From words to integers and beyond in corporate life

Poets have a licence to couch great truths in succinct, emotionally powerful, and perhaps slightly mysterious and ambiguous ways. On the other hand, it is the task of academics to explore such truths intellectually, in depth and detail, identifying the key constructs and their underlying relations and structures, hopefully without impairing the essential truth. So it could be said that in January 2013, around 60 academics gathered at the University of Texas, Austin under the benign and encouraging eye of their own muse, Professor Rod Hart, to play their role in exploring and explaining the underlying truth of Yan Zhen’s words. The goals of this chapter are quite broad. Rod was explicit and yet also somewhat Delphic in his expectations and aspirations for the chapter. Even though DICTION was a key analytic tool in most chapters, this chapter was not to be about DICTION per se, or simply a critique of the individual chapters forming this section of the book. Rather DICTION and these studies, as well as some others that got our attention, were to be more a launching pad for observations on what they revealed about the current state of understanding and research into the language of institutions, as well as some ‘adventurous’, but not too outlandish reflections on future challenges and opportunities.

High-Speed Fully Homomorphic Encryption Over the Integers

A fully homomorphic encryption (FHE) scheme is envisioned as a key cryptographic tool in building a secure and reliable cloud computing environment, as it allows arbitrary evaluation of a ciphertext without revealing the plaintext. However, existing FHE implementations remain impractical due to very high time and resource costs. To the authors’ knowledge, this paper presents the first hardware implementation of a full encryption primitive for FHE over the integers using FPGA technology. A large-integer multiplier architecture utilising Integer-FFT multiplication is proposed, and a large-integer Barrett modular reduction module is designed incorporating the proposed multiplier. The encryption primitive used in the integer-based FHE scheme is designed employing the proposed multiplier and modular reduction modules. The designs are verified using the Xilinx Virtex-7 FPGA platform. Experimental results show that a speed improvement factor of up to 44 is achievable for the hardware implementation of the FHE encryption scheme when compared to its corresponding software implementation. Moreover, performance analysis shows further speed improvements of the integer-based FHE encryption primitives may still be possible, for example through further optimisations or by targeting an ASIC platform.

A Note on Dividing Integers by Two

This note describes a simple method of dividing all integers, positive and negative, by two when represented in two's complement arithmetic.

Table of the first ten powers of the integers from 1 to 1000 ... December 1, 1938.

"Prepared by the 'Project for the computation of mathematical tables' sponsored by Dr. Lyman J. Briggs, director of the National bureau of standards, Washington, D.C., and under the auspices of the U.S. Works progress administration of New York city."--Pref.

Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0

This article provides necessary and sufficient conditions for both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2 to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect square. This is given in terms of the ideal theory of the underlying real quadratic order Z[√D].

Triples of Positive Integers with the same Sum and the same Product

It is proved that for every k there exist k triples of positive integers with the same sum and the same product.

An Efficient and Verifiable Solution to the Millionaire Problem

A new solution to the millionaire problem is designed on the base of two new techniques: zero test and batch equation. Zero test is a technique used to test whether one or more ciphertext contains a zero without revealing other information. Batch equation is a technique used to test equality of multiple integers. Combination of these two techniques produces the only known solution to the millionaire problem that is correct, private, publicly verifiable and efficient at the same time.

Artful determination : "state of the art" and PCME Ltd v. Goyen COntrols Co. UK Ltd

In a recent decision by Mr Justice Laddie, a patent was held anticipated by, inter alia, prior use of a device which fell within the claims of the patent in suit, even though its circuitry was enclosed in resin. The anticipating invention had been "made available to the public" within the terms of section 2 (2) of the Patents Act 1977 because its essential integers would have been revealed by an interesting character, the "skilled forensic engineer".

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to Real-Time Kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least-squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance-covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio-test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.

