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Cryptography and Number Theory Worksheet

Total questions: 100

Worksheet time: 51mins

Name
Class
Date
1.

Determine the complete system of residues mod 7

a)

1, 3, 2, 4,

b)

5, 6, 7, 10

c)

0, 1, 2, 3, 4, 5, 6

d)

3, 4, 5, 8

e)

1, 2, 3, 4, 5

2.

Determine the reduced system of residues modulo 9

a)

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

b)

1, 2, 3, 4, 5,

c)

7, 8, 9

d)

0, 1, 3, 5, 7, 9

e)

1, 2, 4, 5, 7, 8

3.

The strength of the RSA cryptosystem is based

a)

on the complexity of factoring large numbers

b)

on the difficulty of computing discrete logarithms

c)

on the difficulty of computing polynomials

d)

on the difficulty of solving n-degree equations

e)

on the difficulty of finding prime numbers

4.

The Diffie-Hellman system's cryptographic strength is based

a)

on the complexity of factoring large numbers

b)

on the difficulty of computing discrete logarithms

c)

on the difficulty of computing polynomials

d)

on the difficulty of solving n-degree equations

e)

on the difficulty of finding prime numbers

5.

The cryptographic strength of the system based on the "backpack problem" is based on

a)

on the complexity of factoring large numbers

b)

on the difficulty of computing discrete logarithms

c)

on the difficulty of computing polynomials

d)

on the difficulty of solving n-degree equations

e)

on the difficulties of solving problems of finding elements, the sum of which is equal to a given number

6.

Theorem "System of equations {x ≡ a(mod n) x ≡ b(mod m)} has a unique solution modulo m * n" is called ...

a)

Fermat's theorem

b)

Euler's theorem

c)

Legendre's theorem

d)

Jacobi's theorem

e)

Chinese Remainder Theorem

7.

Solve the comparison system {x ≡ 4(mod 7) x ≡ 3(mod 5)}

a)

x ≡ 18(mod 35)

b)

x ≡ 10(mod 35)

c)

x ≡ 12(mod 35)

d)

x ≡ 7(mod 35)

e)

x ≡ 21(mod 35)

8.

Expression of the form ∑i=1naixi\sum_{i=1}^{n} a_i x^i called

a)

polynomial

b)

binomial

c)

monomial

d)

the sum

e)

work

9.

If b= axa^x (mod p), where a is the primitive root modulo p, x ∈ [0,1,...,p-1], then x is called

a)

antiderivative root

b)

exponent

c)

discrete logarithm

d)

a random number

e)

a constant number

10.

Discrete logarithm is called differently

a)

natural

b)

decimal

c)

index

d)

simple

e)

super complicated

11.

Solve comparison 3x ≡ 15(mod 4)

a)

x=5(mod 4)

b)

x=7(mod 4)

c)

x=3(mod 4)

d)

x=4(mod 4)

e)

x=12(mod 4)

12.

Vernal's cipher is

a)

table encryption

b)

encryption substitution

c)

permutation encryption

d)

encryption replacement

e)

bitwise encryption

13.

Given equality 2≡32(mod 5)2 \equiv 3^2 (\text{mod } 5) What is the discrete logarithm of 2 to base 5?

a)

A) 2

b)

B) 3

c)

C) 5

d)

D) 1

e)

E) 4

14.

The Vigenira system is

a)

table cipher

b)

public key system

c)

a complex substitution cipher

d)

permutation cipher

e)

RSA

15.

Ensuring authentication, integrity, non-traceability is solved with the help of

a)

electronic signature

b)

protocols

c)

public keys

d)

cryptosystems

16.

A sequence of steps taken by two or more parties to jointly solve a certain problem is

a)

protocol

b)

electronic signature

c)

ciphertext

d)

coding

e)

decoding

17.

A renegade is

a)

rework

b)

fake

c)

active interception

d)

failure

e)

repeat

18.

Message modification is

a)

rework

b)

failure

c)

fake

d)

active interception

e)

repeat

19.

Imitation is

a)

failure

b)

fake

c)

repeat

d)

disguise

e)

active interception

20.

