Final Permutation Research Articles

Description, Implementation and Performance/Security Analysis of ASCON128

The aim of the report is to introduce detailed description of the functioning of and to provide an efficient implementation (using bit-sliced implementation of S-Box) in C of encryption, decryption and authentication of the lightweight authenticated encryption algorithm ASCON 128 (sponge based SPN network based on Keccak like operations) as per the v 1.2 submitted to NIST. This is achieved using a sponge construction by setting up initialization state and performing 12 rounds of permutations, XORing consecutively the plaintext blocks (encryption) or ciphertext blocks (decryption) with first 64 bits of the state (after 6 rounds of sponge permutations) and after all consecutive operations on ciphertext/plaintext blocks, XORing the last 128 bits of the resultant state with the secret Key (after 12 rounds of final permutation operations) to produce/re-create the tag. Discussions on Key Features, Performance Analysis (comparison of ASCON 128 v/s AES 128 in GCM mode on our own PC), Performance Comparisons with other NIST lightweight cryptography contest finalists on ARM Cortex M3, and discussions on the Security Analysis (side channel attacks: fault injection and power analysis) of ASCON are included in this report.

Symmetrical Cryptosystems based on Cellular Automata

This paper deals with the development of two symmetric encryption algorithms on the basis of cellular automata: a block cipher, that is based on AES and uses three-dimensional cellular automata; a stream cipher, that exploits a hardware-software entropy generation (tracking of keystrokes and mouse pointer movement), as well as the developed hash function, based on “cryptographic sponge” architecture of SHA-3, modified by cellular automata transformations. The block cipher is designed in architecture of SP-network and uses the AES substitution block. Permutation layer and key generation is designed on the basis of cellular automata rules (rules “22”, “105” and “150”). The optimal number of rounds to achieve maximum crypto resistance is determined. The stream cipher is designed on the basis of hardware-software entropy generation and uses the cryptographic hash-function in the SHA-3 architecture. Permutation function is developed on the basis of cellular automata rules (rules “30” and “146”). The procedures of shift and permutation of rows and columns is used for better permutation. A final permutation of state elements is used to improve the avalanche effect. The received results are analyzed and summarized; the conclusions and justifications about cipher parameters (like number of rounds, where needed) are made.

Security of the Suffix Keyed Sponge

We formalize and analyze the general suffix keyed sponge construction, a pseudorandom function built on top of a cryptographic permutation. The construction hashes its data using the (keyless) sponge construction, transforms part of the state using the secret key, and generates the tag from the output of a final permutation call. In its simplest form, if the key and tag size are at most the rate of the sponge, one can see the suffix keyed sponge as a simple sponge function evaluation whose input is the plaintext appended with the key. The suffix keyed sponge is, however, much more general: the key and tag size may exceed the rate without any need to make extra permutation calls. We prove that the suffix keyed sponge construction achieves birthday-bound PRF security in the capacity, even if key and tag size exceed the rate. Furthermore, we prove that if the absorption of the key into the state happens in a leakage resilient manner, the suffix keyed sponge itself is leakage resilient as well. Our findings show that the suffix keyed sponge compares favorably with the hash-then-MAC construction. For instance, to reach a security level of k bits, the side-channel protected component in the suffix keyed sponge just needs to process k bits of input besides the key, whereas schemes following the hash-then-MAC construction need a side-channel protected MAC function that processes 2k bits of input besides the key. Moreover, even if we just consider black-box attacks, the MAC function in a hash-then-MAC scheme needs to be cryptographically strong whereas in the suffix keyed sponge the key may be absorbed by a simple XOR. The security proofs are performed using the H-coefficient technique, and make effective use of the multicollision limit function results of Daemen et al. (ASIACRYPT 2017), both for arguing that state manipulation larger than the rate is tolerated after key processing and for upper bounding the amount of leakage an attacker may gain about the secret key.

