Lecture 19, Thurs March 30: RSA and Shor’s Algorithm Today we’ll see Shor’s algorithm. Given a positive integer ​N​, which we’ll assume for simplicity is a product of two primes |​and , this algorithm lets

Source URL: www.scottaaronson.com

• Cryptography
• Mathematics
• Algebra
• Finite fields
• Computational hardness assumptions
• Integer factorization algorithms
• Emerging technologies
• Quantum computing
• RSA
• Euclidean algorithm
• Quantum algorithm
• XTR

IEEE TRANSACTIONS ON COMPUTERS, VOL. ??, NO. ??, ??? A New Range-Reduction Algorithm N. Brisebarre, D. Defour, P. Kornerup, J.-M Muller and N. Revol

Source URL: perso.ens-lyon.fr

• Mathematics
• Algebra
• Abstract algebra
• Finite fields
• Field theory
• Angle
• Sine
• Factorial
• XTR
• Valuation
• Non-analytic smooth function
• Proof that is irrational

Lecture 22, Tues April 11: Grover The next quantum algorithm we’ll cover is… Grover’s Algorithm which was discovered in 1995, shortly after Shor’s algorithm. Both Grover and Shor were working at Bell Labs at the

Source URL: www.scottaaronson.com

• Theoretical computer science
• Computational complexity theory
• Mathematics
• Emerging technologies
• Quantum computing
• Quantum algorithms
• Quantum information science
• Quantum algorithm
• Algorithm
• P versus NP problem
• NP
• PP

Lecture 23, Thurs April 13: BBBV, Applications of Grover It’s great that we can get a quadratic speedup with Grover’s algorithm, but we were able to get an exponential​ speedup with Shor’s algorithm… So why can

Source URL: www.scottaaronson.com

• Theoretical computer science
• Emerging technologies
• Quantum computing
• Computational complexity theory
• Quantum information science
• Computer science
• Quantum algorithm
• Time complexity
• Asymptotically optimal algorithm
• Grover's algorithm
• Quantum algorithm for linear systems of equations

MATHEMATICS OF COMPUTATION Volume 00, Number 0, Pages 000–000 SXXAN L(1/3) ALGORITHM FOR IDEAL CLASS GROUP AND REGULATOR COMPUTATION IN CERTAIN NUMBER FIELDS

Source URL: www.lix.polytechnique.fr

• Mathematics
• Abstract algebra
• Mathematical analysis
• Algebraic number theory
• Discriminant of an algebraic number field
• Riemann hypothesis
• Algebraic number field
• Table of stars with Bayer designations
• Computational complexity of mathematical operations

On Computing the Resultant of Generic Bivariate Polynomials Gilles Villard Univ Lyon, CNRS, ENS de Lyon, Inria, Université Claude Bernard Lyon 1, LIP UMR 5668, FLyon, France ABSTRACT An algorithm is presented for

Source URL: perso.ens-lyon.fr

Implementing Joux-Vitse’s Crossbred Algorithm for Solving MQ Systems over F2 on GPUs Ruben Niederhagen1 , Kai-Chun Ning2 , and Bo-Yin Yang3 1 2

Source URL: precision.moscito.org

• Algebra
• Mathematics
• Numerical linear algebra
• Equations
• Linear algebra
• Hidden Field Equations
• Multivariate cryptography
• Gaussian elimination
• Recurrence relation
• Equation solving
• APMonitor
• BCD

Motivation Groundwork Algorithm

Source URL: www.cs.purdue.edu

• Evolutionary biology
• Genetics
• Robustness

A systolic architecture for supporting Wiedemann's algorithm

Source URL: www.hyperelliptic.org

• Algebra
• Mathematics
• Linear algebra
• Vectors
• Abstract algebra
• Matrices
• Matrix
• Euclidean vector
• GF

Lecture 21, Thurs April 6: Continued Fractions, Shor Wrap-Up Today we’ll finish Shor’s algorithm and then discuss some of its implications. Last we saw our protagonists, they were in a superposition of the form |​r

Source URL: www.scottaaronson.com

• Cryptography
• Mathematics
• Theoretical computer science
• Computational complexity theory
• Quantum computing
• Group theory
• Emerging technologies
• Quantum algorithm
• Elliptic curve
• Time complexity
• Real number
• NP