Two counterfeit coins

AbstractWe consider the problem of ascertaining the minimum number of weighings which suffice to determine the counterfeit (heavier) coins in a set of n coins of the same appearance, given a balance scale and the information that there are exactly two heavier coins present. An optimal procedure is constructed for infinitely many n's, and for all other n's a lower bound and an upper bound for the maximum number of steps of an optimal precedure are determined which differ by just one unit. Some results of Cairns are improved, and his conjecture at the end of [3] is proved in a slightly modified form

Optimal detection of two counterfeit coins with two-arms balance

AbstractWe consider the following coin-weighing problem: suppose among the given n coins there are two counterfeit coins, which are either heavier or lighter than other n−2 good coins, this is not known beforehand. The weighing device is a two-arms balance. Let NA(k) be the number of coins from which k weighings suffice to identify the two counterfeit coins by algorithm A and U(k)=max{n|n(n−1)⩽3k} be the information-theoretic upper bound of the number of coins then NA(k)⩽U(k). We establish a new method of reducing the above original problem to another identity problem of more simple configurations. It is proved that the information-theoretic upper bound U(k) are always achievable for all even integer k⩾1. For odd integer k⩾1, our general results can be used to approximate arbitrarily the information-theoretic upper bound. The ideas and techniques of this paper can be easily employed to settle other models of two counterfeit coins

Identification of British one pound counterfeit coins using laser-induced breakdown spectroscopy

Acknowledgments The authors are grateful to Robert Matthews, C.Chem., MRSC for his generous loan of seven of the counterfeit coins.Peer reviewedPublisher PD

Selection of Robust Features for Coin Recognition and Counterfeit Coin Detection

Tremendous numbers of coins have been used in our daily life since ancient times. Aside from being a medium of goods and services, coins are items most collected worldwide. Simultaneously to the increasing number of coins in use, the number of counterfeit coins released into circulation is on the rise. Some countries have started to take different security measures to detect and eliminate counterfeit coins. However, the current measures are very expensive and ineffective such as the case in UK which recently decided to replace the whole coin design and release a new coin incorporating a set of security features. The demands of a cost effective and robust computer-aided system to classify and authenticate those coins have increased as a result. In this thesis, the design and implementation of coin recognition and counterfeit coin detection methods are proposed. This involves studying different coin stamp features and analyzing the sets of features that can uniquely and precisely differentiate coins of different countries and reject counterfeit coins. In addition, a new character segmentation method crafted for characters from coin images is proposed in this thesis. The proposed method for character segmentation is independent of the language of those characters. The experiments were performed on different coins with various characters and languages. The results show the effectiveness of the method to extract characters from different coins. The proposed method is the first to address character segmentation from coins. Coin recognition has been investigated in several research studies and different features have been selected for that purpose. This thesis proposes a new coin recognition method that focuses on small parts of the coin (characters) instead of extracting features from the whole coin image as proposed by other researchers. The method is evaluated on coins from different countries having different complexities, sizes, and qualities. The experimental results show that the proposed method compares favorably with other methods, and requires lower computational costs. Counterfeit coin detection is more challenging than coin recognition where the differences between genuine and counterfeit coins are much smaller. The high quality forged coins are very similar to genuine coins, yet the coin stamp features are never identical. This thesis discusses two counterfeit coin detection methods based on different features. The first method consists of an ensemble of three classifiers, where a fine-tuned convolutional neural network is used to extract features from coins to train two classifiers. The third classifier is trained on features extracted from textual area of the coin. On the other hand, sets of edge-based measures are used in the second method. Those measures are used to track differences in coin stamp’s edges between the test coin and a set of reference coins. A binary classifier is then trained based on the results of those measures. Finally, a series of experimental evaluation and tests have been performed to evaluate the effectiveness of these proposed methods, and they show that promising results have been achieved

Quantum Money with Classical Verification

We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. Our scheme is secure against adaptive adversaries - this property is not directly related to the possibility of classical verification, nevertheless none of the earlier quantum money constructions is known to possess it