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Subhash Kak

Publications and source records attributed to Subhash Kak.

At least 55 records · Page 3Linked to original sources
arXiv2013

Threshold Quantum Cryptography

Most current research on quantum cryptography requires transmission and reception of single photons that creates severe implementation challenges and limits range. This paper argues for the development of threshold quantum cryptography protocols in which the system is secure so long as the number of photons being exchanged between Alice and Bob is below a specified threshold. We speak of a (p-k-n) threshold system where if the number of photons exchanged is less than p, the system is completely secure, when it is between p and k, the system is partially secure, and when it exceeds k, the system is insecure. The BB84 protocol is (1-1-1) whereas the three-stage protocol appears to be (p-4p-n), where p is the least number of photons necessary to determine the polarization state of identically prepared photons. New quantum cryptography systems should be sought that provide greater flexibility in the choice of p and k.

quant-ph↗
arXiv2013

iAQC: The Intensity-Aware Quantum Cryptography Protocol

This paper reports a variant of the three-stage quantum cryptography protocol which can be used in low intensity laser output regimes. The variant, which tracks the intensity of the laser beam at the intermediate stages, makes the task of the eavesdropper harder than the standard K06 protocol. The constraints on the iAQC protocol are much less than those on BB84 and in principle it can not only be used for key distribution but also for direct bitwise encryption of data. The iAQC protocol is an improvement on the K06 protocol in that it makes it harder for the eavesdropper to monitor the channel.

quant-ph↗
arXiv2013

From the No-Signaling Theorem to Veiled Nonlocality

According to the no-signaling theorem, the nonlocal collapse of the wavefunction of an entangled particle by the measurement on its twin particle at a remote location cannot be used to send useful information. Given that experiments on nonlocal correlations continue to have loopholes, we propose a stronger principle that the nonlocality of quantum mechanics itself is veiled. In practical terms, decoherence and noise compels us to view the wavefunction as representing knowledge of potential outcomes rather than the reality. Experimental evidence in favor of naked nonlocality would support the view of the wavefunction as an objective description of physical reality.

physics.hist-ph↗
arXiv2013

Probability and the Classical/Quantum Divide

This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being different (Pn). Given three events, Ps/Pn for the classical case, where there are no 3-way coincidences, is one-half whereas for the quantum state it is one-third. For non-maximally entangled objects we find that so long as r < 5.83, we can separate them from classical objects using a probability test. For maximally entangled particles (r = 1), we propose that the value of 5/12 be used for Ps/Pn to separate classical and quantum states when no other information is available and measurements are noisy.

quant-ph↗
arXiv2013

The Number Theoretic Hilbert Transform

This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4-point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cryptographically useful scrambling transformations.

cs.CR↗
arXiv2013

Neural Network Capacity for Multilevel Inputs

This paper examines the memory capacity of generalized neural networks. Hopfield networks trained with a variety of learning techniques are investigated for their capacity both for binary and non-binary alphabets. It is shown that the capacity can be much increased when multilevel inputs are used. New learning strategies are proposed to increase Hopfield network capacity, and the scalability of these methods is also examined in respect to size of the network. The ability to recall entire patterns from stimulation of a single neuron is examined for the increased capacity networks.

cs.NE↗
arXiv2013

Residue Classes of the PPT Sequence

Primitive Pythagorean triples (PPT) may be put into different equivalence classes using residues with respect to primes. We show that the probability that the smaller odd number associated with the PPT triple is divisible by prime p is 2/(p+1). We have determined the autocorrelation function of the Baudhayana sequences obtained from the residue classes and we show these sequences have excellent randomness properties. We provide analytical explanation for the peak and the average off-peak values for the autocorrelation function. These sequences can be used specifically in a variety of key generation and distribution problems and, more generally, as pseudorandom sequences.

cs.CR↗
arXiv2013

Generalized Public Key Transformations with Side Information

This paper presents results on generalized public key cryptography with exponentials modulo primes and composite numbers where the mapping is not one-to-one and the uniqueness is achieved by additional side information. Such transformations may be used for oblivious transfer and generate events of specific probabilities.