Whitman's "Song of Myself" The Structure of "Song of Myself"

Walt Whitman’s "song of myself" is one of the original twelve pieces- first edition of Leaves of Grass appeared in. 1852. Like most of the other Whitman’s poems, "song of myself" is revised extensively till its final permutation in 1881. The song is a sprawling combination of biography, sermon, and poetic meditation. It is not nearly as heavy-handed in its pronouncements as "Starting at Paumanok", rather, Whitman uses symbols and sly commentary to get at important issues. “Song of Myself” is composed more of vignettes than lists, he uses small, precisely drawn scenes to compose his. Song of My Self does not take on the title “Song of Myself” until the 1881 edition. Previously titled “Poem of Walt Whitman, an American” and, in the 1860, 1867, and 1871 editions, simply “Walt Whitman.” The poem’s shifting title suggests Whitman’s intentions. Whitman was acquainted with the varying aspects of the metropolis, listening to the oratory of the time, becoming intimate with drivers of omnibus and ferryboat pilots, joining the crowds at bathing beaches, all of which had an effect on the manner of his poetry. " Song of Myself" and other poems have distinctive features as repetition, parallelism, rhetorical mannerisms and the employment of the phrase instead of the foot as unit of rhythm, to create forms called free verse. "It stands to reason", says one critic, "that Whitman gave much thought to the planning and organizing of his poems" (James Miller, 1964).

APLIKASI ALGORITMA DES (DATA ENCRYPTION STANDARD) UNTUK PENGAMAN DATA

Cryptography is a field of knowledge which uses a mathematical equation to perform the encryption and decryption process. This technique is used to convert the data into a specific code, with the aim that the stored information can not be read by anyone except those who are eligible. In this final project will be presented the design of cryptographic applications with cryptographic algorithm Data Encryption Standard. This cryptographic applications implementing encryption and decryption method using the DES algorithm.This research will presenting application design of crioptographic and its algorithm data of DES. This application will implementing the way of encryption and decription using DES. DES algorithm is adopted as standard algorithm. Since that, DES has been used in desimination information widely to protect data savely. In every day live, DES is using in many applications like to encrypt PIN (Personal Identity Number) in ATM and Banking transactions via internet. Even government organitations in US like Departmen of Energy, Justice Department, and Federal Reserve System are using DES to protect their data desiminations.
 The principt of DES working is devides information in special blocks, so that DES is known as cipherblock. The messages will be randomly using standard matrix in DES alhgorithm. The first proces will generate DES key algorithm. Cipherblock with 64 bits block size. Because in this application we have designed internal key altogether in enription process. The next we will to do enription process. The steps in doine encryption will begin with choosing file .txt. This file contents will be changed as binery numbers using ASCII as reference. The changing file as binary will be devided into 64 bits. Its means automatically that in DES algorithm using 8-characters or 64-bits.
 Next step, the deviding text will be permutated using first permutation matrix, the goal is to randomice plaintext. The randomice text will devivided into 2 blocks which 32-bits in length. Each block will use L0 dan R0 as symbol. The next process will do 16-cycling process. After 16-cycling process, both blocks will put in unity. After that, we will final permutation with using permutation matrix iP-1

Relating the right key to the type A filling map and minimal defining chains

There are several combinatorial methods that can be used to produce type A Demazure characters (key polynomials). The alcove path model of Lenart and Postnikov provides a procedure that inputs a semistandard tableau T and outputs a saturated chain in the Bruhat order. The final permutation in this Bruhat chain determines a family of Demazure characters for which T contributes its weight. Separately, the right key of T introduced by Lascoux and Schützenberger also determines a family of Demazure characters for which T contributes its weight. In this paper we show that the final permutation in this Bruhat chain corresponds bijectively to the right key of the tableau. We will also show that the minimal defining sequence for T, as introduced by Lakshmibai, Musili, and Seshadri, is a sub-chain of this Bruhat chain. Most notably their final elements coincide. From this it follows that the generating sets for the Demazure characters produced by these three methods are equivalent.

