Moving Card <i>i</i> to Position <i>j</i> with Perfect Shuffles

Ramnath, Sarnath; Scully, Daniel J.

doi:10.1080/0025570x.1996.11996475

Cited by 7 publications

(6 citation statements)

References 4 publications

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“…This is referred to as the perfect-2-shuffle or faro shuffle. There exist two instances of perfect-2-shuffle or faro shuffle; an out shuffle which leaves the top card at its original position and the second shuffle which makes the top card the second [35,36], Ramnath and Scully [37], [38]. up to nm.…”

Section: B the K-shufflementioning

confidence: 99%

Enhancing Image Security during Transmission using Residue Number System and k-shuffle

Alhassan

Ansong

Abdul-Salaam

et al. 2020

EJMS

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This paper proposes an algorithm that enhances the speed of transmission and secure images that are transmitted over internet or a network. The proposed cryptosystem uses a modified k-shuffling technique to scramble pixels of images and further decomposes them using Residue Number System. Simulations are done using two moduli sets with the modified k-shuffle technique. Analyses of results showed that both simulations could secure images without any loss of information and also the time taken for a complete encryption/decryption process is dependent on the moduli set. Among the chosen moduli sets, the even moduli set optimizes and completes execution using less time as compared to the traditional moduli set. The proposed scheme also showed resistance to statistical attacks (histogram, ciphertext, correlation attacks) and a significant reduction in the size of cipher images which enhances the speed of transmission over network.

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Section: B the K-shufflementioning

confidence: 99%

Enhancing Image Security during Transmission using Residue Number System and k-shuffle

Alhassan

Ansong

Abdul-Salaam

et al. 2020

EJMS

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“…We begin by reviewing some of the beautiful mathematics underlying standard perfect shuffles (see [4] for the proofs). Further interesting patterns and results (and mathematical card tricks) involving perfect shuffles are plentiful and provide ample opportunity for reading and investigation [5,6,11,13,14].…”

Section: Standard Perfect Shufflesmentioning

confidence: 99%

“…A perfect shuffle splits a deck of cards into two equal stacks and then perfectly interlaces the cards from the two stacks one after the other. Only experienced gamblers and magicians can perform perfect shuffles reliably, and yet the mathematics behind perfect shuffles has a rich history, spanning both recreational mathematics and deep, sophisticated work [2,4,5,6,7,11,13,14].…”

Section: Introductionmentioning

confidence: 99%

A look at generalized perfect shuffles

Johnson,

Manny,

Van Cott

et al. 2020

Preprint

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Standard perfect shuffles involve splitting a deck of 2n cards into two stacks and interlacing the cards from the stacks. There are two ways that this interlacing can be done, commonly referred to as an in shuffle and an out shuffle, respectively. In 1983, Diaconis, Graham, and Kantor determined the permutation group generated by in and out shuffles on a deck of 2n cards for all n. Diaconis et al. concluded their work by asking whether similar results can be found for so-called generalized perfect shuffles. For these new shuffles, we split a deck of mn cards into m stacks and similarly interlace the cards with an in m-shuffle or out m-shuffle (denoted Im and Om, respectively). In this paper, we find the structure of the group generated by these two shuffles for a deck of m k cards, together with m y -shuffles, for all possible values of m, k, and y. The group structure is completely determined by k/ gcd(y, k) and the parity of y/ gcd(y, k). In particular, the group structure is independent of the value of m.

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“…So for example to move the card into the position 20 we write this in binary as 10100 and so perform the following shuffles: in, out, in, out, out. Conversely there is a way to use in and out shuffles to move a card in any position in the deck to the top (see [2,6]).…”

Section: Faro Shufflingmentioning

confidence: 99%

The mathematics of the flip and horseshoe shuffles

Butler,

Diaconis,

Graham

2014

Preprint

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We consider new types of perfect shuffles wherein a deck is split in half, one half of the deck is "reversed", and then the cards are interlaced. Flip shuffles are when the reversal comes from flipping the half over so that we also need to account for face-up/face-down configurations while horseshoe shuffles are when the order of the cards are reversed but all cards still face the same direction. We show that these shuffles are closely related to faro shuffling and determine the order of the associated shuffling groups.

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Moving Card i to Position j with Perfect Shuffles

Cited by 7 publications

References 4 publications

Enhancing Image Security during Transmission using Residue Number System and k-shuffle

Enhancing Image Security during Transmission using Residue Number System and k-shuffle

A look at generalized perfect shuffles

The mathematics of the flip and horseshoe shuffles

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