arXiv subjects

Paul Hriljac

Publications and source records attributed to Paul Hriljac.

6 recordsLinked to original sources

arXiv2025

Some NP Complete Problems Based on Algebra and Algebraic Geometry

This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be converted into membership problems for a new family of algebraic varieties, coloring varieties, which are closely related to determinantal varieties. This in turn shows that the problem of NP vs P can be converted into questions of if certain polynomials of large degree over finite fields have low multiplicative complexity.

math.AG↗

arXiv2020

Constructing Cryptographic Multilinear Maps Using Affine Automorphisms

The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear pairings from the k-fold product of G to H. The construction is reminiscent of techniques in multivariate encryption. We display several different versions of the discrete logarithm problem for these groups. We show that the efficient solution of some of these problems result in efficient algorithms for inverting systems of multivariate polynomials corresponding to affine automorphisms, which implies that such problems are as computationally difficult as breaking multivariate encryption.

cs.CR↗

arXiv2020

Fully Homomorphic Encryption via Affine Automorphisms

Homomorphic encryption is a method used in cryptopgraphy to create programs that can interact with encrypted data without ever leaving the data in the clear. This has many potential applications in cybersecurity. This paper uses automorphisms of affine space to create a form of homomorphic encryption for straight line programs. The encryption method used for the data is known as multivariate encryption. This gives a potentially powerful new method in cyber security based on techniques from algebraic geometry.

cs.CR↗

arXiv2010

The Size of the Broad Line Region in M84 (NGC 4374)

M84 is a giant elliptical galaxy located in the Virgo cluster. Prior imaging with the Hubble Space Telescope (HST) revealed a small, highly inclined, nuclear ionized gas disk, the kinematics of which indicate the presence of a 0.4 -1.5 billion solar mass black hole. Two prominent radio jets emerge perpendicular to the nuclear ionized gas disk terminating in large radio lobes that extend beyond the visible galaxy. Plausible kinematic models are used to constrain the size of the broad line region (BLR) in M84 by modeling the shape of the broad H-alpha emission line profile. The analysis indicates that the emitting region is large with an outer radius between ~ 7 and 9 pc, depending on whether the kinematic model is represented by a spherically symmetric inflow or a Keplerian disk. The inferred size makes the BLR in M84 the largest yet to be measured. The fact that the BLR in M84 is so large may explain why the AGN is unable to sustain the ionization seen there. Thus, the BLR in M84 is not simply that of a scaled down quasar.

astro-ph.CO↗

arXiv2009

Nearby Galaxies in the 2micron All Sky Survey I. K-band Luminosity Functions

Differential K-band luminosity functions (LFs) are presented for a complete sample of 1613 nearby bright galaxies segregated by visible morphology. The LF for late-type spirals follows a power law that rises towards low luminosities whereas the LFs for ellipticals, lenticulars and bulge-dominated spirals are peaked and decline toward both higher and lower luminosities. Each morphological type (E, S0, S0/a-Sab, Sb-Sbc, Sc-Scd) contributes approximately equally to the overall K-band luminosity density of galaxies in the local universe. Type averaged bulge/disk ratios are used to subtract the disk component leading to the prediction that the K-band LF for bulges is bimodal with ellipticals dominating the high luminosity peak, comprising 60% of the bulge luminosity density in the local universe with the remaining 40% contributed by lenticulars and the bulges of spirals. Overall, bulges contribute 30% of the galaxy luminosity density at K in the local universe with spiral disks making up the remainder. If bulge luminosities indicate central black hole masses, then our results predict that the black hole mass function is also bimodal.

astro-ph.CO↗

arXiv2009

The Morphological Type Dependence of K-band Luminosity Functions

Differential 2.2um (K-band) luminosity functions are presented for a complete sample of 1570 nearby Vgsr < 3000 km/s, where Vgsr is the velocity measured with respect to the Galactic standard of rest), bright (K < 10 mag), galaxies segregated by visible morphology. The K-band luminosity function for late-type spirals follows a power law that rises towards low luminosities whereas the K-band luminosity functions for ellipticals, lenticulars and bulge-dominated spirals are peaked with a fall off at both high and low luminosities. However, each morphological type (E, S0, S0/a-Sab, Sb-Sbc, Sc-Scd) contributes approximately equally to the overall K-band luminosity density in the local universe, and by inference, the stellar mass density as well.

astro-ph.CO↗