E CES 212 81 Actual Questions and Correct Answers
Q1
Asymmetric Cryptography
Answer: AKA public key cryptography. Slower than symmetric key cryptography.
Developed to overcome weaknesses in symmetric cryptography. Uses a public and a
private key. Denotes the natural numbers. 1, 2, 3, etc. Denotes the integers. These are
whole numbers -1, 0, 1, 2 etc. Denotes the rational numbers (ratio of integers). Any
number that can be expressed as a ratio of two integers 3/2, 17/4, 1/5 etc. Denotes the
real numbers. This includes the rational numbers as well as numbers that cannot be
expressed as a ratio of two integers, for example √2 Denotes imaginary numbers.
These are numbers whose square is a negative. √-1 = 1i
Q2
Entropy
Answer: A measure of the uncertainty associated with a random variable.
Q3
Prime Number
Answer: Any number whose factors are 1 and itself. Example 2, 3, 5, 7, 11, 13, 17, 23
Q4
Prime Number Theorem
Answer: If a random number N is selected, the chance of it being prime is approx.
1/ln(N), where ln(N) denotes the natural logarithm of N.
Q5
Mersenne Primes
Answer: Uses a formula, Mn = 2n − 1 where n is a prime number, to generate primes.
Works for 2, 3, 5, 7 but fails on 11 and on many other n values.
Q6
Co-prime Numbers
Answer: A number that has no factors in common with another number. For example,
3 and 7 are this.
, Q7
Euler's Totient
Answer: The number of positive integers less than or equal to n that are co-prime to n
is called the ***** ***** of n. For example the number 6; 4 and 5 are co-prime with 6.
Therefore, **** ******=2. Symbolized by ϕ(n). For a prime number p, ϕ(n) is always p-1.
Part of the RSA algorithm!
Q8
Modulus Operator
Answer: Used in a number of cryptography algorithms. Simply divide A by N and return
the remainder. So 5 mod 2 = 1 So 12 mod 5 = 2 Sometimes symbolized as % as in 5 %
2=1
Q9
Fibonacci Numbers
Answer: Named after Leonardo of Pisa who was also known a *********. Sequence of
numbers are derived by adding the last two numbers to create the next number, N1 +
N2 = n3. Example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 35, 56. Some random number generators
use this.
Q10
Birthday Theorem
Answer: The number of people you would have to invite to a party so that two will
have the same birthday (with high probability). √365 You need √N to have a high
probability of collision. Answer is approximately 1.174 √365 to have a high probability
of collision.
Q11
Birthday Paradox
Answer: The number of people you need to have a high likelihood that two share the
same birthday. The answer is 23. This is a classic math problem that relates to hashes.
Q12
Birthday Attack
Answer: Name used to refer to a class of brute force attacks against hashes. Attempts
to find a collision.
Q1
Asymmetric Cryptography
Answer: AKA public key cryptography. Slower than symmetric key cryptography.
Developed to overcome weaknesses in symmetric cryptography. Uses a public and a
private key. Denotes the natural numbers. 1, 2, 3, etc. Denotes the integers. These are
whole numbers -1, 0, 1, 2 etc. Denotes the rational numbers (ratio of integers). Any
number that can be expressed as a ratio of two integers 3/2, 17/4, 1/5 etc. Denotes the
real numbers. This includes the rational numbers as well as numbers that cannot be
expressed as a ratio of two integers, for example √2 Denotes imaginary numbers.
These are numbers whose square is a negative. √-1 = 1i
Q2
Entropy
Answer: A measure of the uncertainty associated with a random variable.
Q3
Prime Number
Answer: Any number whose factors are 1 and itself. Example 2, 3, 5, 7, 11, 13, 17, 23
Q4
Prime Number Theorem
Answer: If a random number N is selected, the chance of it being prime is approx.
1/ln(N), where ln(N) denotes the natural logarithm of N.
Q5
Mersenne Primes
Answer: Uses a formula, Mn = 2n − 1 where n is a prime number, to generate primes.
Works for 2, 3, 5, 7 but fails on 11 and on many other n values.
Q6
Co-prime Numbers
Answer: A number that has no factors in common with another number. For example,
3 and 7 are this.
, Q7
Euler's Totient
Answer: The number of positive integers less than or equal to n that are co-prime to n
is called the ***** ***** of n. For example the number 6; 4 and 5 are co-prime with 6.
Therefore, **** ******=2. Symbolized by ϕ(n). For a prime number p, ϕ(n) is always p-1.
Part of the RSA algorithm!
Q8
Modulus Operator
Answer: Used in a number of cryptography algorithms. Simply divide A by N and return
the remainder. So 5 mod 2 = 1 So 12 mod 5 = 2 Sometimes symbolized as % as in 5 %
2=1
Q9
Fibonacci Numbers
Answer: Named after Leonardo of Pisa who was also known a *********. Sequence of
numbers are derived by adding the last two numbers to create the next number, N1 +
N2 = n3. Example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 35, 56. Some random number generators
use this.
Q10
Birthday Theorem
Answer: The number of people you would have to invite to a party so that two will
have the same birthday (with high probability). √365 You need √N to have a high
probability of collision. Answer is approximately 1.174 √365 to have a high probability
of collision.
Q11
Birthday Paradox
Answer: The number of people you need to have a high likelihood that two share the
same birthday. The answer is 23. This is a classic math problem that relates to hashes.
Q12
Birthday Attack
Answer: Name used to refer to a class of brute force attacks against hashes. Attempts
to find a collision.