The simplest and most common electronic signature tool is the algorithm

a)

RSA

b)

CBA

c)

ElGamal

d)

backpack problem

e)

Diffie-Hellman

21.

A digital signature is

a)

a sequence of random numbers

b)

a series of natural numbers

c)

a string of characters depending on the sender ID and the content of the message

d)

set of primes

e)

an increasing sequence of integers

22.

True digital signature if

a)

the signed message is sent through a third party

b)

the signed message is sent directly from the sender to the recipient

c)

the signed message is sent through some third party

d)

the signed message is not sent to the recipient, but to the second person

e)

the signed message is passed from the sender to the recipient's proxy

23.

Key management is an informational process that includes

a)

generating keys

b)

accumulation of keys

c)

key distribution

d)

declassifying keys

e)

selection of keys

24.

Pseudo-random number sensors are used

a)

to generate keys

b)

to get primes

c)

solving comparisons

d)

receiving ciphers

e)

the formation of number sequences

25.

The organization of storage of keys, their accounting and deletion is called

a)

generating keys

b)

key distribution

c)

accumulation of keys

d)

deleting keys

e)

generating keys

26.

Promptness, secrecy and accuracy of key distribution is a requirement for

a)

generating keys

b)

accumulation of keys

c)

key distribution

d)

deleting keys

e)

key storage

27.

Galois field is denoted

a)

GF(p)

b)

G

c)

F(p)

d)

Dp

e)

p

28.

Field with elements {0,1,2, ... p-1} – all possible remainders from dividing integers by p and algebraic actions modulo p are called

a)

by the Diffie field

b)

Galois field

c)

Caesar's field

d)

by the Viginier field

e)

by Shannon field

29.

The smallest positive number k for which k*a≡0(mod p) for ∀ a ∈ GF(p) called

a)

field characteristic

b)

field boundary

c)

field area

d)

field length

e)

the perimeter of the field

30.

The trade-off between public key systems and conventional algorithms, which require the sender and recipient to have the same key, is

a)

using "roaming keys"

b)

using public keys

c)

using private keys

d)

use of voice communication

e)

using voicemail

31.

Square tables with sequential natural numbers inscribed in their cells, starting from 1, which add up the same number for each column, each row and each diagonal, are called

a)

fairy squares

b)

unreal squares

c)

magic squares

32.

The permutation cipher "skital" uses devices

a)

conical shape

b)

cylindrical

c)

ball shape

d)

combined form

e)

truncated-conical shape

33.

One of the first ciphers of simple replacement is the Polybian square, which was proposed by the Greek writer and historian Polybius for encryption purposes. It is a square size

a)

2×2

b)

3×3

c)

4×4

d)

5×5

e)

7×7

34.

The virtue of the Caesar encryption system

a)

ease of encryption

b)

ease of decryption

c)

low durability

d)

high durability

e)

impossibility of breaking

35.

Disadvantages of Caesar's encryption system

a)

the frequency of appearance of the letters of the original text is not masked

b)

the alphabetical order of the sequence of replacement letters is preserved

c)

the number of possible keys is small and the cipher is easily revealed based on the analysis of the frequencies of occurrence of letters in the ciphertext

d)

ease of encryption

e)

ease of decryption

36.

The process of imposing a cipher on open data according to a certain gamma law is called

a)

gamming

b)

encryption

c)

decryption

d)

permutation

e)

tabling

37.

Asymmetric cryptosystems include

a)

RSA

b)

El Gamal

c)

Diffie-Hellman

d)

Caesar

e)

Vignera

38.

The plaintext encryption procedure is as follows

1. selects 2 large primes p и q and calculate n=pq and m=(p-1)(q-1)

2. chooses an integer k such that K<m and (e,m.)=1

3. вычисляет число k, удовлетворяющее условию K*kº1 (mod m)

4. the subscriber's secret key is a triplet of numbers (p,q,k), open - a pair of numbers (n,K)

Such a cryptosystem is called

a)

El Gamal

b)

RSA

c)

Vigniera

d)

Diffie-Hellman

39.