Fixed failure rate ambiguity validation methods for GPS and compass

Ambiguity resolution plays a crucial role in real time kinematic GNSS positioning which gives centimetre precision positioning results if all the ambiguities in each epoch are correctly fixed to integers. However, the incorrectly fixed ambiguities can result in large positioning offset up to several meters without notice. Hence, ambiguity validation is essential to control the ambiguity resolution quality. Currently, the most popular ambiguity validation is ratio test. The criterion of ratio test is often empirically determined. Empirically determined criterion can be dangerous, because a fixed criterion cannot fit all scenarios and does not directly control the ambiguity resolution risk. In practice, depending on the underlying model strength, the ratio test criterion can be too conservative for some model and becomes too risky for others. A more rational test method is to determine the criterion according to the underlying model and user requirement. Miss-detected incorrect integers will lead to a hazardous result, which should be strictly controlled. In ambiguity resolution miss-detected rate is often known as failure rate. In this paper, a fixed failure rate ratio test method is presented and applied in analysis of GPS and Compass positioning scenarios. A fixed failure rate approach is derived from the integer aperture estimation theory, which is theoretically rigorous. The criteria table for ratio test is computed based on extensive data simulations in the approach. The real-time users can determine the ratio test criterion by looking up the criteria table. This method has been applied in medium distance GPS ambiguity resolution but multi-constellation and high dimensional scenarios haven't been discussed so far. In this paper, a general ambiguity validation model is derived based on hypothesis test theory, and fixed failure rate approach is introduced, especially the relationship between ratio test threshold and failure rate is examined. In the last, Factors that influence fixed failure rate approach ratio test threshold is discussed according to extensive data simulation. The result shows that fixed failure rate approach is a more reasonable ambiguity validation method with proper stochastic model.

GNSS ambiguity resolution with controllable failure rate for long baseline network RTK

Many large-scale GNSS CORS networks have been deployed around the world to support various commercial and scientific applications. To make use of these networks for real-time kinematic positioning services, one of the major challenges is the ambiguity resolution (AR) over long inter-station baselines in the presence of considerable atmosphere biases. Usually, the widelane ambiguities are fixed first, followed by the procedure of determination of the narrowlane ambiguity integers based on the ionosphere-free model in which the widelane integers are introduced as known quantities. This paper seeks to improve the AR performance over long baseline through efficient procedures for improved float solutions and ambiguity fixing. The contribution is threefold: (1) instead of using the ionosphere-free measurements, the absolute and/or relative ionospheric constraints are introduced in the ionosphere-constrained model to enhance the model strength, thus resulting in the better float solutions; (2) the realistic widelane ambiguity precision is estimated by capturing the multipath effects due to the observation complexity, leading to improvement of reliability of widelane AR; (3) for the narrowlane AR, the partial AR for a subset of ambiguities selected according to the successively increased elevation is applied. For fixing the scalar ambiguity, an error probability controllable rounding method is proposed. The established ionosphere-constrained model can be efficiently solved based on the sequential Kalman filter. It can be either reduced to some special models simply by adjusting the variances of ionospheric constraints, or extended with more parameters and constraints. The presented methodology is tested over seven baselines of around 100 km from USA CORS network. The results show that the new widelane AR scheme can obtain the 99.4 % successful fixing rate with 0.6 % failure rate; while the new rounding method of narrowlane AR can obtain the fix rate of 89 % with failure rate of 0.8 %. In summary, the AR reliability can be efficiently improved with rigorous controllable probability of incorrectly fixed ambiguities.

Reversible and blind database watermarking using difference expansion

There has been significant research in the field of database watermarking recently. However, there has not been sufficient attention given to the requirement of providing reversibility (the ability to revert back to original relation from watermarked relation) and blindness (not needing the original relation for detection purpose) at the same time. This model has several disadvantages over reversible and blind watermarking (requiring only the watermarked relation and secret key from which the watermark is detected and the original relation is restored) including the inability to identify the rightful owner in case of successful secondary watermarking, the inability to revert the relation to the original data set (required in high precision industries) and the requirement to store the unmarked relation at a secure secondary storage. To overcome these problems, we propose a watermarking scheme that is reversible as well as blind. We utilize difference expansion on integers to achieve reversibility. The major advantages provided by our scheme are reversibility to a high quality original data set, rightful owner identification, resistance against secondary watermarking attacks, and no need to store the original database at a secure secondary storage. We have implemented our scheme and results show the success rate is limited to 11% even when 48% tuples are modified.