Mathematics and Number Systems Worksheet

Front

What is the decryption key d in RSA?

Back

The decryption key d is the inverse of the public key e mod φ(N).

Front

What is the binary (base 2) representation of the decimal number 43?

Back

The binary representation of 43 is 101011.

Front

How many base cases are needed for a proof using strong induction?

Back

You can have as many base cases as you want.

Front

Using a Caesar cipher with a shift of 3, decode the message: 'pdwk hdvb'.

Back

The decoded message is 'math easy'.

Front

How many numbers between 1 and 63 are relatively prime to 63?

Back

There are 36 numbers between 1 and 63 that are relatively prime to 63.

Front

What is the definition of a prime number?

Back

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Front

What is the formula for calculating the Euler's totient function φ(n)?

Back

For a number n = p1^k1 * p2^k2 * ... * pm^km, φ(n) = n * (1 - 1/p1) * (1 - 1/p2) * ... * (1 - 1/pm).

Front

What is the significance of the modulus in modular arithmetic?

Back

The modulus defines the range of integers in modular arithmetic, creating a cyclic group of integers from 0 to (modulus - 1).

Front

What is the process of converting a decimal number to binary?

Back

To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders.

Front

What is the definition of relatively prime numbers?

Back

Two numbers are relatively prime if their greatest common divisor (GCD) is 1.