Introduction To Research
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The document discusses two research studies: 1. TeleMed, a system that aims to control a microscope from a computer for use in pathology and medicine. It allows remote off-site control of microscope functions through software and an interface board. 2. A comparative study of the antibacterial properties of three chili pepper varieties on human dental microflora. It found that C. frutescens was most effective at inhibiting two bacterial species, while C. annuum var. longgum worked best against one isolate. Minimum inhibitory and bactericidal concentrations were determined.
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This document provides an overview of key concepts in research methods. It defines research as a systematic, objective inquiry undertaken to find answers to specific problems. The purposes of research are then outlined, including reviewing existing knowledge, investigating problems or situations, providing solutions, and generating new knowledge. Quantitative and qualitative approaches as well as deductive and inductive research are briefly described. Several research methodologies such as surveys, experiments, longitudinal studies, and case studies are then defined. The document concludes by outlining steps in the research process such as developing a research proposal, literature review, objectives, variables, conceptual framework, hypotheses, methods, and limitations.
1.a brief introduction to reserach methodlogy
Research involves defining problems, formulating hypotheses, collecting and evaluating data, reaching conclusions, and testing those conclusions. It is a systematic process that requires accurate data collection and adherence to ethical standards. Research aims to generate new knowledge and insights through logical reasoning using both inductive and deductive methods. The purpose of research can be descriptive, explanatory, or exploratory. There are different types of research methodologies including basic vs applied, descriptive vs exploratory, correlational vs explanatory, qualitative vs quantitative, and conceptual vs empirical research.
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This document discusses key aspects of research methodology. It begins by defining research as a systematic process of examining a topic closely through various methods such as observation and experimentation. The document then outlines several types of research including pure research, applied research, descriptive research, and correlational research. It also discusses different research methods like library research, field research, and laboratory research. The rest of the document delves into various steps of research methodology such as formulating hypotheses, preparing a research design, identifying variable types, and qualifying a rigorous research. Overall, the document provides a comprehensive overview of conceptualizing and planning a scientific research study.
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This document discusses research methods and design. It defines research as a systematic, scientific investigation of a topic to discover new facts or test hypotheses. Research aims to contribute new knowledge through carefully defining problems, formulating hypotheses, collecting and analyzing data, reaching conclusions, and testing conclusions. The key objectives of research are exploratory, descriptive, diagnostic, and hypothesis testing. Characteristics of good research include being directed, empirical, carefully recorded and reported. The common steps in research are formulating the problem, reviewing literature, developing hypotheses, deciding design, collecting and analyzing data, testing hypotheses, and reporting conclusions.
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This document provides an overview of research methodology. It discusses what research is, different types of research including quantitative, qualitative, descriptive, and longitudinal research. It also outlines the research process and covers topics such as research questions, hypotheses, data collection methods, analysis, and reporting. Research is defined as a systematic and organized way to find answers to questions. It is considered a more valid basis of knowledge than alternatives like authority, tradition, or personal experiences.
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Research is the systematic and objective analysis and recording of controlled observations that may lead to the development of generalizations, principles, or theories, resulting in prediction and possible control of events .
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1.a brief introduction to reserach methodlogy
Research involves defining problems, formulating hypotheses, collecting and evaluating data, reaching conclusions, and testing those conclusions. It is a systematic process that requires accurate data collection and adherence to ethical standards. Research aims to generate new knowledge and insights through logical reasoning using both inductive and deductive methods. The purpose of research can be descriptive, explanatory, or exploratory. There are different types of research methodologies including basic vs applied, descriptive vs exploratory, correlational vs explanatory, qualitative vs quantitative, and conceptual vs empirical research.
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The document discusses various aspects of research methodology including defining the research problem, reviewing literature, and formulating hypotheses. It provides details on:
1) Defining the research problem involves identifying and selecting a problem and then precisely formulating it.
2) Reviewing literature helps gain background knowledge and identify relationships between concepts to form hypotheses. Literature is recorded systematically.
3) A hypothesis is a testable statement about the relationship between variables. It predicts the influence of independent variables on dependent variables.
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Research methodology
Research is defined as a systematic, scientific search for information to increase knowledge. It involves defining problems, formulating hypotheses, collecting and analyzing data, reaching conclusions, and testing conclusions. The main types of research are fundamental/basic research, which seeks knowledge without a defined goal, and applied research, which is problem-oriented and directed toward a specific end. The objectives of research are to discover new information, develop new tools and techniques, gain familiarity with phenomena, describe characteristics accurately, and identify causal relationships between variables. Problems that can arise in research include a lack of scientific training, delays in accessing data, human biases, insufficient time and funding, and uncontrolled variables.