cs.CR↗
arXiv2013

The Quartic Public Key Transformation

This paper presents the quartic public key transformation which can be used for public key applications if side information is also used. This extends an earlier work where the cubic transformation was similarly used. Such a transformation can be used in multiparty communications protocols.

cs.CR↗
arXiv2013

Another Look at Quantum Neural Computing

The term quantum neural computing indicates a unity in the functioning of the brain. It assumes that the neural structures perform classical processing and that the virtual particles associated with the dynamical states of the structures define the underlying quantum state. We revisit the concept and also summarize new arguments related to the learning modes of the brain in response to sensory input that may be aggregated in three types: associative, reorganizational, and quantum. The associative and reorganizational types are quite apparent based on experimental findings; it is much harder to establish that the brain as an entity exhibits quantum properties. We argue that the reorganizational behavior of the brain may be viewed as inner adjustment corresponding to its quantum behavior at the system level. Not only neural structures but their higher abstractions also may be seen as whole entities. We consider the dualities associated with the behavior of the brain and how these dualities are bridged.

cs.NE↗
arXiv2013

Simulating Entanglement in Classical Computing

This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the case where the mapping is of order k, we prove a theorem that gives us the function of the entangled state. A useful generalization beyond this research will be the implementation of quantum states with arbitrary probability amplitude functions.

quant-ph↗
arXiv2013

The Piggy Bank Cryptographic Trope

This paper presents applications of the trope of the locked and sealed piggy-bank into which the secret can be easily inserted but from which it cannot be withdrawn without opening the box. We present a basic two-pass cryptographic scheme that can serve as template for a variety of implementations. Together with the sealed piggy-bank is sent a coded letter that lists and certifies the contents of the box. We show how this idea can help increase the security of cryptographic protocols for classical systems as well as those based on "single-state" systems. More specifically, we propose the use of a hashing digest (instead of the coded letter) to detect loss of key bits to the eavesdropper and use in communication systems where error correction is an important issue.

cs.CR↗
arXiv2012

Random Sequences Based on the Divisor Pairs Function

This paper investigates the randomness properties of a function of the divisor pairs of a natural number. This function, the antecedents of which go to very ancient times, has randomness properties that can find applications in cryptography, key distribution, and other problems of computer science. It is shown that the function is aperiodic and it has excellent autocorrelation properties.

cs.CR↗
arXiv2012

Random Sequences from Primitive Pythagorean Triples

This paper shows that the six classes of PPTs can be put into two groups. Autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D (in which the largest term is divisible by 5) are different from the other four classes in their randomness properties if they are ordered by the largest term. In the other two orderings each of the six random Baudhayana sequences has excellent randomness properties.

cs.CR↗
arXiv2012

An Alignment Algorithm for Sequences

This paper describes a new alignment algorithm for sequences that can be used for determination of deletions and substitutions. It provides several solutions out of which the best one can be chosen on the basis of minimization of gaps or other considerations. The algorithm does not use similarity tables and it performs aspects of both global and local alignment. The algorithm is compared with other sequence alignment algorithms.

cs.IT↗
arXiv2012

Goldbach Circles and Balloons and Their Cross Correlation

Goldbach partitions can be used in creation of ellipses and circles on the number line. We extend this work and determine the count and other properties of concentric Goldbach circles for different values of n. The autocorrelation function of this sequence with respect to even and odd values suggests that it has excellent randomness properties. Cross correlation properties of ellipse and circle sequences are provided that indicate that these sequences have minimal dependencies and, therefore, they can be used in spread spectrum and other cryptographic applications.

cs.CR↗
arXiv2012

An Empirical Study of How Users Adopt Famous Entities

Users of social networking services construct their personal social networks by creating asymmetric and symmetric social links. Users usually follow friends and selected famous entities that include celebrities and news agencies. In this paper, we investigate how users follow famous entities. We statically and dynamically analyze data within a huge social networking service with a manually classified set of famous entities. The results show that the in-degree of famous entities does not fit to power-law distribution. Conversely, the maximum number of famous followees in one category for each user shows power-law property. To our best knowledge, there is no research work on this topic with human-chosen famous entity dataset in real life. These findings might be helpful in microblogging marketing and user classification.

cs.SI↗