f_{i-1}}which was studied by Maitra and Paul [6] in FSE 2008. We provide more accurate formulas for the probability of both{z_{i}=i-f_{i}}and{z_{i}=f_{i-1}}for differenti’s than the existing works.

scholarly journals On Subsequence Sums of a Zero-sum Free Sequence

10.37236/970 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Fang Sun
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Zero Sum ◽  
Open Question

Let $G$ be a finite abelian group with exponent $m$, and let $S$ be a sequence of elements in $G$. Let $f(S)$ denote the number of elements in $G$ which can be expressed as the sum over a nonempty subsequence of $S$. In this paper, we show that, if $|S|=m$ and $S$ contains no nonempty subsequence with zero sum, then $f(S)\geq 2m-1$. This answers an open question formulated by Gao and Leader. They proved the same result with the restriction $(m,6)=1$.

Sign in / Sign up

Export Citation Format

Share Document