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This document is quoted from Academic Writing Skill, IFL, Cambodia. It's for students in year three not only at IFL but also other universities in Cambodia.
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The document discusses various types of research including descriptive research, which describes characteristics without determining causes, and analytical research, which evaluates facts and information. It also discusses applied research which aims to solve immediate problems, and basic research which improves scientific understanding without specific applications. Additional types discussed are quantitative research using measurement, qualitative research investigating human behavior, conceptual research developing new ideas, empirical research using observation, and historical research studying past events.
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The document discusses various aspects of research methodology including defining the research problem, reviewing literature, and formulating hypotheses. It provides details on:
1) Defining the research problem involves identifying and selecting a problem and then precisely formulating it.
2) Reviewing literature helps gain background knowledge and identify relationships between concepts to form hypotheses. Literature is recorded systematically.
3) A hypothesis is a testable statement about the relationship between variables. It predicts the influence of independent variables on dependent variables.
Research methodology
This document outlines the key steps in the research methodology process. It defines research as a systematic effort to gain new knowledge. The main steps include: reviewing existing literature, identifying problems, setting objectives and hypotheses, planning the methodology, executing the research, analyzing data, drawing inferences, and disseminating findings. It also discusses defining the research problem precisely, formulating objectives, conducting a literature review to learn from past studies, and concluding the research by summarizing the findings and their significance.
Research methodology
Research is defined as a systematic, scientific search for information to increase knowledge. It involves defining problems, formulating hypotheses, collecting and analyzing data, reaching conclusions, and testing conclusions. The main types of research are fundamental/basic research, which seeks knowledge without a defined goal, and applied research, which is problem-oriented and directed toward a specific end. The objectives of research are to discover new information, develop new tools and techniques, gain familiarity with phenomena, describe characteristics accurately, and identify causal relationships between variables. Problems that can arise in research include a lack of scientific training, delays in accessing data, human biases, insufficient time and funding, and uncontrolled variables.
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This document provides an introduction to research methodology. It defines what research is, including that it is a formal, systematic process using the scientific method. The document discusses the aims of research as discovering new information, expanding knowledge, and solving problems. Basic research aims to contribute to knowledge, while applied research aims to solve current problems. The document also discusses internal vs. external research teams, how managers should interact with researchers, research ethics, and the scientific investigation process. It provides examples of research areas and defines different types of hypotheses used in research.
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The document discusses different types of quantitative research, including experimental research which treats subjects in a definite manner to determine the effects of a treatment. Experimental research uses two groups - an experimental group that receives treatment and a control group that does not. Experimental research is further classified into true experimental and quasi-experimental research. The document provides key terms related to quantitative research such as control group, comparative, and correlational research.
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The document discusses various aspects of research design. It defines research design and notes that it involves decisions about what, where, when, how much and by what means an inquiry will be conducted. It outlines requirements like identifying the type of research, being realistic and precise. Factors affecting research design are also discussed, like availability of data, time and resources. The main parts of research design are described as sampling design, observational design, statistical design and operational design. Different types of research designs are explained, including exploratory, descriptive, diagnostic and experimental designs. Key concepts in research design are also covered.
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This document discusses research in health and social care. It begins by defining research and explaining why it is needed to systematically build knowledge and test treatments. The document then outlines three basic characteristics of research in this field - that it must be logical, understandable, and useful. Next, it describes the overall research process and some common research philosophies and methodologies, including quantitative, qualitative and mixed methods approaches. Examples of different types of research projects are also provided.
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This document discusses research questions and the process of formulating research problems. It begins by defining research and different types of research. It then covers developing research questions, including originating questions from prior literature and formulating questions that are feasible, interesting, novel, ethical and relevant. The document outlines steps for formulating a research problem, including selecting a broad subject area and narrowing it to specific questions. It stresses reviewing literature throughout the process and considering available data, resources, and ethics. Finally, it discusses writing research protocols that specify predictors, outcomes, populations and study plans to address potential problems.
