Achyut BharadwajApril 2023
Introduction–The Shuffling Problem
#
Card shuffling is an important part of playing any card game. When a
card deck isn’t shuffled properly, it leads to uneven and unfair
distribution of cards. It would certainly help if you knew what cards
other players had!
Suppose we have a specified shuffling algorithm. Is
it possible for us to guess the outcome of the card shuffling? Is it
possible that the card deck will at some point return to its original
configuration? In a previous article
we explored ways of trying to guess the outcome of a specific type of card
shuffling, known as the riffle shuffle. In this article, we modify the shuffling
algorithm to introduce a flip that introduces some interesting complexities.
...Achyut BharadwajFebruary 2022
An Interesting Card Trick
#
The Problem
#
Suppose you have a deck of $52$ cards. You perform a riffle
shuffle on these cards. Can you say what the new position of the first
card in the deck is, after the shuffle? What about the second card in
the deck? The third? In general, is it possible to predict the new
position of the $k$th card in the original deck after a new deck is
produced through a riffle shuffle?
...Achyut BharadwajSeptember 2021
cryptography,
RSA,
encryption,
decryption,
one-way function,
factorization,
prime,
modular arithmetic,
modular inverse,
kid-RSA,
Euclid's division,
gcd,
Bezout,
Euler,
totient,
Fermat,
primality test,
Miller-Rabin A presentation on the mathematics of cryptography, with an emphasis on RSA. A link to the writeup is here.
Achyut BharadwajSeptember 2021
cryptography,
RSA,
encryption,
decryption,
one-way function,
factorization,
prime,
modular arithmetic,
modular inverse,
kid-RSA,
Euclid's division,
gcd,
Bezout,
Euler,
totient,
Fermat,
primality test,
Miller-Rabin A presentation on the mathematics of cryptography, with an emphasis on RSA. A link to the slides is here.
Basic Cryptography
#
Sending Messages
#
Say, there are 3 people, Aditi, Bhaskar and Diti.
Aditi wants to send the message “HELLO” to Bhaskar, using her computer.
Computers, however, can only store numbers. How will she send the
message “HELLO” to Bhaskar?
To store characters, there is a code called the ASCII code. In ASCII,
each character is given a value in binary.
“HELLO” is coded as: 1001000 1000101 1001100 1001100 1001111
So, Aditi has to send the above code to Bhaskar.
...