One of the useful features of the Chinese remainder theorem is that it provides a way to manipulate potentially very large numbers mod M in terms of tuples of smaller numbers.

An important requirement in a number of cryptographic algorithms is the ability to choose a large prime number.

All integers have primitive roots.

An area of ongoing research is the development of efficient algorithms for determining if a randomly chosen large integer is a prime number.

The first assertion of the CRT, concerning arithmetic operations, follows from the rules for modular arithmetic.

Discrete logarithms are not fundamental to public-key algorithms.

The number 37 is prime so therefore all of the positive integers from 1 to 36 are relatively prime to 37.

Discrete logarithms are analogous to ordinary logarithms but are defined using modular arithmetic.

The Chinese Remainder Theorem is believed to have been discovered by the Chinese mathematician Agrawal in 100 A.D.

A                   number can only be divided by +/- values of itself and 1 and cannot have a remainder.

1.     An important quantity in number theory referred to as                     , is defined as the number of positive integers less than n and relatively prime to n.

Miller's test will return                     if it fails to detect that n is not prime.

Prime numbers play a                   role in number theory.

If p is prime and a is a positive integer, then ap = a(mod p) is an alternative form of theorem.

The algorithm is typically used to test a large number for primality.

The procedure TEST takes a candidate integer n as input and returns the result if n is definitely not a prime.

Two numbers are relatively prime if they have prime factors in common.

Discrete logarithms are fundamental to the ____________.

The procedure TEST takes a candidate integer n as input and returns the result if n may or may not be a prime.

The procedure TEST takes a candidate integer n as input and returns the result if n may or may not be a prime.

The Diffie-Hellman key exchange is a simple public-key

algorithm.

The security of ElGamal is based on the difficulty of

computing discrete logarithms.

Most of the products and standards that use public-key

cryptography for encryption and digital signatures use RSA.

ECC is fundamentally easier to explain than either RSA or

Diffie-Hellman.

Elliptic curves are ellipses.

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.

The form of cubic equation appropriate for cryptographic applications for elliptic curves is somewhat different for GF(2m) than for Zp.

An encryption/decryption system requires that point Pm be encrypted as plaintext.

The security of ECC depends on how difficult it is to determine k given kP and P.

A considerably larger key size can be used for ECC compared to RSA.

The ____________ protocol enables two users to establish a secret key using a public-key scheme based on discrete logarithms.

__________ can be used to develop a variety of elliptic curve cryptography schemes.

The key exchange protocol is vulnerable to a __________ attack because it does not authenticate the participants.

The __________ cryptosystem is used in some form in a number of standards including DSS and S/MIME.

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

A number of public-key ciphers are based on the use of

an abelian group.

There is not a computational advantage to using ECC

with a shorter key length than a comparably secure TSA.

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

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

infinite field.

__________ are best for software applications.

Asymmetric encryption utilizes only a public key for encryption

and decryption.

Asymmetric encryption can be used for confidentiality but not for

authentication.

Plaintext is transformed into ciphertext using two keys and a

decryption algorithm.

A major advance in symmetric cryptography occurred with the

development of the rotor encryption/decryption machine.

Public-key encryption is more secure from cryptanalysis than

symmetric encryption.

Much of the theory of public-key cryptosystems is based on

number theory.

Asymmetric algorithms rely on one key for encryption and a

different but related key for decryption.

The encryption algorithm performs various transformation on the

ciphertext.

If the authenticator is encrypted with the sender's private key, it

serves as a signature that verifies origin, content, and sequencing.

A public-key encryption scheme is not vulnerable to a brute-force

attack.

Asymmetric encryption is also known as ___________.

Public-key encryption is also known as ___________.

Asymmetric encryption transforms plaintext into ciphertext.

Asymmetric encryption transforms plaintext into ciphertext.

Asymmetric encryption can be used for __________.

Plaintext is recovered from the ciphertext using the paired key and a _____________.

The most widely used public-key cryptosystem is __________.

__________ are two related keys, a public key and a private key that are used to perform complementary operations, such as encryption and decryption or signature generation and signature verification.

Public-key algorithms are based on __________.

The __________ indicates that the subscriber identified in the certificate has sole control and access to the private key.

Virtually all cryptographic hash functions involve the iterative use of a compression function.

Limited characteristics make it impossible for hash functions to be used to determine whether or not data has changed.

Hash functions can be used for intrusion and virus detections.

The cryptographic hash function is not a versatile cryptographic algorithm.

it is possible to use a hash function but no encryption for message authentication.

Hash functions are commonly used to create a one-way password file.

A weak hash function is sufficient to protect against an attack in which one party generates a message for another party to sign.

The way to measure the resistance of a hash algorithm to cryptanalysis is to compare its strength to the effort required for a

        brute-force attack.

It can be shown that some form of birthday attack will succeed against any hash scheme involving the use of cipher block         chaining without a secret key, provided that either the resulting hash code is small enough or that a larger hash code can be

        decomposed into independent subcodes.

The most widely used hash function has been the Whirlpool.

The principal object of a hash function is __________.

A ___________ accepts a variable length block of data as input and produces a fixed size hash value h = H(M).

The Secure Hash Algorithm design closely models and is based on, the hash function __________ .

A ___________ is an algorithm for which it is computationally infeasible to find either (a) a data object that maps to a pre-specified hash result or (b) two data objects that map to the same hash result.

The cryptographic hash function requirement that guarantees that it is impossible to find an alternative message with the same hash value as a given message and prevents forgery when an encrypted hash code is used is the ___________.

__________ is a mechanism or service used to verify the integrity of a message.

Message authentication is achieved using a __________.

__________ are measures of the number of potential collisions for a given hash value.

The effort required for a collision-resistant attack is explained by a mathematical result referred to as the ___________.

The SHA-512 algorithm has the property that every bit of the hash code is a function of every bit of the input.

Message authentication is a mechanism or service used to verify the integrity of a message.

The order in which the frame check sequence and encryption functions are performed is not critical for authentication.

A recipient in possession of the secret key cannot generate an authentication code to verify the integrity of the message.

One means of forming a MAC is to combine a cryptographic hash function in some fashion with a secret key.

A brute-force attack on a MAC is easier than a brute-force attack on a hash function.

The __________ mode of operation is designed to be parallelizable so that it can provide high throughput with low cost and low latency.

Insertion of messages into the network from a fraudulent source is a __________ attack.

Confidentiality can be provided by performing message encryption __________ the MAC algorithm.

A __________ is an algorithm that requires the use of a secret key.

"Release of message contents to any person or process not possessing the appropriate cryptographic key" is a __________ attack.

The principle requirement of random or pseudorandom number

generation is that the generated number stream be unpredictable.

Random numbers play an important role in the use of encryption

for various network security applications.

With true random sequences each number is statistically independent of other numbers in the sequence and therefore

unpredictable.

The true random number generator may simply involve conversion of an analog source to a binary output.

Examples of a pseudorandom function are decryption keys and

nonces.

The best that can be done to determine if a PRNG generates numbers that

have the characteristic of randomness is on the basis of multiple tests. These

tests should seek to establish uniformity, scalability, and __________ .

A pseudorandom number generator takes as input a fixed value called the __________ and produces a sequence of output bits using a deterministic algorithm.

The __________ test is the most basic test of randomness and must be included in any test suite.

A secret key for symmetric encryption that is generated for use for a short period of time is called a _________ .

A __________ is used to produce a pseudorandom string of bits of some fixed length.