Scientific Research and its Types
There are two basic types of scientific research: inductive and deductive. Inductive research involves assuming theoretical concepts and patterns from observed data to build theories, while deductive research tests concepts and patterns using empirical data to evaluate theories. Additionally, there are three types of scientific research based on purpose: exploratory research investigates new areas of interest to generate initial ideas and test feasibility; descriptive research carefully observes and documents phenomena through reliable scientific methods; and explanatory research seeks explanations for observed phenomena by answering "why" and "how" questions.
Research types
This document discusses research methods and methodologies. It defines research methods as how to accomplish research tasks through procedures to initiate, carry out, and complete projects. Research methodology provides principles for organizing, planning, designing, and conducting research. The document then outlines different types of studies including deductive vs inductive, exploratory vs explanatory, descriptive vs analytical, basic vs applied, quantitative vs qualitative, one-time vs longitudinal, laboratory vs on-field, and test vs diagnostic research. It concludes by listing characteristics of good business research such as having a clearly defined purpose, detailed research process, thorough planning, high ethics, limitations revealed, adequate analysis, unambiguous findings, and justified conclusions.
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The document discusses scientific method and research. It defines scientific method as integrating deductive and inductive reasoning to systematically study problems through hypothesis formulation, evidence collection, and hypothesis testing. Research is defined as the objective analysis and recording of controlled observations that can lead to generalizations, principles, or theories. The key aspects of research discussed include formulating problems, developing hypotheses, collecting evidence, analyzing data, and reporting results. Both qualitative and quantitative research approaches are described.
Chapter 3 research design
The document discusses different types of research designs used in conducting research studies. It begins by defining research design and its purpose, which is to obtain answers to research questions and minimize variance. The key types of research designs covered are experimental, quasi-experimental, descriptive, and correlational designs. Experimental design aims to test causal relationships through manipulation of independent variables. Descriptive design observes and measures variables without manipulation to understand characteristics and trends. Correlational design examines relationships between non-manipulated variables. The document provides examples and comparisons of when each design is most applicable.
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This document is quoted from Academic Writing Skill, IFL, Cambodia. It's for students in year three not only at IFL but also other universities in Cambodia.
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This document provides an introduction to research concepts. It defines research as a systematic process of collecting and analyzing information to increase understanding. The scientific method involves tentative, empirically testable, and publicly shared approaches. Research can be basic, applied, or action-oriented. Qualitative research explores meanings through words and images, while quantitative research analyzes numerical data. Methods include experimental, case study, survey, and time-series designs. Research helps address problems in fields like public administration, through approaches such as needs assessment, process and outcome evaluations.
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- The qualities of a good researcher, such as being resourceful, creative, honest, and religious.
- The values of research to humanity, such as improving quality of life, instruction, and satisfying needs through new discoveries and applications.
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This document provides an overview of the key concepts and branches of philosophy. It begins by defining philosophy etymologically as the love of wisdom. The main branches of philosophy discussed are ethics, epistemology, metaphysics, politics, aesthetics, logic, religion, and the philosophy of science. For each branch, the document outlines some of the fundamental questions addressed within that area of philosophy to illustrate the nature and scope of the various fields.
Introduction to the philosophy of the human person
This document provides an introduction to a philosophy of the human person course. It covers several key topics:
- The human person in their environment, and how humans were created to live in harmony with nature. Respect for the environment is discussed.
- Freedom of the human person, including lessons on free will, voluntary actions and their consequences, and arguments for and against freedom of the will.
- Intersubjectivity, which examines human relationships and interactions between people.
Various learning activities are suggested such as poster making, travelogue creation, and recycling projects to reinforce the lessons. The document outlines rationales, objectives and content for each topic area.
Research methodology ppt babasab
The document discusses research methodology and defines research. It provides examples of what constitutes research and what does not. Research is defined as a systematic, logical process that includes understanding the problem, reviewing literature, collecting and analyzing data, drawing conclusions, and generalizing findings. The document also discusses types of research questions, purposes of research, and common challenges in conducting research.
Lecture 1 Introduction to Philosophy
1. Philosophy is defined as the love of wisdom and the rational attempt to understand fundamental problems regarding existence, knowledge, values, reason, mind, and language.
2. The main branches of philosophy are logic, metaphysics, epistemology, and value theory. Logic studies rules of reasoning. Metaphysics examines reality. Epistemology considers the nature and sources of knowledge. Value theory encompasses ethics, aesthetics, and social/political philosophy.
3. Ethics examines concepts of right and wrong through descriptive, normative, and metaethical approaches. Aesthetics concerns theories of art and beauty.
