Modular Arithmetic and Caesar Cipher Flashcard

Front

What is modular arithmetic?

Back

A system of arithmetic for integers, where numbers wrap around after reaching a certain value (modulus).

Front

What does 'a ≡ b (mod n)' signify?

Back

It means that a and b have the same remainder when divided by n.

Front

What is the result of adding two numbers in modular arithmetic?

Back

The result is the remainder when the sum is divided by the modulus.

Front

Is division always possible in modular arithmetic?

Back

No, division is not always possible; it requires the divisor to have a multiplicative inverse.

Front

What happens when you apply a shift of 26 in a Caesar cipher?

Back

Nothing changes; the letters wrap around the alphabet.

Front

How does a Caesar cipher work?

Back

It shifts each letter in the plaintext by a fixed number of positions down the alphabet.

Front

What is the shift used to transform 'HELLO' to 'IFMMP'?

Back

The shift is 1.

Front

What letter does 'D' encrypt to with a shift of 3 in a Caesar cipher?

Back

G.

Front

What is the multiplicative inverse in modular arithmetic?

Back

A number 'b' such that (a * b) mod n = 1.

Front

What is the closure property in modular arithmetic?

Back

The sum or product of two integers in modular arithmetic is also an integer in that system.