Representing Permutations with Few Moves

Consider a finite sequence of permutations of the elements $1,\ldots,n$ with the property that each element changes its position by at most 1 from any permutation to the next. We call such a sequence a tangle, and we define a move of element $i$ to be a maximal subsequence of at least two consecutive permutations during which its positions form an arithmetic progression of common difference +1 or -1. We prove that for any initial and final permutations, there is a tangle connecting them in which each element makes at most 5 moves, and another in which the total number of moves is at most 4n. On the other hand, there exist permutations that require at least 3 moves for some element, and at least 2n-2 moves in total. If we further require that every pair of elements exchange positions at most once, then any two permutations can be connected by a tangle with at most $O(\log n)$ moves per element, but we do not know whether this can be reduced to O(1) per element, or to O(n) in total. A key tool is the introd...

Inversions and longest increasing subsequence for $k$-card-minimum random permutations

A random $n$-permutation may be generated by sequentially removing random cards $C_1,...,C_n$ from an $n$-card deck $D = \{1,...,n\}$. The permutation $\sigma$ is simply the sequence of cards in the order they are removed. This permutation is itself uniformly random, as long as each random card $C_t$ is drawn uniformly from the remaining set at time $t$. We consider, here, a variant of this simple procedure in which one is given a choice between $k$ random cards from the remaining set at each step, and selects the lowest numbered of these for removal. This induces a bias towards selecting lower numbered of the remaining cards at each step, and therefore leads to a final permutation which is more ''ordered'' than in the uniform case (i.e. closer to the identity permutation id $=(1,2,3,...,n)$). We quantify this effect in terms of two natural measures of order: The number of inversions $I$ and the length of the longest increasing subsequence $L$. For inversions, we establish a weak law of large numbers and central limit theorem, both for fixed and growing $k$. For the longest increasing subsequence, we establish the rate of scaling, in general, and existence of a weak law in the case of growing $k$. We also show that the minimum strategy, of selecting the minimum of the $k$ given choices at each step, is optimal for minimizing the number of inversions in the space of all online $k$-card selection rules.

A UNIQUE SORTING ALGORITHM WITH LINEAR TIME & SPACE COMPLEXITY

Sorting a list means selection of the particular permutation of the members of that list in which the final permutation contains members in increasing or in decreasing order. Sorted list is prerequisite of some optimized operations such as searching an element from a list, locating or removing an element to/ from a list and merging two sorted list in a database etc. As volume of information is growing up day by day in the world around us and these data are unavoidable to manage for real life situations, the efficient and cost effective sorting algorithms are required. There are several numbers of fundamental and problem oriented sorting algorithms but still now sorting a problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently and effectively despite of its simple and familiar statements. Algorithms having same efficiency to do a same work using different mechanisms must differ their required time and space. For that reason an algorithm is chosen according to one’s need with respect to space complexity and time complexity. Now a day, space (Memory) is available in market comparatively in cheap cost. So, time complexity is a major issue for an algorithm. Here, the presented approach is to sort a list with linear time and space complexity using divide and conquer rule by partitioning a problem into n (input size) number of sub problems then these sub problems are solved recursively. Required time and space for the algorithm is optimized through reducing the height of the recursive tree and reduced height is too small (as compared to the problem size) to evaluate. So, asymptotic efficiency of this algorithm is very high with respect to time and space.