Research Methodology
The document outlines key aspects of research methodology including:
1. The objectives of research such as defining problems, formulating hypotheses, collecting and evaluating data, making deductions, and testing conclusions.
2. The different types of research including descriptive, applied, quantitative, conceptual, empirical, qualitative, fundamental, and analytical research.
3. The methods of collecting data including primary methods like questionnaires, observations, interviews, and schedules and secondary methods of collecting published and unpublished data from various sources.
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basic research concepts, history, trends & types of study.
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BAEB601 Chapter 1(part 2): Introduction to Research Methodology
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Similar to Introduction To Research
Intro to Research.pptx
This document discusses two research papers:
1) "TeleMed" which aims to control a microscope remotely through connecting stepper motors to the microscope knobs and creating software to operate the motors via signals, enabling off-site microscope control.
2) A study comparing the antibacterial properties of three chili pepper varieties against toothache-causing bacteria, finding Capsicum frutescens most effective against two bacteria and Capsicum annuum var longgum most effective against one isolate. The minimum inhibitory concentration of plant extracts on bacteria was 25% while minimum bactericidal concentration was 100%.
Types of Research
This document provides an overview of research methodologies in architecture. It discusses qualitative and quantitative research, including common approaches like interviews, surveys, observation, and case studies. Qualitative research focuses on collecting and analyzing non-numerical data through methods like ethnography and narrative research, while quantitative research uses statistical analysis and sampling. The document also outlines different types of research like descriptive, exploratory, experimental, and longitudinal research as well as key concepts in research methodology like variables, hypotheses, and validity.
Operational reseach ppt
Operational research is the scientific study of operations aimed at improving decision-making. It originated from military planning in World War II and has since expanded to various industries. In public health, operational research uses analytical methods to identify health program problems, potential solutions, and test solutions to inform evidence-based decisions around programs. It involves interdisciplinary teams that study issues like disease screening, outbreak response, and health behavior programs. Societies like IFORS and journals promote the field. Overall, operational research integrates data analysis into program management to enhance monitoring and evaluation.
Peter Keating Dec2008
- Data monitoring committees (DMCs) emerged in the 1970s to periodically review accumulating clinical trial data and monitor safety and efficacy. They issue judgments to stop or continue trials.
- DMCs have become reflexive institutions that engage in endogenous critical inquiry. They focus on issues like membership qualifications and attributes, and how much trials can be redefined based on interim data.
- Guidelines have been issued to provide standards around DMC roles, structures, and decision-making processes. There is debate around how independent DMCs should be and what level of access they should have to trial data and ability to influence trial parameters.
CRIS LUTHER's RESEARCH METHODOLOGIES COMPILATION
RESEARCH METHODOLOGIES
by Cris Luther, B.S.N.,R.N.
This material is a compilation of various information on generally acceptable knowledge, concepts, principles, theories and practices in RESEARCH. It adapts contents from various publicly acknowledged publications, authors, theorists, authorities and practitioners whose works are commonly utilized in the academe and practice, and are frequently-tested competencies locally and abroad.
The works of these authors, theorists, authorities and practitioners are indispensable in learning research methodologies as they are indispensable in the completeness of this compilation.
Care has been taken to confirm accuracy of the information presented and describes generally accepted practices. However the student who prepared this material is not responsible for errors or omissions or for any consequences from application of the information in this compilation.
The primary goal of the student is to familiarize concepts in the subject RESEARCH METHODOLOGIES based on the COURSE OUTLINE provided by his Graduate School Professor DR. HELEN B. AGGABAO. It is not intended for commercial publication and resources were acquired legally.
It is his great pleasure that this compilation be reproduced for reference of other students aiming to thoroughly understand RESEARCH METHODOLOGIES.
OR.pptx
This document provides an overview of operational research. It discusses how operational research uses analytical methods to help make better decisions and optimize resource allocation. The history section notes that operational research originated from military planning efforts in World War II and has since expanded into various industries. Some key methods covered include simulation, optimization, and data analysis. The operational research process typically involves identifying problems, finding potential solutions, testing solutions, utilizing and disseminating results. Various models are also used like allocation, inventory, sequencing and waiting line models.
OPERATIONAL RESEARCH (OR)
Operational research is becoming important in real world setting of health care as it always tried to find out challenges or gaps in any health related issues or in program. For health program improvement, OR should be conducting frequently. Program manager and doctors should be involve in OR and encourage to do so.
