Chapter 10 1 The Diffiehellman Key Exchange Formula For Calculation

CHAPTER 10: OTHER PUBLIC-KEY CRYPTOSYSTEMS

TRUE OR FALSE

T F 1. The Diffie-Hellman key exchange is a simple public-key

algorithm.

T F 2. The security of ElGamal is based on the difficulty of

computing discrete logarithms.

T F 3. For purposes of ECC, elliptic curve arithmetic involves

the use of an elliptic curve equation defined over an

infinite field.

T F 4. The Diffie-Hellman algorithm depends on the difficulty of

computing discrete logarithms for its effectiveness.

T F 5. There is not a computational advantage to using ECC

with a shorter key length than a comparably secure TSA.

T F 6. Most of the products and standards that use public-key

cryptography for encryption and digital signatures use

RSA.

T F 7. ECC is fundamentally easier to explain than either RSA or

Diffie-Hellman.

T F 8. A number of public-key ciphers are based on the use of

an abelian group.

T F 9. Elliptic curves are ellipses.

T F 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.

T F 11. The form of cubic equation appropriate for

cryptographic applications for elliptic curves is

somewhat different for GF(2m) than for Zp.

T F 12. An encryption/decryption system requires that point

Pm be encrypted as a plaintext.

T F 13. The security of ECC depends on how difficult it is to

determine k given kP and P.

T F 14. A considerably larger key size can be used for ECC

compared to RSA.

T F 15. Since a symmetric block cipher produces an apparently

random output it can serve as the basis of a

pseudorandom number generator.

MULTIPLE CHOICE

1. 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

2. __________ 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

3. 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

4. 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

5. A(n) __________ is defined by an equation in two variables with

coefficients.

A. abelian group B. binary curve

C. cubic equation D. elliptic curve

6. __________ are best for software applications.

A. Binary curves B. Prime curves

C. Bit operations D. Abelian groups

7. 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)

8. For cryptography the variables and coefficients are restricted to

elements in a __________ field.

A. primitive B. infinite

C. public D. finite

9. If three points on an elliptic curve lie on a straight line their

sum is __________ .

A. 0 B. 1

C. 6 D. 3

10. ____________ 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

11. 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

12. 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

13. 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

14. 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

15. 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

SHORT ANSWER

1. Elliptic curve arithmetic can be used to develop a variety of

elliptic curve cryptography schemes, including key exchange,

encryption, and ___________ .

2. 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.

3. The key exchange protocol vulnerability can be overcome with

the use of digital signatures and __________ certificates.

4. 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.

5. 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.

6. Two families of elliptic curves are used in cryptographic

applications: prime curves over Zp and __________ over

GF(2m).

7. 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.

8. A __________ GF(2m) consists of 2m elements together with

addition and multiplication operations that can be defined over

polynomials.

9. The addition operation in elliptic curve cryptography is the

counterpart of modular multiplication in RSA, and multiple

addition is the counterpart of __________ .

10. 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.

11. Eq(a,b) is an elliptic curve with parameters a, b, and q, where

_________ is a prime or an integer of the form 2m.

12. The fastest known technique for taking the elliptic curve

logarithm is known as the _________ method.

13. Asymmetric algorithms are typically much slower than

symmetric algorithms so they are not used to generate open-

ended __________ generator bit streams.

14. The __________ pseudorandom number generator is

recommended in the ANSI standard X9.82 (Random Number

Generation) and in the ISO standard 18031 (Random Bit

Generation).

15. The PRNG variable ___________ is defined in NIST SP 800-90 as

a number associated with the amount of work required to break

a cryptographic algorithm or system.

TRUE OR FALSE

MULTIPLE CHOICE

SHORT ANSWER