Routo Terada

Automatic Programming of Morphological Machines by PAC Learning

An important aspect of mathematical morphology is the description of complete lattice operators by a formal language, the Morphological Language (ML), whose vocabulary is composed of infimum, supremum, dilations, erosions, anti-dilations and anti-erosions. This language is complete (i.e., it can represent any complete lattice operator) and expressive (i.e., many useful operators can be represented as phrases with relatively few words). Since the sixties special machines, the Morphological Machines (MMachs), have been built to implement the ML restricted to the lattices of binary and gray-scale images. However, designing useful MMach programs is not an elementary task. Recently, much research effort has been addressed to automate the programming of MMachs. The goal of the different approaches for this problem is to find suitable knowledge representation formalisms to describe transformations over geometric structures and to translate them automatically into MMach programs by computational systems. We present here the central ideas of an approach based on the representation of transformations by collections of observed-ideal pairs of images and the estimation of suitable operators from these data. In this approach, the estimation of operators is based on statistical optimization or, equivalently, on a branch of Machine Learning Theory known as PAC Learning. These operators are generated as standard form morphological operators that may be simplified (i.e., transformed into equivalent morphological operators that use fewer vocabulary words) by syntactical transformations.

Text segmentation by automatically designed morphological operators

Identification of areas corresponding to text in document images is an important step for a character recognition system. We briefly review a technique for automatic design of binary morphological operators and show its application to the segmentation of text areas from document page images. We also present an heuristic filter used to refine the segmentation results. Results obtained for two different sets of images are shown.

OCR based on mathematical morphology

We present the prototype of an OCR that was designed and implemented at the Institute of Mathematics and Statistics of the University of Sao Paulo. The remarkable characteristic of this system is that all the necessary image processing tasks are performed by Mathematical Morphology operators (the so called morphological operators). Thus, we have developed morphological operators to segment scanned images (i.e., identify objects as characters, words and paragraphs), and recognize font styles and character semantics. The morphological operators that perform segmentation were designed by classical heuristic techniques, while the ones that recognize fonts and characters were designed automatically by new computational learning techniques. The fundamental idea under these techniques is the estimation of a morphological operator from observations of input-output image pairs, that describe its ideal performance. The morphological operators designed have been integrated in a system that translate scanned images into RTF text files, with reasonable correction and time performance. This system has been developed in the KHOROS platform, using the MMach (for morphological operators design heuristically) and PAC (for morphological operators designed by learning) toolboxes.

Boosting OCR Classifier by Optimal Edge Noise Filtering

The problem of Optical Character Recognition (OCR) can be solved by set operators implemented as programs for a Morphological Machine (MMach). In this paper, we present two techniques to boost such programs: (1) Anchoring and (2) Edge Noise Filtering by Stamp. The power of these techniques is demonstrated by some impressive experimental results.

AUTOMATIC PROGRAMMING OF MMACH'S FOR OCR·

Binary Image Analysis problems can be solved by set operators implemented as programs for a Morphological Machine (MMach). These programs can be generated automatically by the description of the goals of the user as a collection of input-output image pairs and the estimation of the target operator from these data. In this paper, we present a software, installed as a Toolbox for the KHOROS system, that implements this technique and some impressive results of applying this tool in shape recognition for OCR.

Multi-resolution classification trees in OCR design

The paper recalls the idea of classification trees in OCR (optical character recognition) systems and proposes a technique for the automatic design of these classification trees. The design of both the classification trees and of the classification operators are based on training from sample pairs of observed-ideal images, allowing the development of customized OCRs.

An Augmented Family of Cryptographic Parity Circuits

A computationally inexpensive involution called value dependent swapping is introduced. This involution is included in the non-linear cryptographic family of functions called Parity Circuits to increase its non-affineness and thus increase its strength against cryptanalysis. Our analysis shows that this augmented version of Parity Circuits still has fundamental cryptographic properties. The addition of this involution introduces a new type of randomization while preserving the invertibility of the functions being defined. We formulate affineness for a general function, and introduce a normalized non-affineness measure. We prove some non-affineness conditions for the augmented Parity Circuits, and evaluate their non-affineness. We suggest the value-dependent swapping can also be incorporated into DES-like cryptographic functions as well to make them stronger against cryptanalysis.

Proposal of Enhancement for Quartz Digital Signature

Today, we see a large dependence on systems developed with cryptography. Especially in terms of public key cryptosystems, which are widely used on the Internet. However, public key cryptography was threatened and new sources began to be investigated when Shor in 1997 developed a polynomial time algorithm for factoring integers and to compute the discrete logarithm with a quantum computer. In this context, Patarin proposed Hidden Field Equations (HFE), a trapdoor based on MQ (Multivariate Quadratic) and IP (Isomorphism of Polynomials) problems. Such problems are not affected by the Shor algorithm, moreover MQ Problem was proved by Patarin and Goubin to be NP-complete. Despite the basic HFE has been broken, there are variants that are secure, obtained by a generic modification. The Quartz - digital signature scheme based on HFEv-, with special choice of parameters - is a good example of this resistance to algebraic attacks aimed at the recovery of the private key, because even today it remains secure. Furthermore, it also generates short signatures. However, Joux and Martinet, based on axioms of Birthday Paradox Attack, proved that Quartz is malleable, showing that if the adversary has a valid pair (message, signature), he can get a second signature with 250 computations and 250 calls to the signing oracle, so that the estimated current security standards are at least 2112. Thus, based on Quartz, we present a new digital signature scheme, achieving the adaptive chosen message attacks that make calls to the random oracle, with a security level estimated at 2112. Our cryptosystem also provides an efficiency gain in signature verification algorithm and vector initializations that will be used for signing and verification algorithms. Furthermore we provide an implementation of Original Quartz and Enhanced Quartz in the Java programming language.

RSA and Elliptic Curve Least Significant Bit Security

The security of the least significant bit (LSB) of the secret key in the Elliptic Curve Diffie-Hellman protocol (and of the message in the RSA) is related to the security of the whole key (and of the whole message, respectively). Algorithms to invert these cryptographic algorithms, making use of oracles that predict the LSB, have been published. We implement two of these algorithms, identify critical parameters, and modify the sampling to achieve a significant improvement in running times.

Factoring a Multiprime Modulus N with Random Bits

In 2009, Heninger and Shacham presented an algorithm using the Hensels lemma for reconstructing the prime factors of the modulus