TYPES OF RESEARCH
There are several types of research methods described in the document. Exploratory research gathers preliminary information to define a problem through secondary data review and qualitative interviews. Descriptive research aims to describe characteristics of people or environments. Research can be cross-sectional, collecting data at a point in time, or longitudinal, studying a sample over intervals. Conclusive research tests hypotheses quantitatively while fundamental research expands knowledge without immediate applications. Qualitative research explores reasons and motivations through discussion while quantitative research generalizes statistically from samples.
PR2_Wk1-2.pptx
Quantitative research uses objective measurements and statistical analysis of numeric data to understand phenomena and test hypotheses. It is used across many fields to generalize results from a sample to a population, test cause-and-effect relationships through experiments, and structure the collection of standardized and reliable data. Some key uses of quantitative research include understanding human behavior, evaluating business strategies and product testing, advancing medical knowledge, and analyzing the impacts of interventions.
Research A way of thinking...Mahmoud Al-Dali.......pptx
This document provides an overview of research as a way of thinking and an integral part of professional practice. It discusses how research involves critically examining work, understanding principles, and testing new theories. The document also covers the characteristics of rigorous, systematic, controlled, valid, empirical, and critical research. It describes different types of research based on their application, objectives, and type of information sought, including applied vs. pure research and qualitative vs. quantitative approaches. The main paradigms of research are the positivist/scientific approach and the qualitative/naturalistic approach.
quantitative research approaches
The document discusses quantitative research approaches, including types, characteristics, advantages, and disadvantages. It defines quantitative research as a formal, objective process for generating information about the world through variables studied in numerical form. The main types of quantitative research designs are experimental (true experimental, quasi-experimental, pre-experimental) and non-experimental (descriptive, correlational, exploratory, survey). True experiments aim to establish causal relationships but have limitations, while quasi-experiments and non-experimental designs are more practical but cannot prove causation. Advantages include the ability to test hypotheses statistically while disadvantages include inability to control all variables and lack of understanding of context.
Health system research
The document discusses different types of research methods including quantitative, qualitative, and mixed methods research. Quantitative research uses objective measurements and statistical analysis, while qualitative research explores underlying reasons and motivations through methods like interviews. Mixed methods research incorporates both quantitative and qualitative data collection. The document also describes observational studies like case studies and longitudinal studies, as well as experimental research methods like randomized controlled trials that manipulate variables and use control groups.
Research Design and Types of Research Design Arun Joseph MPhil ppt
Research Design and Types of Research Design Arun Joseph MPhil pptArun Joseph (Librarian), MLISc, UGC NET
This document discusses research design and different types of research designs. It defines research design as the conceptual structure and plan for conducting research to answer research questions. The main types of research designs covered are exploratory, descriptive, diagnostic, and experimental. Exploratory design is used when little is known about a topic to discover variables and relationships. Descriptive design aims to describe phenomena by observing behaviors. Diagnostic design involves problem identification and finding causes. Experimental design tests hypotheses by manipulating variables and measuring outcomes. The document provides details on each design type, including their purposes and methodologies.Operationalreseacrh
This document provides an overview of operational research. It begins with definitions, describing it as the scientific study of operations to make better decisions. It discusses the history, noting it originated from military planning in World War II and has since expanded to other fields. The objectives are outlined as improving decision making and identifying optimal solutions. The scope includes various sectors like health, defense, business and agriculture. Methods typically involve simulation, optimization and data analysis. The operational research process is also summarized as identifying problems, potential solutions, testing solutions, disseminating results. Applications in public health are discussed along with composition of operational research teams and the process. Finally, it briefly outlines some key societies and journals in the field like IFORS and INFORMS
OR
This document provides an overview of operational research. It begins with a brief history, noting that operational research originated during World War II to analyze military problems scientifically. It grew in the post-war decades and is now used widely in both public and private sectors. The document defines operational research and lists its objectives. It describes the scope, methods, and process of operational research. Applications in public health are discussed, along with composition of operational research teams and their processes. Finally, some prominent societies and journals related to operational research are mentioned.
Operational reseach
This document provides an overview of operational research. It begins with defining operational research as the scientific study of operations to make better decisions. It then discusses the history, originating from efforts during World War II to study military problems scientifically. Methods include simulation, optimization, and data analysis. The document outlines the objectives, scope, and process of operational research. It describes the use of operational research in public health and health systems. Finally, it discusses key societies and journals in the field, such as IFORS, ORSI, and INFORMS.
