《密码学与网络安全》.pdf-资料库

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课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！ Introduction (Solution to Practice Set) CHAPTER 1 khdaw.com Review Questions 1. The three security goals are confidentiality, integrity, and availability. Confidentiality means protecting confidential information. Integrity means that changes to the information need to be done only by Availability means that information needs to be available to authorized enti- authorized entities. 课后答案网 www.hackshp.cn ties. 2. In a passive attack, the attacker’s goal is just to obtain information. This means that the attack does not modify data or harm the system. Examples of passive attacks are snooping and traffic analysis. An active attack may change the data or harm the system. Attacks that threaten the integrity and availability are active attacks. Examples of active attacks are modification, masquerading, replaying, repudiation, and denial of service. 3. We mentioned five security services: data confidentiality, data integrity, authenti- cation, nonrepudiation, and access control. Data confidentiality is to protect data from disclosure attack. Data integrity is to protect data from modification, insertion, deletion, and khdaw.com 1 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com replaying. the line. Authentication means to identify and authenticate the party at the other end of Nonrepudiation protects against repudiation by either the sender or the receiver of the data. Access control provides protection against unauthorized access to data.

课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！ 2 4. Eight security mechanisms were discussed in this chapter. encipherment, data integrity, digital signature, authentication exchange, traffic padding, routing con- trol, notarization, and access control. Encipherment provides confidentiality. The data integrity mechanism appends a short checkvalue to the data. The checkvalue is created by a specific process from the data itself. A digital signature is a means by which the sender can electronically sign the data and the receiver can electronically verify the signature. In authentication exchange, two entities exchange some messages to prove their identity to each other. khdaw.com Traffic padding means inserting some bogus data into the data traffic to thwart the adversary’s attempt to use the traffic analysis. Routing control means selecting and continuously changing different avail- able routes between the sender and the receiver to prevent the opponent from eavesdropping on a particular route. Notarization means selecting a third trusted party to control the communica- Access control uses methods to prove that a user has access right to the data or tion between two entities. 课后答案网 www.hackshp.cn resources owned by a system. 5. Cryptography, a word with origin in Greek, means “secret writing.” We used the term to refer to the science and art of transforming messages to make them secure and immune to attacks. Steganography, a word with origin in Greek, means "covered writing." Stega- nography refers to concealing the message itself by covering it with some- thing else. Exercises 6. a. A regular mail guarantees no security services. It is the best-effort delivery ser- vice. The mail can be lost, altered in the mail, opened by somebody other than the intended recipient. b. A regular mail with delivery confirmation can only show that the mail has been delivered. This can only give peace of mind to the sender that the packet is not lost. However, since there is no signature from the recipient, it does not guaran- tee any of the security services. c. A regular mail with delivery confirmation and the recipient signature can pro- vide nonrepudiation service only at the mail level, not the contents level. In other words, the recipient of the mail cannot deny that she has not received the mail, but she can deny that the mail contained some specific information. For khdaw.com 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com

3 khdaw.com example, if Alice sends a mail with $100 cash inside to Bob via this type of mail, Bob cannot deny that he has received the mail, but he can deny that the mail contained some cash inside. In some cases, the sender is an authority and it is enough that Bob accepts he has received the mail. In this case, if there is a dispute, the court accept the testimony of the sender about the contents. d. A certified mail is actually the same as the regular mail with delivery confirma- tion and the recipient signature. e. A mail can be insured. However, this is not security in the sense we are talking in this chapter. Secured mail can only provide compensation if the mail is lost. f. A registered mail is different from all of the previous delivery methods. A reg- istered mail is carried by the post office under the tight security. This means that the confidentiality and integrity of the mail is guaranteed. Since a registered mail normally includes the signed receipt, the nonrepudiation is also guaran- teed. However, nonrepudiation is only at the mail level, not the content level. The recipient of the registered mail cannot deny that the mail has been deliv- ered, but it can deny that it contained a special message or an item of some value. 7. 8. 9. a. This is snooping (attack to the confidentiality of stored data). Although the con- tents of the test is not confidential on the day of the test, it is confidential before the test day. b. This is modification (attack to the integrity of data). The value of the check is changed (from $10 to $100). c. This is denial of service (attack to availability). Sending so many e-mails may crash the server and the service may be interrupted. a. This provides access control mechanism. The process is to prove that the stu- dent has right to access the school resources. b. This can provide routing control. The school may be doing this to prevent a stu- dent from eavesdropping on a particular route. c. This can be authentication exchange mechanism. The professor needs to authenticate the student before sending the grade. The preassigned identifica- tion is a secret between the student and the professor. d. The mechanism is similar to digital signature. It can be used for two purposes. If the signature of the customer is checked against a signature on the file, it can provide authentication. The signature on the withdrawal document definitely is served as the nonrepudiation. The customer cannot later denies that she has not received the cash. khdaw.com a. This is steganography. The answers to the test has not been changed; they have been only hidden. 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com 课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！课后答案网 www.hackshp.cn

b. This is cryptography. The characters in the message are not hidden; they are replaced by another characters. 4 c. This is steganography. The special ink hides the actual writing on the check. d. This is steganography. The water marks hides the actual contents of the thesis. 10. A signature on a document is like a digital signature on a message. It protects the integrity of the document, it provides authentication, and it protects non-repudia- tion. khdaw.com khdaw.com 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com 课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！课后答案网 www.hackshp.cn

