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### 40 Cards in this Set

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 Define cryptology Cryptology is a all-inclusive term for the study of communication over nonsecure channels, and related problems. Define cryptography Cryptography is the study of designing systems that implement elements of cryptogology. Define cryptanalysis Cryptanalysis is the study of breaking systems developed with cryptgoraphy. Define coding theory Coding theory is used to describe cryptography: however the term can often lead to confusion. Coding theory deals with represeting input information symbols by output symbols called code symbols. There are three basic applications that coding theory covers: compresssion, secrecy, and error correction. Over the past few decades, coding theory has become predominantly associated with error correcting codes. What is a plaintext, who is classically associated with the plaintext? A plaintext is a message, Alice classically sends the plaintext. What is a ciphertext, who is classically classically associated with the ciphertext? A cyphertext is a plaintext message that has been encrypted using a key. Alice classically creates the cyphertext, which she then passes to Bob. What is a key A key is something that allows you to use a function to change a plaintext into a cyphertext and a cyphertext back into a plaintext. What are the four main type of attacks that eve might attempt? 1) Cyphertext only 2) Known Plaintext 3) Chosen Plaintext 4) Chosen ciphertext What is a ciphertext only attack? In a ciphertext only attack Eve has only one copy of the ciphertext. What is a known plaintext attack? Eve has a copy of the ciphertext and the corresponding plaintext. What is a chosen plaintext attack? Eve gains temporary access to the encryption machine. She cannot open it to find the key; however, she can encrypt a large number of suitably chosen plaintexts and try to use the resulting ciphertexts to deduce the key. What is a chosen ciphertext attack? Eve gains temporary access to the decryption machine, uses it to "decrypt" several strings of symbols, and tries to use the results to deduce the key. What is Kerckhoffs's principle Kerckhoffs's principle states that in assessing the security of a cryptosystem, one should always assume the enemy knows the method being used. What are the two general categories of encryption/decryption methods? symmetric key and public key What is symmetric key cryptography? Symmetric key algorithms, the encryption and decryption are known to both Alice and Bob. AES and DES are symmetric key algorithms. What is public key cryptography? Public key alrgorithms make the encryption key public. However, due to fundamental mathematical truths, finding the decryption algorithm is computationally infeasible. What are the four main methods of cryptography? The four main methods of cryptography are: 1) Confidentiality 2) Data Integrity 3) Authentication 4) Non-repudiation What does confidentiality mean in the context of cryptography? Eve should not be able to read Alices message to Bob. The main tools are encryption and decryption algorithms. What does data integrity mean in the context of cryptography? Bob wants to be sure that Alices message has not been altered. Eg. Transmition errors might have occured or Eve might have altered it. What does authentication mean in the context of cryptography? Bob wants to be sure that only Alice could have sent the message he received. What does non-repudiation mean in the context of cryptography? Alice cannot claim she did not send the message. What is Divisibility? What does it mean to say that a divides b? Let a and b be integers with a != 0. We say that a divides b, if there is an integer k such that b = ak. This is denoted by a|b. Another way to express this is that b is a multiple of a. What is a prime number? A numper p > 1 that is divisible only by 1 and itself is called a prime number. What is a composite number? A composite number is a number that is not prime, which means that n must be expressible as a product ab of integers with 1 < a, b < n. What is the Prime Number Theorem? Prime Number Theorem: Let PIE(x) be teh number of primes less than x. Then PIE(x) ≈ x / ln(x) in the sense that the ratio PIE(x)/(x / ln(x)) -> 1 as x -> ∞ What is the positive integers and primes Theorem? Every positive integer is a product of primes. This factorization into primes is unique, up to reordering the factors. What is the greatest common devisor of two numbers? How is greatest common divisor dentoted (mathematical and CS)? The greatest common devisor of two numbers (say a and b) is the largest positive integer dividing both a and b. In CS this is denoted by gcd(a,b) in mathematics this is denoted by (a, b) What does it mean to say that two numbers are relativly prime? it means that two numbers (say a and b) have a gcd(a,b) that is equal to 1. What is the simple way to find gcd of integer a and b? If you can factor a and b into primes, do so. Fore each prime number, look at the powers that it appears in the factorizations of a and b. Take the smaller of the two. Put these prime powers together to get the gcd. this is easiest to understand by examples: 576=2^6*3^2, 135=3^3*5, gcd(576,135)=3^2=9 What is the Euclidian algorithm? The Euclidian algorithm is an algorithm that allows you to find the gcd of two numbers even if the numbers are two large to factor by hand. How do you perform the Euclidean algorithm on two numberes a and b? Suppose that a is greater than b. If not, switch a and b. The first step is to divide a by b, hence represent a in the form r₁ = q₁r₂ + r₃, where r₁ = a, r₂ = b, n starts at 3. If r₁ = 0, then b divides a and the greatest common divisor is b. If r₁ is not equal to 0, then continue by representing b in the form r(n-2) = q(n)r(n-1) + r(n) What is the algorithm to find x and y in ax + by = gcd(a, b) and how do we use it? The algorithm is the extended eucledian algorithm. The Extended Euclidian Algorithm is as follows, ________________________________________________________ What is another word for modular arithmetic? congruence If a - b (mod n) is a multiple of (positive or negative) of n, then we can write a ≡ b (mod n) (read: a is congruent to b mod n) *as a more standard equation, it can be said that a = b + nk for some integer k (positive or negative)* What is true of the ability to do division mod n The general rule is that you can divide by a (mod n) when gcd(a, n) = 1. How does one find a^(-1) (mod n) To find a^(-1) (mod n), 1. Use the extended Euclidean algorithm to find integers s and t such that as + nt = 1 2. a^(-1) ≡ s (mod n) What is the Chinese Remainder Theorem? Suppose gcd(m,n) = 1. Given integers a and b, there exists exactly one solution x (mod mn) to the simultaneous congruence x ≡ a (mod m), x ≡ b (mod n). (this can be taken to any number of m and n as long as all of the m or n have gcd(m,n) = 1) How do you perform x^a (mod n) ? Modular exponentiation is easy. Simply take the base value of the sum of the power of 2 values of x that sum to a, and then multiply them together. What is Fermat's Little Theorem? Fremat's Little Theorem states that: If p is a prime and p does not divide a, then a^(p-1) ≡ 1 (mod p) What is Euler's Theorem? If gcd(a,n) = 1, then a^(∅(n))≡1 (mod n), where ∅(n) is the number of integers 1 ≤ a ≤ n such that gcd(a,n) = 1.