개인 클라우드 컴퓨팅 환경을 위한 스프레드 랜덤 인터리버 기반의 효율적인 DES 알고리즘

본 논문에서는 개인기반 클라우드 컴퓨팅 환경에서 복잡하고 시간이 많이 소요되는 3DES 알고리즘에 비해 기존의 DES 암호화 알고리즘을 기반으로 안정성과 속도를 개선한 알고리즘을 제안한다. 제안하는 알고리즘은 DES 알고리즘에 있어 안전성 측면에서 단점인 초기치환 및 최종치환을 위한 고정된 치환테이블을 스프레드 랜덤 인터리버 기법을 적용한 동적 치환박스를 적용하여 보안성을 제고하였다. 기존 알고리즘과의 시뮬레이션 결과 비교를 통해 제안하는 알고리즘을 활용할 경우 최소한의 변경으로 전달 데이터에 대한 기밀성과 안정성을 확보하고 빠른 속도로 암호화 및 복호화를 달성할 수 있음을 확인할 수 있었으며 CBC 모드를 적용하여 가변 길이의 데이터에 대해서도 효과적인 암호화가 가능하다. An efficient encryption algorithm based on the Data Encryption Standard (DES) for personal cloud computing environments is presented. The proposed algorithm improves data privacy, security and also encryption speed, compared with the triple DES. The improvement of the proposed algorithm stems from enhanced privacy inherent from the use of spread random interleaver in the place of the known substitution table for initial and final permutations in the DES algorithm. The simulation results demonstrate that the interleaver based DES (I-DES) is found to run faster than the triple DES algorithm and also offer improved security. The proposed algorithm also offers encryption for variable-length data using the Cipher Block Chaining (CBC).

Strong convergence in posets

We consider the following solitaire game whose rules are reminiscent of the childrenʼs game of leapfrog. The game is played on a poset (P,≺) with n elements. The player is handed an arbitrary permutation π=(x1,x2,…,xn) of the elements in P. At each round an element may “skip over” a smaller element preceding it, i.e. swap positions with it. For example, if xi≺xi+1, then it is allowed to move from π to the permutation (x1,x2,…,xi−1,xi+1,xi,xi+2,…,xn) of Pʼs elements. The player is to carry out such steps as long as such swaps are possible. When there are several consecutive pairs of elements that satisfy this condition, the player can choose which pair to swap next. Does the playerʼs choice of swaps matter for the final permutation or is it uniquely determined by the initial order of Pʼs elements? The reader may guess correctly that the latter proposition is correct. What may be more surprising, perhaps, is that this question is not trivial. The proof works by constructing an appropriate system of invariants.

Subtalar Arthroscopy and Flurosocopy in Percutaneous Fixation of Intra-Articular Calcaneal Fractures: The Best of Both Worlds

Fixation of intra-articular calcaneal fractures has traditionally been guided by intraoperative fluoroscopy. Recent reports indicate that there is a role for subtalar arthroscopy in surgical fixation of these fractures. The earliest reports described the use of subtalar arthroscopy for joint assessment during late hardware removal. It then served as an adjunct for joint inspection in open reduction and internal fixation. In its final permutation, percutaneous arthroscopy was performed with minimally invasive reduction and fixation, minimizing soft tissue complications commonly associated with the open approach. In practiced hands, this technique yields good results with minimal morbidity. We performed a prospective analysis of 22 consecutive patients with Sanders II, AO-OTA 83-C2 intra-articular calcaneal fractures who underwent dual-modality imaging (subtalar arthroscopic- and intraoperative fluoroscopic-) guided percutaneous fracture fixation with a minimum follow-up of 2 years. Maximum accepted postreduction step-off was 1 mm. Fractures were fixed definitively with four to eight percutaneous cancellous screws. There was significant correction of Böhler's tuberosity-joint angle from 4.2 degrees±11.1 degrees preoperatively to 21.3 degrees±8.8 degrees on immediate postoperative radiographs, with minimal subsidence to 20.1 degrees±8.2 degrees at 2 years. Böhler's angle correction and joint surface restoration could not be achieved percutaneously in one patient with an impacted, depressed joint fragment. Compared with preoperative values, there was significant improvement in mean Visual Analog Scale, American Orthopedic Foot and Ankle Society Ankle-Hindfoot Score, and Short Form-36 (Physical Function) scores at 3 months, with further improvement up to 2-years. Subtalar arthroscopy augments intraoperative fluoroscopy in anatomic reduction of the posterior calcaneal facet of the subtalar joint and is most useful for Sanders type II, AO-OTA 83-C2 fractures. The percutaneous approach further avoids soft tissue complications associated with open reduction. However, this procedure has a steep learning curve, and conversion to open reduction must be considered when percutaneous reduction fails.