A function with the following properties: 1. function description H(k,x) should be open, and secret information should only be contained in the choice of the key k 2. function x argument H(k, x) can be an arbitrary length string, and the function value must be a fixed length string 3. for any given k and x, the calculation H(k, x) must be fast (in polynomial time) 4. for any given x it should be hard to guess the value H(k, x) with a probability greater than 1/2n, where n – the number of bits in the output string. It should be difficult to determine the key k even over a large number of pairs {x, H(k,x) } or calculate from this information H(k,x) for x≠x₁ called

a)

exponential

b)

hash function

c)

unilateral

d)

unidirectional

e)

polynomial

40.

Keyless hash functions are divided into 2 classes

a)

weak one-way hash functions

b)

strong one-way hash functions

c)

weak two-way hash functions

d)

strong two-way hash functions

e)

weak two-way hash functions

41.

Distributed algorithm, i.e. a set of algorithms for each of the participants, plus the specifications of the message formats sent between the participants, plus the specifications for synchronizing the actions of the participants, plus a description of actions in case of errors is called

a)

by signature

b)

protocol

c)

cipher system

d)

electronic signature

e)

RSA algorithm

42.

The difference between a protocol and a cryptosystem

a)

ensuring confidentiality

b)

ensuring integrity, ensuring non-traceability

c)

interactivity, having more than two participants

d)

participants do not trust each other; protection not only from the enemy, but also from dishonest actions of partners

e)

providing special key storage

43.

Solve comparison x+5=20(mod18)

a)

x≡25(mod18)

b)

x≡15(mod18)

c)

x≡4(mod18)

d)

x≡2(mod18)

e)

x≡100(mod18)

44.

Solve the comparison system 2x ≡ 5(mod 7) x ≡ 3(mod 10)

a)

x≡4(mod70)

b)

x≡8(mod70)

c)

x≡13(mod70)

d)

x≡9(mod70)

e)

x≡18(mod70)

45.

By system RSA known p=2, q=11, public key K=3, find the private key.

a)

8

b)

5

c)

11

d)

7

e)

9

46.

Fermat's theorem is expressed by the equality

a)

ap≡1(mod p)a^p \equiv 1 \text{(mod } p)

b)

ap-2º1(mod p)

c)

ap+1≡1(modp)a^p+1 \equiv 1(mod p)

d)

ap-1º1(mod p)

e)

ap−2≡0(mod p)a^p-2 \equiv 0(mod \ p)

47.

Euler's theorem can be written as the equality

a)

aϕ(m)≡1(modm)a^\phi(m) \equiv 1(mod m)

b)

am≡1(modϕ(m)a^m \equiv 1(mod \phi(m)

c)

a2φ(m)≡1(modm)a^2φ(m) ≡ 1(mod m)

d)

aϕ(n)−1≡1(mod m)a^{\phi(n)-1} \equiv 1 \text{(mod m)}

e)

aϕ(n)+1≡1(mod m)a^{\phi(n)+1} \equiv 1 \text{(mod } m)

48.

If in the RSA cryptosystem K is the public key, k is the secret key, then from which equality can the private key be found, knowing the public key?

a)

K+k ≡ 1 (mod φ(n))

b)

K*k ≡ 1 (mod φ(n))

c)

K-k ≡ 1 (mod φ(n))

d)

K*k ≡ 1 (mod n)

e)

K+k ≡ 1 (mod n)

49.

In the RSA cryptosystem, the public key is K = 7. Find the private key k if n = 22.

a)

5

b)

7

c)

4

d)

11

e)

3

50.

Solve the comparison system {x ≡ 3 (mod 2) x ≡ 2 (mod 5)}

a)

x ≡ 2(mod 5)

b)

x ≡ 3(mod 2)

c)

x ≡ 4(mod 7)

d)

x ≡ 7(mod 10)

e)

x ≡ 5(mod 10)

51.

A and B are remote legitimate users of the protected information, then P –

a)

illegal user

b)

buddy A

c)

buddy B

d)

buddy A and B

e)

outsider

52.

the message is converted at once

a)

the whole message is converted at once

b)

the message is converted into blocks of a certain length

c)

the message is converted piece by piece

d)

the message is converted into blocks of different lengths

e)

the message is transformed in halves

53.

