Modular Math
Reduce 320 {mod 17}
What is 14?
(Since 17 x 18 = 306, 320 - 306 = 14)
If a 2x2 matrix has a determinant of 0, what does that tell us about our ability to decrypt a Hill Cipher message made with it?
What is it cannot be decrypted
OR
The matrix has no inverse?
Solve the shift cipher f d w t t i t n s g n y w n l m y
if the key is a shift of 5 spaces forward (A -> F)
What is "areyoudoingitright"?
Julius Caesar famously protected his military messages by shifting every letter in the alphabet three spaces forward. What is the specific name given to this type of cipher?
What is a Caesar Cipher
OR
Shift Cipher
According to the "Be Appropriate" section, the Code of Conduct explicitly states that CTY is rated what?
What is "G"?
Find the gcd(320, 85)using the Euclidean Algorithm.
What is 5?
Calculate the determinant of the matrix
([4,9],[5,8])
What is -13?
(From 4x8) - (9x5) = 32 - 45)
Encrypt the short string "MATH" using a Vigenère cipher with the repeating keyword "KEY".
What is WEDR?
What is the primary operational difference between the standard Euclidean Algorithm and the Extended Euclidean Algorithm?
What is the Extended algorithm finds the multiplicative inverse / linear combinations?
Under the "Be Responsible" guidelines, you must get clear permission before doing these three physical or digital actions regarding another person. (Name two).
What are touching someone, touching someone's belongings, or taking pictures/recording anyone?
Calculate the multiplicative inverse of 11 modulo 412 using the Extended Euclidean Algorithm.
What is 225?
(Since 11 x 225 = 2475, and 2475 = 412 x 6 + 1)
Find the determinant of this alternative encryption key matrix: ([4,7],[1,8])
What is 25?
(From 4x8) - (7x1) = 32 - 7)
message is encrypted using an Affine cipher on a 29-character alphabet. It is known to begin with the word "NEXT". Decrypt the ciphertext string Iqbyubv.lqtup.
What is "Next_question"?
A student tries to find the number of ways to color a standard regular hexagon with 6 different colors and guesses $6!$. What structural property are they overcounting?
What are rotations?
According to the Digital Conduct rules, what is the policy for using personal electronic devices during academic classes and activities?
What is only use devices when staff say it is okay / focus on engaging with people?
If we expand our alphabet system from 29 characters to include three new symbols (like a question mark, exclamation point, and a dash), what would our new modulus size be?
What is Modulo 32?
Multiply the following matrices to find the top-left entry of the resulting matrix:
([2,5],[1,3]) ([4,9],[5,8])
What is 33?
(From (2 x 4) + (5 x 5) = 8 + 25)
If you encrypt the word "SECRET" using a Playfair cipher, you must first split the message into pairs of letters. How would you write those pairs out?
What are SE, CR, ET?
To correct the student's overcount for the regular hexagon coloring problem, what number must you divide $6!$ by?
What is 6?
(Because a hexagon has 6 equivalent rotational positions)
Under the "Be Safe" rules, what must a student never do before leaving the physical boundaries of the campus?
What is leave without being signed out by an authorized adult?
If gcd(a, m)/1, what does this mathematically guarantee about the number a within that modulo m system?
What is it has no multiplicative inverse / cannot be used to decrypt?
Suppose you calculate the determinant of a key matrix modulo 29 and get a result of -5. What is the positive equivalent value of this determinant in Modulo 29 arithmetic?
What is 24?
(From -5 + 29 = 24)
What is the specific geometric shape or framework used to track and encrypt pairs of letters when setting up a Playfair Cipher?
What is a 5x5 Grid
(or Matrix)?
If you are trying to color a 3D geometric cube using 6 different colors, why is dividing 6! by 4 not enough to fix the overcount?
What is a cube can rotate in three dimensions / it has 24 equivalent rotational positions, not just 4?
Serious violations of the Code of Conduct will result in a direct referral to what specific group, potentially leading to dismissal?
What is the CTY Student Conduct Committee?