When learning algorithms, such as RSA, it is important to understand the mathematics being used. In RSA, the number of positive integers less than or equal to some number is critical in key generation. The number of positive integers less than or equal to n that are coprime to n is called ______.
Euler's totient
https://en.wikipedia.org/wiki/Euler%27s_totient_function
In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n.
Incorrect answers:
Fibonacci number - commonly denoted Fn, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1.
Fermat's number - named after Pierre de Fermat, who first studied them, is a positive integer of the form Fn = 2^2^n+1 where n is a non-negative integer. The first few Fermat numbers are:
3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ...
Mersenne prime -- prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2^n 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.
Which of the following is a fundamental principle of cryptography that holds that the algorithm can be publicly disclosed without damaging security?
Kerkchoff's principle
https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle
Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Netherlands born cryptographer Auguste Kerckhoffs in the 19th century: A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.
Kerckhoffs's principle was reformulated (or possibly independently formulated) by American mathematician Claude Shannon as 'the enemy knows the system', i.e., 'one ought to design systems under the assumption that the enemy will immediately gain full familiarity with them'. In that form, it is called Shannon's maxim. This concept is widely embraced by cryptographers, in contrast to 'security through obscurity', which is not.
You are explaining the details of the AES algorithm to cryptography students. You are discussing the derivation of the round keys from the shared symmetric key. The portion of AES where round keys are derived from the cipher key using Rijndael's key schedule is called what?
The key expansion phase
https://en.wikipedia.org/wiki/Advanced_Encryption_Standard
KeyExpansion -- round keys are derived from the cipher key using the AES key schedule. AES requires a separate 128-bit round key block for each round plus one more.
Calculates the average LSB and builds a table of frequencies and Pair of Values. Performs a test on the two tables. It measures the theoretical vs. calculated population difference.
Chi-Square Analysis
https://en.wikipedia.org/wiki/Chi-squared_test
A chi-squared test, is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.
In cryptanalysis, the chi-squared test is used to compare the distribution of plaintext and (possibly) decrypted ciphertext. The lowest value of the test means that the decryption was successful with high probability. This method can be generalized for solving modern cryptographic problems.
Incorrect answers:
Raw Quick Pair - statistical analysis on number of unique colors and color number pairs in the picture and you look for least significant bits and manipulation of data in those bits, typically inside of whitespace.
SP network - substitution--permutation network is a series of linked mathematical operations used in block cipher algorithms such as AES (Rijndael), 3-Way, Kalyna, Kuznyechik, PRESENT, SAFER, SHARK, and Square.
Certificate Authority - component of a PKI that creates and maintains digital certificates throughout their life cycles.
A part of understanding symmetric cryptography understands the modes in which it can be used. You are
explaining those modes to a group of cryptography students. The most basic encryption mode is____________.
The message is divided into blocks, and each block is encrypted separately with no modification to the process.
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