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Questions and Answers
Which of the following is an example of a publication in which confidentiality of the stored data is the most important requirement?
Which of the following is an example of a publication in which confidentiality of the stored data is the most important requirement?
- An information system in a pathological laboratory maintaining patient's data (correct)
- An examination section of a university managing sensitive exam papers
- A student information system used for maintaining student data in a university
- A student maintaining a blog to post public information
Which of the following is an example of a publication in which data integrity is the most important requirement?
Which of the following is an example of a publication in which data integrity is the most important requirement?
- An information system in a pathological laboratory maintaining patient's data
- A student information system used for maintaining student data in a university
- An examination section of a university managing sensitive exam papers (correct)
- A student maintaining a blog to post public information
Which of the following is an example in which system availability is the most important requirement?
Which of the following is an example in which system availability is the most important requirement?
- An information system in a pathological laboratory maintaining patient's data
- A student maintaining a blog to post public information
- An examination section of a university managing sensitive exam papers
- A university library managing the distribution of books (correct)
Which set represents the set of nonnegative integers less than 8?
Which set represents the set of nonnegative integers less than 8?
What is the multiplicative inverse of 3 modulo 8?
What is the multiplicative inverse of 3 modulo 8?
Which property of modular arithmetic is represented by the equation (w * (x + y)) mod n = [(w * x) + (w * y)] mod n?
Which property of modular arithmetic is represented by the equation (w * (x + y)) mod n = [(w * x) + (w * y)] mod n?
What is the smallest nonnegative integer to which 23 is congruent modulo 8?
What is the smallest nonnegative integer to which 23 is congruent modulo 8?
According to the Euclidean algorithm, what is the greatest common divisor of 710 and 310?
According to the Euclidean algorithm, what is the greatest common divisor of 710 and 310?
What is the gcd(a, b) if a = 1160718174 and b = 316258250?
What is the gcd(a, b) if a = 1160718174 and b = 316258250?
What is the remainder when 1160718174 is divided by 316258250?
What is the remainder when 1160718174 is divided by 316258250?
What is the gcd(r1, r2) if r1 = 104314826 and r2 = 3313772?
What is the gcd(r1, r2) if r1 = 104314826 and r2 = 3313772?
Which equation represents the definition of modular arithmetic?
Which equation represents the definition of modular arithmetic?
What is the congruence relation between 73 and 4 modulo 23?
What is the congruence relation between 73 and 4 modulo 23?
What is the result of $(11 \mod 8) + (15 \mod 8) \mod 8$?
What is the result of $(11 \mod 8) + (15 \mod 8) \mod 8$?
What is the multiplicative inverse of 5 modulo 8?
What is the multiplicative inverse of 5 modulo 8?
Which integers have a multiplicative inverse in Z8?
Which integers have a multiplicative inverse in Z8?
What is the greatest common divisor (gcd) of 55 and 22?
What is the greatest common divisor (gcd) of 55 and 22?
What is the relationship between the set of common divisors of a and b, and the set of common divisors of b and (a mod b)?
What is the relationship between the set of common divisors of a and b, and the set of common divisors of b and (a mod b)?
According to the text, what is the division algorithm?
According to the text, what is the division algorithm?
According to the text, what is the greatest common divisor (gcd) of two integers?
According to the text, what is the greatest common divisor (gcd) of two integers?
According to the text, when are two integers considered relatively prime?
According to the text, when are two integers considered relatively prime?
According to the text, what is the Euclidean algorithm used for?
According to the text, what is the Euclidean algorithm used for?
Which of the following is the definition of divisibility?
Which of the following is the definition of divisibility?
Which of the following is true about the positive divisors of 24?
Which of the following is true about the positive divisors of 24?
Which of the following is true about modular arithmetic?
Which of the following is true about modular arithmetic?
What is the gcd(710, 310) according to the Euclidean algorithm?
What is the gcd(710, 310) according to the Euclidean algorithm?
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Study Notes
Publication Requirements
- Confidentiality of stored data is most important in publications related to personal or sensitive information (e.g., medical records, financial data).
- Data integrity is most important in publications related to critical systems or applications where data accuracy is crucial (e.g., financial transactions, scientific research).
- System availability is most important in publications related to real-time systems or applications where downtime is not acceptable (e.g., emergency services, online banking).
Modular Arithmetic
- The set of nonnegative integers less than 8 is {0, 1, 2, 3, 4, 5, 6, 7}.
- The multiplicative inverse of 3 modulo 8 is 3.
- The equation (w * (x + y)) mod n = [(w * x) + (w * y)] mod n represents the distributive property of modular arithmetic.
- The smallest nonnegative integer to which 23 is congruent modulo 8 is 7.
Greatest Common Divisors (GCDs)
- The GCD of 710 and 310 is 10.
- The GCD of 1160718174 and 316258250 is 2.
- The remainder when 1160718174 is divided by 316258250 is 2.
- The GCD of 104314826 and 3313772 is 2.
Modular Arithmetic Properties
- The equation a ≡ b (mod n) is the definition of modular arithmetic.
- The congruence relation between 73 and 4 modulo 23 is 73 ≡ 4 (mod 23).
- The result of $(11 \mod 8) + (15 \mod 8) \mod 8$ is 4.
- The multiplicative inverse of 5 modulo 8 is 5.
Integers with Multiplicative Inverses
- The integers with multiplicative inverses in Z8 are 1, 3, 5, and 7.
Greatest Common Divisors and Divisibility
- The GCD of 55 and 22 is 11.
- The set of common divisors of a and b is a subset of the set of common divisors of b and (a mod b).
- The definition of divisibility is "a divides b" if and only if there exists an integer k such that b = ka.
- The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Euclidean Algorithm
- The Euclidean algorithm is used to find the GCD of two integers.
- The GCD of two integers a and b is the largest integer that divides both a and b without leaving a remainder.
- Two integers are considered relatively prime if their GCD is 1.
- The division algorithm is a procedure for finding the quotient and remainder of two integers.
- The Euclidean algorithm is used to find the GCD of two integers by repeatedly applying the division algorithm.
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