Solve comparison 2x+5=19(mod 13)

a)

x=5(mod 13)

b)

x=7(mod 13)

c)

x=1(mod 13)

d)

x=12(mod 13)

e)

x=10(mod 13)

54.

Solve comparison 2x=18(mod 11)

a)

x=5(mod 11)

b)

x=10(mod 11)

c)

x=1(mod 11)

d)

x=12(mod 11)

e)

x=9(mod 11)

55.

Block ciphers are

a)

imposition on the source text of some pseudo-random sequence generated based on the key

b)

a sequence (with possible repetition and alternation) of basic transformation methods applied to a block of ciphertext

c)

replacing characters of the original text with others of the same alphabet

d)

imposition on the source text of some pseudo-random sequence generated based on the key

e)

Caesar cipher

56.

Converting ciphertext characters to replacement ciphers

a)

is transformed using a matrix

b)

are rearranged according to some rule within some block of this text

c)

are transformed according to some analytical rule

d)

are replaced by characters of another or the same alphabet in accordance with the replacement scheme.

e)

is transformed using an inverse key matrix

57.

Convert cipher text characters to permutation ciphers

a)

are replaced by symbols of a different or the same alphabet in accordance with the replacement scheme.

b)

is transformed using an inverse key matrix

c)

are transformed according to some analytical rule

d)

is transformed using a matrix

e)

are rearranged according to some rule within some block of this text.

58.

Substitution types used in cryptography

a)

Huffman, Caesar, Playfair

b)

mono-alphabetic, homophonic, polyalphabetic

c)

Markov, homophonic, Playfair

d)

mono-alphabetic, homophonic, polyalphabetic and polygram

e)

Vizhner, Caesar, Playfer, analytical

59.

Principle of mono-alphabet substitution

a)

each letter of the plaintext alphabet is assigned one letter of the ciphertext from the same alphabet.

b)

each letter of the plaintext alphabet is associated with two letters of the ciphertext from the same alphabet.

c)

each letter of the plaintext is assigned a letter with a shift

d)

each letter of the plaintext alphabet is associated with one letter of the key

e)

each plaintext letter is assigned a closedtext letter

60.

The principle of polyalphabetic substitution

a)

each letter of the plaintext alphabet is assigned one letter of the ciphertext from the same alphabet.

b)

each letter of the plaintext alphabet is associated with two letters of the ciphertext from the same alphabet.

c)

uses multiple ciphertext alphabets

d)

maps several ciphertext characters to one plaintext character.

e)

each letter of the plaintext alphabet is associated with one letter of the key

61.

Cryptographic protocols must protect against the following violations and attackers:

a)

renegade (rejection), repeat

b)

modification (rework)

c)

counterfeit, imitation, active interception

d)

copy

e)

mailing

62.

Conversions that can be used as a one-way function

a)

exponential transformations

b)

sum of matrices

c)

matrix difference

d)

matrix zero multiplication

e)

multiplication by the identity matrix

63.

Gumming -

a)

replacing characters of the original text with others from the other alphabet

b)

Caesar cipher

c)

replacement of symbols of the source text with others (of the same alphabet) according to a more or less complex rule

d)

imposing on the source text some pseudo-random sequence generated based on the key

e)

imposition on the source text of some pseudo-random sequence generated based on the key

64.

For which function is the inverse operation computationally time consuming?

a)

straight

b)

bilateral

c)

reverse

d)

unilateral

e)

terminal

65.

What fact did the creators of RSA take advantage of?

a)

finding large primes is computationally laborious, and factoring the product of two such numbers is practically impossible

b)

finding large primes is computationally easy, but factoring the product of two such numbers is practically impossible

c)

factoring the product of two numbers is easy

d)

finding primes is computationally easy

e)

finding prime divisors is computationally easy

66.

Solve comparison x+2=17(mod18)

a)

x=25(mod18)

b)

x=15(mod18)

c)

x=4(mod18)

d)

x=2(mod18)

e)

x=100(mod18)

67.

Solve the comparison system 2x ≡ 5 (mod 7) 3x ≡ 9 (mod 10)

a)

xº4(mod70)

b)

xº8(mod70)

c)

xº13(mod70)

d)

xº9(mod70)

e)

xº18(mod70)

68.

