Advanced Data Structures, RSA and Quantum Algorithms

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Advanced Data Structures, RSA and Quantum Algorithms

This course is part of Foundations of Data Structures and Algorithms Specialization

Instructor: Sriram Sankaranarayanan

6,816 already enrolled

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4 modules

Gain insight into a topic and learn the fundamentals.

Advanced level

Recommended experience

5 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Build toward a degree

Learn more

4 modules

Gain insight into a topic and learn the fundamentals.

Advanced level

Recommended experience

5 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Build toward a degree

Learn more

What you'll learn

Explore how basic number-theoretic concepts are used to build the RSA crypto-system.
Examine the foundations of quantum computation and its basic building blocks.
Explore how quantum computers can be used to break the RSA cryptosystem.
Explore the differences between classical and quantum algorithms.

Skills you'll gain

Tools you'll learn

Mathematical Software

Details to know

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Assessments

12 assignments

Taught in English

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This course is part of the Foundations of Data Structures and Algorithms Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

Introduces number-theory based cryptography, basics of quantum algorithms and advanced data-structures.

This course can be taken for academic credit as part of CU Boulder’s Masters of Science in Computer Science (MS-CS) degrees offered on the Coursera platform. This fully accredited graduate degree offer targeted courses, short 8-week sessions, and pay-as-you-go tuition. Admission is based on performance in three preliminary courses, not academic history. CU degrees on Coursera are ideal for recent graduates or working professionals. Learn more: MS in Computer Science: https://coursera.org/degrees/ms-computer-science-boulder

This module covers a brief recap of elementary number theory, GCD, Euclid's algorithm, Bezout coefficients and presents the RSA public key cryptosystem. It then shows how the security of RSA relies on the supposed hardness of the factoring problem for numbers that are semi-primes

What's included

5 videos5 readings5 assignments1 programming assignment2 ungraded labs

5 videosTotal 148 minutes

Introduction to Public Key Cryptography21 minutes
Euclid's Algorithm and GCD23 minutes
Extended Euclid Bezout Coefficients18 minutes
RSA Cryptography44 minutes
Quantum Physics Computing Basics42 minutes

5 readingsTotal 36 minutes

Course Updates and Accessibility Support1 minute
Earn Academic Credit for your Work!10 minutes
Course Support10 minutes
Assessment Expectations5 minutes
AI Citation and Acknowledgement10 minutes

5 assignmentsTotal 125 minutes

AI Policy Quiz5 minutes
Quiz on Public Key Cryptography20 minutes
GCD and Euclid's Algorithm30 minutes
Bezout Coefficients20 minutes
Quiz on RSA50 minutes

1 programming assignmentTotal 180 minutes

Week 1 Programming Assignment180 minutes

2 ungraded labsTotal 120 minutes

Notes on GCD, Euclid's Algorithm and Extended GCD60 minutes
Notes on RSA public key cryptosystem60 minutes

This module covers the basics of quantum computing with an introduction to qubits, the concept of a superposition, the effect of measuring a qubit, elementary quantum gates, direct/tensor products, entanglements, quantum parallelism and ends with a presentation of Grover's search algorithm. We will have a brief introduction to IBM qiskit package for exploring quantum circuits.

What's included

8 videos5 assignments1 programming assignment3 ungraded labs

8 videosTotal 180 minutes

Qubits and Super Positions30 minutes
Unitary Operators and Reversible Computation7 minutes
Multi Qubit Quantum States30 minutes
Multi Qubit Quantum Gates 29 minutes
Quantum Parallelism15 minutes
No Cloning Theorem5 minutes
Bells Inequality Power of Entangled States22 minutes
Grover Search Algorithm 43 minutes

5 assignmentsTotal 295 minutes

Qubits45 minutes
Single Qubit Quantum Gates45 minutes
Multiple Qubit Quantum States120 minutes
Multiple Qubit Quantum Gates40 minutes
Quantum Parallelism and Implementing Classical Gates45 minutes

1 programming assignmentTotal 180 minutes

Week 2 Programming Assignment180 minutes

3 ungraded labsTotal 180 minutes

Interactive Notes on Basics of Quantum Computation60 minutes
Interactive Notes on Multi-Qubit Quantum Systems60 minutes
Interactive Notes: Grover's Search Algorithm60 minutes

We will describe Shor's algorithm and as part of Shor's algorithm show how Quantum Fourier Transform (a very useful operation for quantum systems) is computed. We will show how the power of quantum parallelism combines with the divide-and-conquer paradigm for algorithm design to yield exponential speedups for computing Quantum Fourier Transforms.

What's included

7 videos1 reading2 assignments1 programming assignment2 ungraded labs

7 videosTotal 202 minutes

Order Finding and Factoring23 minutes
Order Finding on a Quantum Computer26 minutes
Recap: FFT Basics of Complex Numbers and Roots of Unity48 minutes
Recap: Discrete-Time Fourier Transforms 35 minutes
Recap: FFT Divide and Conquer Algorithm22 minutes
Quantum Fourier Transform: Part 119 minutes
Quantum Fourier Transform: Part 228 minutes

1 readingTotal 10 minutes

Note10 minutes

2 assignmentsTotal 240 minutes

Order Finding And Factoring180 minutes
Quantum Fourier Transform60 minutes

1 programming assignmentTotal 180 minutes

Week 3 Programming Assignment180 minutes

2 ungraded labsTotal 120 minutes

Detailed Notes on Shor's Algorithm60 minutes
Interactive Detailed Notes on Quantum Fourier Transform60 minutes

We will learn two important and interesting data structures to round off this course. The first data structure will be the widely used B-Tree data structure which is used in indexing and storing large amounts of data on a disk. Next, we will study algorithms on strings esp. string search algorithm. We will study the suffix trie data structure: a very useful data structure for fast searching over strings.

What's included

12 videos1 programming assignment2 ungraded labs

12 videosTotal 191 minutes

Introduction to B-Trees4 minutes
Structure and Properties of B-Trees18 minutes
Simple Example3 minutes
Searching for a Key in a B-Tree6 minutes
B-Tree Key Insertion Algorithm9 minutes
B-Tree Key Deletion Algorithm11 minutes
Tries: Basics40 minutes
Suffix Tries13 minutes
Generalized Suffix Tries34 minutes
Ukkonen's Algorithm - Part 125 minutes
Ukkonen's Algorithm - Part 226 minutes
Concluding Remarks3 minutes

1 programming assignmentTotal 180 minutes

Week 4 Programming Assignment180 minutes

2 ungraded labsTotal 120 minutes

Interactive Notes on B-Trees60 minutes
Interactive Notes on Suffix Tries60 minutes

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Build toward a degree

This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

Instructor

Sriram Sankaranarayanan

University of Colorado Boulder

5 Courses103,802 learners

Offered by

University of Colorado Boulder

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