Cryptography Flashcards

(41 cards)

1
Q

Cryptography

A

The study of mathematical techniques related to aspects of information security such as confidentiality, data integrity, entity authentication, and data authentication

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2
Q

Data integrity

A

A service which addresses the unauthorised alteration of data.

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3
Q

Entity authentication

A

A service that determines if an entity is who it claims to be.

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4
Q

Data origin authentication

A

A service that determines if an entity claiming to be the sender of a message really is the one from whom it originates.

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5
Q

Non-reputation

A

A service that prevents an entity from denying previous commitments or actions.

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6
Q

A

A

alphabet of definition

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7
Q

M

A

Message space

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8
Q

plaintext

A

Element of the message space

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9
Q

C

A

Ciphertext space

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10
Q

ciphertext

A

Element of the ciphertext space, or element of key space

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11
Q

K

A

Key space

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12
Q

Encryption function E_e

A

Bijection from M to C

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13
Q

Decryption function

A

Bijection from C to M

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14
Q

Symmetric-key

A

The encryption scheme is symmetric-key if for each associated encryption/ decryption key pair (e; d), if is computationally “easy” to determine d knowing only e, and to determine e from d.

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15
Q

Block cipher

A

An encryption scheme which breaks up the plaintext messages to be transmitted into strings of a fixed length t over an alphabet A and encrypts one block at a time.

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16
Q

Stream ciphers

A

Very simple block ciphers having block length equal to one.

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17
Q

Public-key

A

For each associated encryption/ decryption key pair (e, d). if given e it is infeasible to determine the corresponding decryption key d.

18
Q

Equivaltence class

A

Set of numbers all equivalent to a modulo n

19
Q

The integers modulo n

A

The set of all equivalence classes of integers in {0, …, n-1}

20
Q

Binary operation (on a set S)

A

A function f:SxS->S, implies closure

21
Q

A group satisfies…

A

Associativity, Identity, Inverse

22
Q

COmmutative/ abelian

23
Q

Homomorphism

A

(G,) and (H,.) groups A function h: G -> H such that h(ab) = h(a).h(b) for all a, b in G

24
Q

Isomorphism

A

A bijective homomorphism

25
Subgroup
A subset that is also a group
26
Order (of G)
Number of elements in G
27
Lagrange's theorem
If G is a finite group and H is a subgroup of G, then |H| divides |G|. Hence, if a is in G, the order of a divides |G|.
28
Generators
The set S in G if, for all y in G, x^i = y for some integer i in S. S generates G. Notation = G
29
A Ring (R, +, x) satisfies ...
(R, +) is abelian group with identity 0 x is associative multiplicative identity 1, not equal to 0 such that ax1 = 1Xa for all a x is distributive over +
30
Commutative ring
axb = bxa for all a, b in the ring
31
Ring of polynomials over R
The commutative ring formed by the set of all such polynomials, denoted R[x]
32
Unit
a in R is a unit if there exists a b in r such that axb = 1
33
Group of units
The set of units in a ring R that forms a group under multiplication.
34
A field (K, +, x) satisfies...
(K, +, x) is a ring with identities 0 and 1 | (K\{0}, x) is a commutative group
35
Finite field
A field with a finite number of elements
36
(Z_m, +, x) is a field iff
m is a prime number
37
The ring F[x]/f(x) is a field iff
f(x) is irreducible in F[x]
38
Relatively prime
GCD = 1
39
Fermat's little theorem
Suppose n and x are relatively prime, with n prime, then x^(n-1) is congruent to 1 (mod n)
40
Public key
pair (e, n)
41
Private key
d, or (d, p, q)