Mathematics of Cryptography Part I CHAPTER 2 khdaw.com (Solution to Practice Set) Review Questions 1. The set of integers is Z. It contains all integral numbers from negative infinity to positive infinity. The set of residues modulo n is Zn. It contains integers from 0 to n − 1. The set Z has non-negative (positive and zero) and negative integers; the set Zn has only non-negative integers. To map a nonnegative integer from Z to Zn, we need to divide the integer by n and use the remainder; to map a negative integer from Z to Zn, we need to repeatedly add n to the integer to move it to the range 0 to n − 1. 2. We mentioned four properties: Property 1: if a | 1, then a = ±1. Property 2: if a | b and b | a, then a = ±b. Property 3: if a | b and b | c, then a | c. Property 4: if a | b and a | c, then a | (m × b + n × c), where m and n are arbi- trary integers. 3. The number 1 is an integer with only one divisor, itself. A prime has only two divi- sors: 1 and itself. For example, the prime 7 has only two divisor 7 and 1. A com- posite has more than two divisors. For example, the composite 42 has several divisors: 1, 2, 3, 6, 7, 14, 21, and 42. 4. The greatest common divisor of two positive integers, gcd (a, b), is the largest pos- itive integer that divides both a and b. The Euclidean algorithm can find the great- est common divisor of two positive integers. 5. A linear Diophantine equation of two variables is of the form ax + by = c. We need to find integer values for x and y that satisfy the equation. This type of equation has either no solution or an infinite number of solutions. Let d = gcd (a, b). If d does not divide c then the equation have no solitons. If d divides c, then we have an infi- nite number of solutions. One of them is called the particular solution; the rest, are /. called the general solutions. khdaw.com 1 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com 课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！课后答案网 www.hackshp.cn

2 khdaw.com 6. The modulo operator takes an integer a from the set Z and a positive modulus n. The operator creates a nonnegative residue, which is the remainder of dividing a by n. We mentioned three properties for the modulo operator: First: (a + b) mod n = [(a mod n) + (b mod n)] mod n Second: (a − b) mod n = [(a mod n) − (b mod n)] mod n Third: (a × b) mod n = [(a mod n) × (b mod n)] mod n 7. A residue class [a] is the set of integers congruent modulo n. It is the set of all inte- gers such that x = a (mod n). In each set, there is one element called the least (non- negative) residue. The set of all of these least residues is Zn. 8. The set Zn is the set of all positive integer between 0 and n − 1. The set Zn∗ is the set of all integers between 0 and n − 1 that are relatively prime to n. Each element in Zn has an additive inverse; each element in Zn∗ has a multiplicative inverse. The extended Euclidean algorithm is used to find the multiplicative inverses in Zn∗. 9. A matrix is a rectangular array of l × m elements, in which l is the number of rows and m is the number of columns. If a matrix has only one row (l = 1), it is called a row matrix; if it has only one column (m = 1), it is called a column matrix. A square matrix is a matrix with the same number of rows and columns (l = m). The determinant of a square matrix A is a scalar defined in linear algebra. The multipli- cative inverse of a square matrix exists only if its determinant has a multiplicative inverse in the corresponding set. 10. A linear equation is an equation in which the power of each variable is 1. A linear congruence equation is a linear equation in which calculations are done modulo n. An equation of type ax = b (mod n) can be solved by finding the multiplicative inverse of a. A set of linear equations can be solved by finding the multiplicative inverse of a matrix. Exercises 11. a. It is false because 26 = 2 × 13. b. It is true because 123 = 3 × 41. c. It is true because 127 is a prime. d. It is true because 21 = 3 × 7. e. It is false because 96 = 25 × 3. f. It is false because 8 is greater than 5. 12. khdaw.com 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com 课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！课后答案网 www.hackshp.cn

a. gcd (88, 220) = 44, as shown in the following table: 3 b. gcd (300, 42) = 6, as shown in the following table: gcd (24, 320) = 8, as shown in the following table: khdaw.com c. q 0 2 2 r1 88 220 88 44 r2 220 88 44 0 r 88 44 0 q 7 7 r1 300 42 6 r2 42 6 0 r 6 0 q 0 13 3 r1 24 320 24 8 r2 320 24 8 0 r 24 8 0 d. gcd (401, 700) = 1 (coprime), as shown in the following table: q 0 1 1 2 1 13 1 1 3 r1 401 700 401 299 102 95 7 4 3 1 13. r2 700 401 299 102 95 7 4 3 1 0 r 401 299 102 95 7 4 3 1 0 khdaw.com a. gcd (a, b, 16) = gcd (gcd (a, b), 16) = gcd (24, 16) = 8 b. gcd (a, b, c, 16) = gcd (gcd (a, b, c), 16) = gcd (12, 16) = 4 c. gcd (200, 180, 450) = gcd (gcd (200, 180), 450) = gcd (20, 450) = 10 d. gcd (200, 180, 450, 600) = gcd (gcd (200, 180, 450), 600) = gcd (10, 600) = 10 若侵犯了您的版权利益，敬请来信通知我们！ ℡ www.khdaw.com 课后答案网：www.hackshp.cn 若侵犯了您的版权利益，敬请来信告知！课后答案网 www.hackshp.cn

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