# Quiz 10: Other Public-Key Cryptosystems

Computing

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True False

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True False

True

Q 3Q 3

For purposes of ECC, elliptic curve arithmetic involves
the use of an elliptic curve equation defined over an
infinite field.

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True False

False

Q 4Q 4

the Diffie-Hellman algorithm depends on the difficulty of
computing discrete logarithms for its effectiveness.

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True False

Q 5Q 5

there is not a computational advantage to using ECC
with a shorter key length than a comparably secure tS
A.

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True False

Q 6Q 6

Most of the products and standards that use public-key
cryptography for encryption and digital signatures use RS
A.

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True False

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True False

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True False

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True False

Q 10Q 10

For determining the security of various elliptic curve
ciphers it is of some interest to know the number of
points in a finite abelian group defined over an elliptic
curve.

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True False

Q 11Q 11

the form of cubic equation appropriate for
cryptographic applications for elliptic curves is
somewhat different for GF(2

^{m}) than for Z_{p}.Free

True False

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True False

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True False

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True False

Q 15Q 15

Since a symmetric block cipher produces an apparently
random output it can serve as the basis of a
pseudorandom number generator.

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True False

Q 16Q 16

the ____________ protocol enables two users to establish a secret key using a public-key scheme based on discrete logarithms.
A)Micali-Schnorr
B)Elgamal-Fraiser
C)Diffie-Hellman
D)Miller-Rabin

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Multiple Choice

Q 17Q 17

__________ can be used to develop a variety of elliptic curve cryptography schemes.
A)Elliptic curve arithmetic
B)Binary curve
C)Prime curve
D)Cubic equation

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Multiple Choice

Q 18Q 18

the key exchange protocol is vulnerable to a __________ attack because it does not authenticate the participants.
A)one-way function
B)time complexity
C)chosen ciphertext
D)man-in-the-middle

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Multiple Choice

Q 19Q 19

the __________ cryptosystem is used in some form in a number of standards including DSS and S/MIME.
A)Rabin
B)Rijnedel
C)Hillman
D)ElGamal

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Multiple Choice

Q 20Q 20

A(n) __________ is defined by an equation in two variables with coefficients.
A)abelian group
B)binary curve
C)cubic equation
D)elliptic curve

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Multiple Choice

Q 21Q 21

__________ are best for software applications.
A)Binary curves
B)Prime curves
C)Bit operations
D)Abelian groups

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Multiple Choice

Q 22Q 22

An encryption/decryption system requires a point G and an elliptic group _________ as parameters.
A)Eb(a,q)
B)Ea(q,b)
C)En(a,b)
D)Eq(a,b)

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Multiple Choice

Q 23Q 23

For cryptography the variables and coefficients are restricted to elements in a __________ field.
A)primitive
B)infinite
C)public
D)finite

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Multiple Choice

Q 24Q 24

If three points on an elliptic curve lie on a straight line their sum is __________ .
A)0
B)1
C)6
D)3

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Multiple Choice

Q 25Q 25

____________ makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.
A)Prime curve
B)Elliptic curve cryptography (ECC)
C)abelian group
D)Micali-Schnorr

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Multiple Choice

Q 26Q 26

For a ___________ defined over GF(2m), the variables and coefficients all take on values in GF(2m) and in calculations are performed over GF(2m).
A)cubic equation
B)prime curve
C)binary curve
D)abelian group

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Multiple Choice

Q 27Q 27

If a secret key is to be used as a _________ for conventional encryption a single number must be generated.
A)discrete logarithm
B)prime curve
C)session key
D)primitive root

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Multiple Choice

Q 28Q 28

the Diffie-Hellman key exchange formula for calculation of a secret key by User A is:
A)K = nB x PA
B)K = nA x PB
C)K = nP x BA
D)K = nA x PA

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Multiple Choice

Q 29Q 29

Included in the definition of an elliptic curve is a single element denoted O and called the point at infinity or the __________ .
A)prime point
B)zero point
C)abelian point
D)elliptic point

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Multiple Choice

Q 30Q 30

the __________ key exchange involves multiplying pairs of nonzero integers modulo a prime number q.Keys are generated by exponentiation over the group with exponentiation defined as repeated multiplication.
A)Diffie-Hellman
B)Rabin-Miller
C)Micali-Schnorr
D)ElGamal

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Multiple Choice

Q 31Q 31

Elliptic curve arithmetic can be used to develop a variety of elliptic curve cryptography schemes, including key exchange, encryption, and ___________ .

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Short Answer

Q 32Q 32

the purpose of the ___________ algorithm is to enable two users to securely exchange a key that can then be used for subsequent encryption of messages.

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Short Answer

Q 33Q 33

the key exchange protocol vulnerability can be overcome with the use of digital signatures and __________ certificates.

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Short Answer

Q 34Q 34

the principal attraction of __________, compared to RSA, is that it appears to offer equal security for a far smaller key size, thereby reducing processing overhead.

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Short Answer

Q 35Q 35

A(n) ___________ G is a set of elements with a binary operation, denoted by *, that associates to each ordered pair (a,b) of elements in G an element ( a*b) in G.

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Short Answer

Q 36Q 36

two families of elliptic curves are used in cryptographic applications: prime curves over Zp and __________ over GF(2m).

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Short Answer

Q 37Q 37

We use a cubic equation in which the variables and coefficients all take on values in the set of integers from 0 through p - 1 and in which calculations are performed modulo p for a __________ over Zp.

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Short Answer

Q 38Q 38

A __________ GF(2m) consists of 2m elements together with addition and multiplication operations that can be defined over polynomials.

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Short Answer

Q 39Q 39

the addition operation in elliptic curve cryptography is the counterpart of modular multiplication in RSA, and multiple addition is the counterpart of __________ .

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Short Answer

Q 40Q 40

to form a cryptographic system using __________ we need to
find a "hard-problem" corresponding to factoring the product of two primes or taking the discrete logarithm.

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Short Answer

Q 41Q 41

Eq(a,b) is an elliptic curve with parameters a, b, and q, where
_________ is a prime or an integer of the form 2

^{m}.Free

Short Answer

Q 42Q 42

the fastest known technique for taking the elliptic curve
logarithm is known as the _________ method.

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Short Answer

Q 43Q 43

Asymmetric algorithms are typically much slower than
symmetric algorithms so they are not used to generate open-ended __________ generator bit streams.

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Short Answer

Q 44Q 44

the __________ pseudorandom number generator is
recommended in the ANSI standard X9.82 (Random Number Generation) and in the ISO standard 18031 (Random Bit Generation).

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Short Answer

Q 45Q 45

A __________ of a prime number p is one whose powers
modulo p generate all the integers from 1 to p-1.

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Short Answer