According to the RSA system, the public key K=3, p=2, q=11. What will the private key be?

a)

A) 8

b)

B) 7

c)

C) 11

d)

D) 5

e)

E) 9

69.

Solve the comparison system x ≡ 3(mod 2) 2x ≡ 4(mod 5)

a)

x ≡ 2(mod 5)

b)

x ≡ 7(mod 10)

c)

x ≡ 4(mod 7)

d)

x ≡ 3(mod 2)

e)

x ≡ 5(mod 10)

70.

In RSA cryptosystem, the private key k=3, n=22. Find the public key K.

a)

5

b)

3

c)

4

d)

11

e)

7

71.

How is a message transformed in streaming cryptosystems?

a)

the message is converted immediately

b)

the message is converted into blocks of a certain length

c)

the message is converted piece by piece

d)

the message is converted into blocks of different lengths

e)

the message is transformed in halves

72.

In which cryptosystem the message is transformed into blocks of a certain length?

a)

in a streaming cryptosystem

b)

in a block cryptosystem

c)

in the RSA system

d)

in the El Gamal system

e)

in a combined system

73.

Solve comparison 2x ≡ 18(mod 13)

a)

x ≡ 5(mod 13)

b)

x ≡ 1(mod 13)

c)

x ≡ 9(mod 13)

d)

x ≡ 12(mod 13)

e)

x ≡ 10(mod 13)

74.

The RSA algorithm is named -

a)

honoring the creators: Ron Rivest, Adi Shamir and Leonard Adelman

b)

by the name of the algorithm - random number algorithm (Random Seek Acess)

c)

by the name of the algorithm - speed algorithm

d)

random selection of characters

e)

by the name of the company that developed this method

75.

Knowing the public key in the RSA cryptosystem, how can you find the private key?

a)

K+k ≡ 1 (mod φ(n))

b)

K*k ≡ 1 (mod φ(n))

c)

K*k ≡ 1 (mod φ(n))

d)

K*k ≡ 1 (mod n)

e)

K+k ≡ 1 (mod n)

76.

What Yi is - in the mono-alphabetic substitution formula: Yi=kl*Xi + k2 (mod N)

a)

i-th character of the alphabet

b)

constant;

c)

i-th plaintext character;

d)

alphabet length

e)

key length

77.

What Xi is - in the monoalphabetic substitution formula: Yi = k1 * Xi + k2 (mod N)

a)

i-th character of the alphabet

b)

constant;

c)

i-th plaintext character;

d)

the length of the alphabet used

e)

key length

78.

Gronsfeld cipher - cipher modification

a)

Caesar's numeric key

b)

Vigenere, for m = 2

c)

Vernam's numeric key

d)

DES numeric key

e)

GOST symbolic key

79.

Vigenère code: yi = xi + ki (mod n), where ki is

a)

i-th letter of the key, which is used as a word or phrase

b)

i-th letter of the alphabet

c)

i-th letter of the key

d)

key

e)

alphabet

80.

With Homophonic Replacement

a)

each letter of the plaintext alphabet is associated with one letter of the ciphertext from the same alphabet

b)

each letter of the plaintext alphabet is associated with two letters of the ciphertext from the same alphabet

c)

each letter of the plaintext is assigned a letter with a shift

d)

each letter of the plaintext alphabet is associated with one letter of the key

e)

maps several ciphertext characters to one plaintext character

81.

With polyalphabetic substitution

a)

each letter of the plaintext alphabet is associated with one letter of the ciphertext from the same alphabet

b)

each letter of the plaintext alphabet is associated with two letters of the ciphertext from the same alphabet

c)

uses multiple ciphertext alphabets

d)

each letter of the plaintext alphabet is associated with one letter of the key

e)

maps several ciphertext characters to one plaintext character

82.

In the problem of packing a knapsack, the ciphertext is obtained as

a)

dot product

b)

cross product

c)

prime power

d)

binary key decomposition

83.

