Elliptic curve arithmetic can be used to develop a variety of elliptic curve

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.

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