Mycin
MYCIN was an early expert system developed at Stanford University in 1972 to assist physicians in diagnosing and selecting treatment for bacterial and blood infections. It used over 600 production rules encoding the clinical decision criteria of infectious disease experts to diagnose patients based on reported symptoms and test results. While it could not replace human diagnosis due to computing limitations at the time, MYCIN demonstrated that expert knowledge could be represented computationally and established a foundation for more advanced machine learning and knowledge base systems.
Component of a Research Design
The slides will help you in knowing the components of research design in brief what is research design, components of research design, differnt types of research design
Aviation Labor Relations Use the Internet to answer the followin.docx
Aviation Labor Relations
Use the Internet to answer the following items. Be sure to cite your sources.
1. A major part of the study of labor law and collective bargaining is the unique vocabulary that has developed over the period of time; accordingly, define the following terms and concepts:
a) Closed Shop
b) National Unions
c) American Federation of Labor (AFL)
d) Strikebreakers
e) Arbitrators
f) Good-faith Bargaining
g) Picketing
h) Boycotts
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j) Secondary Boycotts
k) Yellow-dog Contracts
2. In three sentences, summarize the railroad labor gains during World War I.
RUNNING HEAD: QUANTITATIVE AND QUALITATIVE RESEARCH METHODS
QUANTITATIVE AND QUALITATIVE RESEARCH METHODS 3
Quantitative and Qualitative Research Methods
Name:
Course:
Instructor:
Date:
Week 2
QUANTITATIVE AND QUALITATIVE RESEARCH METHODS
3
The article illustrates how conclusions about a given study are attained using case studies. Case study research is a qualitative research method that may be experimental or non-experimental depending on the type of study being conducted. The article indicates that conducting a case study demands that the researcher identifies its subjects mainly through random sampling. In non-experimental situations, the researcher may employ surveys to complete their study. Therefore, much of case studies depend on propositions at the beginning. While utilizing experimental designs, the researcher will subject its samples to a laboratory tests by establishing a control and placebos.
The purpose of the article is to provide insights into how to utilize case studies to attain a valid and reliable data for the study. Notably, case studies ensure that the expected result is obtained accurately. Case studies a significant to a research designing a new study because it employs evidence-based studies in most cases. Thus, any information supplied in the findings represents real-time data from the subjects. Case studies aid a research to repeat a given subset of study until their desired result is obtained.
Historical research is a qualitative method that allows a researcher to examine previous happenings regarding a particular area of study. The purpose of the journal is to examine the historical perspective of the buyer-supplier relationship over time. It illustrates the ways in which the relationships have been changing with time.
With historical research, individuals base their conclusion on past data for example interviews, documentaries, journals and field notes. Present and future situations of a certain environment or individuals are determined by their historical behaviors and way of living. For example, a business enterprise that wants to postulate the situation of their firm in future will have to evaluate their past sales, revenues, and net incomes so that they do not over or underestimate their worth.
Historical research method is practical thus vital for an individual designing a new study. With this met ...
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Transcription is the process of converting DNA into RNA, while translation is the process by which cells assemble amino acids into proteins based on the genetic code found in messenger RNA. Transcription occurs in the cell nucleus and uses one of the DNA strands as a template to produce a complementary RNA copy. During translation, transfer RNAs carry individual amino acids and match them to a messenger RNA through codon-anticodon base pairing, assembling a polypeptide chain through the action of ribosomes in the cytoplasm.
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Folding is a recent technique for building efficient recursive SNARKs. Several elegant folding protocols have been proposed, such as Nova, Supernova, Hypernova, Protostar, and others. However, all of them rely on an additively homomorphic commitment scheme based on discrete log, and are therefore not post-quantum secure. In this work we present LatticeFold, the first lattice-based folding protocol based on the Module SIS problem. This folding protocol naturally leads to an efficient recursive lattice-based SNARK and an efficient PCD scheme. LatticeFold supports folding low-degree relations, such as R1CS, as well as high-degree relations, such as CCS. The key challenge is to construct a secure folding protocol that works with the Ajtai commitment scheme. The difficulty, is ensuring that extracted witnesses are low norm through many rounds of folding. We present a novel technique using the sumcheck protocol to ensure that extracted witnesses are always low norm no matter how many rounds of folding are used. Our evaluation of the final proof system suggests that it is as performant as Hypernova, while providing post-quantum security.
Paper Link: https://eprint.iacr.org/2024/257
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