The creators of RSA took advantage of the fact that

a)

finding large primes is computationally easy, but factoring the product of two such numbers is practically impossible

b)

finding large primes is computationally laborious, and factoring the product of two such numbers is practically impossible

c)

factoring the product of two numbers is easy

d)

finding primes is computationally easy

e)

finding prime divisors is computationally easy

84.

For increased secrecy, the length of the password should be (when the user is forced to set passwords not with a word, but at least with a phrase)

a)

must not be shorter than 12 characters

b)

must not be shorter than 7 characters

c)

must not be shorter than 5 characters

d)

must not be shorter than 4 characters

e)

must be at least 1024 characters

85.

The alphanumeric key must be

a)

at least 7 characters

b)

at least 6 characters

c)

at least 5 characters

d)

at least 12 characters

e)

maximum of 7 characters

86.

What are the names of cryptoalgorithms in which the encoding unit is one bit, and the encoding result does not depend on the previously passed input stream:

a)

Blocky

b)

Wildcards

c)

Streaming

d)

Asymmetrical

e)

Permutation

87.

What are the names of the cryptoalgorithms in which the encoding unit is a block of several bytes (from 4 to 32), and the encoding result depends on all the original bytes of this block:

a)

Blocky

b)

Wildcards

c)

Streaming

d)

Asymmetrical

e)

Permutation

88.

The secret system includes

a)

two statistical choices: message selection and key selection

b)

three statistical choices: message choice and key choice, ciphertext choice

c)

message selection

d)

key selection

e)

encryption algorithm

89.

The only key is used in cryptosystems

a)

symmetrical

b)

with public key

c)

asymmetric

d)

with private key

e)

Class D

90.

Two keys are used in cryptosystems

a)

symmetrical

b)

with public key

c)

asymmetric

d)

with private key

e)

Class D

91.

Which group does the Caesar Cipher belong to?

a)

mono-alphabetic

b)

homophonic

c)

polyalphabetic

d)

polygram

e)

packing the knapsack

92.

Comparison is given as x≡b(mod m). Please enter an invalid equality.

a)

2x≡2b(mod m)

b)

3x≡b(mod m)

c)

ax+c≡b+c(mod m)

d)

ax≡b+m*k(mod m)

e)

ax+m≡b(mod m)

93.

The most popular public key encryption algorithms are

a)

PGP и RSA

b)

PGP и DES

c)

RSA и DES

d)

Gost и DES

e)

Gost

94.

Solve the comparison system 2x ≡ 6 (mod 2) x ≡ 2 (mod 5)

a)

x≡1(mod 5)

b)

x≡5(mod 10)

c)

x≡4(mod 7)

d)

x≡13(mod 2)

e)

x≡7(mod 10)

95.

The process of breaking a cipher without knowing the key (checking the strength of the cipher):

a)

Code

b)

Cryptography

c)

Coding

d)

Cryptanalysis

e)

Key

96.

The specific secret state of some parameters of the cryptographic data transformation algorithm, which ensues the selection of only one option out of all possible for this algorithm:

a)

Code

b)

Cryptography

c)

Coding

d)

Cryptanalysis

e)

Key

97.

The first stage in the work of any asymmetric cryptoalgorithm is:

a)

Distributing the public key "worldwide"

b)

Message encryption

c)

Decrypting the message

d)

Create a key pair: public and private

e)

Message transmission

98.

The basis for creating keys for any asymmetric cryptoalgorithm are:

a)

Differentiating the message length value

b)

Logarithm of the message length

c)

Bijective mathematical functions

d)

Third order equations

e)

Prime numbers and operations on them

99.

The main idea of asymmetric cryptoalgorithms:

a)

Session key is used to encrypt plaintext

b)

One key is used to encrypt a message, and another key is used when decrypting a message

c)

The same key is used for both encrypting and decrypting the message

d)

Knowing the public key, you can calculate the private key

e)

The encryption procedure is reversible

100.

Solve the comparison system (x = 6(mod 17)

x= 4(mod 11)

(x = -3(mod 8)

a)

xº125(mod 1496)

b)

xº125 (mod 1494)

c)

xº125(mod 1498)

d)

xº125(mod 1499)

e)

xº125(mod 1490)