Shannon Entropy Versus Renyi Entropy from a Cryptographic Viewpoint

Skorski, Maciej

doi:10.1007/978-3-319-27239-9_16

Cited by 13 publications

(9 citation statements)

References 21 publications

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“…The relation between the results of evaluating a cryptosystem using Shannon entropy and collision entropy was studied by Skorski [ 18 ], and the worst possible collision entropy for random variables with a given Shannon entropy was calculated.…”

Section: Entropy Measures and Related Conceptsmentioning

confidence: 99%

The Odyssey of Entropy: Cryptography

Zolfaghari

Bibak

Koshiba

2022

Entropy

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After being introduced by Shannon as a measure of disorder and unavailable information, the notion of entropy has found its applications in a broad range of scientific disciplines. In this paper, we present a systematic review on the applications of entropy and related information-theoretical concepts in the design, implementation and evaluation of cryptographic schemes, algorithms, devices and systems. Moreover, we study existing trends, and establish a roadmap for future research in these areas.

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Section: Entropy Measures and Related Conceptsmentioning

confidence: 99%

The Odyssey of Entropy: Cryptography

Zolfaghari

Bibak

Koshiba

2022

Entropy

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“…, P k ] b−1 , for some elements x there will be many patterns that give x = g (a,as,b) , while for other elements x there will be a few. To formalize this discussion we adapt the approach that Smith proposed in [22] about the Shannon entropy of completely partitioned sets, and the relations between Shannon entropy and several instances of Rényi entropy (such as collision entropy and min-entropy) studied by Cachin in [23] (see also the work of Skórski [24]).…”

Section: Dichotomy Between Odd and Even Basesmentioning

confidence: 99%

Entropoid Based Cryptography

Gligoroski

2021

Preprint

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The algebraic structures that are non-commutative and non-associative known as entropic groupoids that satisfy the "Palintropic" property i.e., x AB = (x A ) B = (x B ) A = x BA were proposed by Etherington in '40s from the 20th century. Those relations are exactly the Diffie-Hellman key exchange protocol relations used with groups. The arithmetic for non-associative power indices known as Logarithmetic was also proposed by Etherington and later developed by others in the 50s-70s. However, as far as we know, no one has ever proposed a succinct notation for exponentially large non-associative power indices that will have the property of fast exponentiation similarly as the fast exponentiation is achieved with ordinary arithmetic via the consecutive rising to the powers of two.In this paper, we define ringoid algebraic structures (G, , * ) where (G, ) is an Abelian group and (G, * ) is a non-commutative and non-associative groupoid with an entropic and palintropic subgroupoid which is a quasigroup, and we name those structures as Entropoids. We further define succinct notation for non-associative bracketing patterns and propose algorithms for fast exponentiation with those patterns.Next, by an analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman problem (CEDHP), and Decisional Entropoid Diffie-Hellman Problem (DEDHP). We post a conjecture that DEDHP is hard in Sylow q-subquasigroups. Next, we instantiate an entropoid Diffie-Hellman key exchange protocol. Due to the non-commutativity and non-associativity, the entropoid based cryptographic primitives are supposed to be resistant to quantum algorithms. At the same time, due to the proposed succinct notation for the power indices, the communication overhead in the entropoid based Diffie-Hellman key exchange is very low: for 128 bits of security, 64 bytes in total are communicated in both directions, and for 256 bits of security, 128 bytes in total are communicated in both directions.Our final contribution is in proposing two entropoid based digital signature schemes. The schemes are constructed with the Fiat-Shamir transformation of an identification scheme which security relies on a new hardness assumption: computing roots in finite entropoids is hard. If this assumption withstands the time's test, the first proposed signature scheme has excellent properties: for the classical security levels between 128 and 256 bits, the public and private key sizes are between 32 and 64, and the signature sizes are between 64 and 128 bytes. The second signature scheme reduces the finding of the roots in finite entropoids to computing discrete entropoid logarithms. In our opinion, this is a safer but more conservative design, and it pays the price in doubling the key sizes and the signature sizes.We give a proof-of-concept implementation in SageMath 9.2 for all proposed algorithms and schemes in an app...

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“…Observe that A cannot be considered a stochastic, or conditional probability, matrix, this is, in general ∑ j a ij = ∑ j t ij /y j = 1. However, the transposed matrix A is a stochastic matrix, and, by construction, it defines a Markov chain with stationary distribution y, this is, y = yA , Equation (13).…”

Section: Sam Coefficient Matrix As a Markov Chainmentioning

confidence: 99%

“…The minimum value of

is 0, when for some x ,

= 1 and all other probabilities are thus 0. Thus, entropy can be considered too a measure of homogeneity or uniformity of a distribution [ 13 ] or a diversity index [ 14 ], the higher its value the more homogeneous is the distribution and vice versa.…”

Section: Information Measures and Information Channelmentioning

confidence: 99%

Interpreting Social Accounting Matrix (SAM) as an Information Channel

Sbert

Chen

Feixas

et al. 2020

Entropy

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Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, we use the theory behind the information channel to provide an enhanced interpretation to a Social Accounting Matrix (SAM), a square matrix whose columns and rows present the expenditure and receipt accounts of economic actors. Under our interpretation, the SAM’s coefficients, which, conceptually, can be viewed as a Markov chain, can be interpreted as an information channel, allowing us to optimize the desired level of aggregation within the SAM. In addition, the developed information measures can describe accurately the evolution of a SAM over time. Interpreting the SAM matrix as an ergodic chain could show the effect of a shock on the economy after several periods or economic cycles. Under our new framework, finding the power limit of the matrix allows one to check (and confirm) whether the matrix is well-constructed (irreducible and aperiodic), and obtain new optimization functions to balance the SAM matrix. In addition to the theory, we also provide two empirical examples that support our channel concept and help to understand the associated measures.

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Shannon Entropy Versus Renyi Entropy from a Cryptographic Viewpoint

Cited by 13 publications

References 21 publications

The Odyssey of Entropy: Cryptography

The Odyssey of Entropy: Cryptography

Entropoid Based Cryptography

Interpreting Social Accounting Matrix (SAM) as an Information Channel

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