On biases of permutation and keystream bytes of RC4 towards the secret key

A theoretical analysis of the RC4 Key Scheduling Algorithm (KSA) is presented in this paper, where the nonlinear operation is swapping among the permutation bytes. Explicit formulae are provided for the probabilities with which the permutation bytes at any stage of the KSA are biased to the secret key. Theoretical proofs of these formulae have been left open since Roos’ work (1995). Next, a generalization of the RC4 KSA is analyzed corresponding to a class of update functions of the indices involved in the swaps. This reveals an inherent weakness of shuffle-exchange kind of key scheduling. Moreover, we show that biases towards the secret key also exist in S[S[y]], S[S[S[y]]], and so on, for initial values of y. We additionally show that each byte of SN actually reveals secret key information. Looking at all the elements of the final permutation SN and its inverse \(S^{-1}_N\), the value of the hidden index j in each round of the KSA can be estimated from a “pair of values” in 0, ..., N − 1 with a constant probability of success \(\pi = \frac{N-2}{N}\cdot(\frac{N-1}{N})^{N-1} + \frac{2}{N}\) (we get π ≈ 0.37, for N = 256), which is significantly higher than the random association. Using the values of two consecutive j’s, we estimate the y-th key byte from at most a “quadruple of values” in 0, ..., N − 1 with a probability > 0.12. As a secret key of l bytes is repeated at least \(\lfloor \frac{N}{l}\rfloor\) times in RC4, these many quadruples can be accumulated to get each byte of the secret key with very high probability (e.g., 0.8 to close to 1) from a small set of values. Based on our analysis of the key scheduling, we show that the secret key of RC4 can be recovered from the state information in a time much less than the exhaustive search with good probability. Finally, based on the above biases of the permutation after the KSA and other related results, a complete framework is presented to show that many keystream output bytes of RC4 are significantly biased towards several linear combinations of the secret key bytes. The results do not assume any condition on the secret key. We find new biases in the initial as well as in the 256-th and 257-th keystream output bytes.

The Linear Ordering Problem with cumulative costs

The optimization problem of finding a permutation of a given set of items that minimizes a certain cost function is naturally modeled by introducing a complete digraph G whose vertices correspond to the items to be sorted. Depending on the cost function to be used, different optimization problems can be defined on G. The most familiar one is the min-cost Hamiltonian path problem (or its closed-path version, the Traveling Salesman Problem), arising when the cost of a given permutation only depends on consecutive node pairs. A more complex situation arises when a given cost has to be paid whenever an item is ranked before another one in the final permutation. In this case, a feasible solution is associated with an acyclic tournament (the transitive closure of an Hamiltonian path), and the resulting problem is known as the Linear Ordering Problem (LOP). In this paper we introduce and study a relevant case of LOP arising when the overall permutation cost can be expressed as the sum of terms α u associated with each item u, each defined as a linear combination of the values α v of all items v that follow u in the permutation. This setting implies a cumulative (nonlinear) propagation of the value of variables α v along the node permutation, hence the name Linear Ordering Problem with Cumulative Costs. We illustrate the practical application in wireless telecommunication system that motivated the present study. We prove complexity results, and propose a Mixed-Integer Linear Programming model as well as an ad hoc enumerative algorithm for the exact solution of the problem. A dynamic-programming heuristic is also described. Extensive computational results on large sets of instances are presented, showing that the proposed techniques are capable of solving, in reasonable computing times, all the instances coming from our application.

The Fundamental DistinctionDogmatik des christlichen Glaubens, Vol. 3, Der Glaube an Gott den Vollender der Welt. Gerhard Ebeling

Previous articleNext article No AccessReview ArticlesThe Fundamental Distinction Dogmatik des christlichen Glaubens, Vol. 3, Der Glaube an Gott den Vollender der Welt. Gerhard Ebeling Duane A. PriebeDuane A. Priebe Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Journal of Religion Volume 61, Number 3Jul., 1981 Article DOIhttps://doi.org/10.1086/486875 Views: 2Total views on this site Copyright 1981 The University of ChicagoPDF download Crossref reports no articles citing this article.

An algorithm for computing the mixed radix fast Fourier transform

This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.