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Class: MATH 4175 - Cryptography; Subject: Mathematics; University: Virginia Polytechnic Institute And State University; Term: Fall 2015;
Typology: Quizzes
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Science of hidden communication TERM 2
DEFINITION 2 Makes hidden messages TERM 3
DEFINITION 3 Breaking hidden messages TERM 4
DEFINITION 4 the message TERM 5
DEFINITION 5 the encrypted message
Algorithm for taking PT -> CT and CT -> PT TERM 7
DEFINITION 7 26 possible keyschange characters but not order; change order but not characterse(x) = (x + d) mod 26d(x) = (y - d) mod 26encrypt: PT + Key % 26decrypt: CT - Key % 26on average, PT will be computed by brute force for shift cipher after 26/2=13 decryption rules. TERM 8
DEFINITION 8 suppose a and b are ints, and m is a positive int. then we write a b(mod m) if m divides b-a (or b-a = mc). TERM 9
DEFINITION 9 -101 mod 7 = (7)(-15) + 4divide 101 by 7. this gives you 14. add 1 to get 15 and multiply 7 by 15 to get 105. 105-101 = 4**use -15 and not -14 because you want the smallest num closest to -101 (-105 is smaller than -98) TERM 10
DEFINITION 10 A key for sub cipher just consists of a permutation of 26 alphabetic chars -> 26! permutationsIn cryptography, a substitution cipher is a method of encoding by which units of plaintext are replaced with ciphertext, according to a fixed system; the "units" may be single letters, pairs of letters, triplets of letters, mixtures of the above, and so forth.
NOT monoalphabeticusing correspondence A<->1, B<-> ... Z<->25, we can associate ea/ key K w/ an alphabetic string of length m = keyword.Key K = (k1, k2, ...km)e_k(x1, x2, .., xm) = (x1+k1, x2+k2, ..., xm+km) : PT+keyd_k(y1, y2, ...ym) = (y1-k1, y2-k2, ...ym-km) : CT-keynumber of possible key words of len m = 26^m TERM 17
DEFINITION 17 ~1860's: security depends on protecting the key and not the method TERM 18
DEFINITION 18 Cryptosystem must have confusion (each CT char does not relate to the key in a simple way) and diffusion TERM 19
DEFINITION 19 A CT char string of len >= 3 appearing in 2 places in the CT might give info about key length (difference between 2 positions where they started thn take the gcd -> most likely the length; or else it's one of the factors.) TERM 20
DEFINITION 20 find the length of recurrence by using matrices to solve for coefficients -> Z_(i+m) = c0zi +c1zi+1 + ... + cm-1zi+m-
In cryptography, coincidence counting is the technique of putting two texts side-by-side and counting the number of times that identical letters appear in the same position in both texts.NEEDS MORE DEFINITION TERM 22
DEFINITION 22 encr = decr; no fixed points - no letter encr to itselfhow many keys? security of enigma depends on wiring of plugboard, internal positions of rotors, and their order in which they're placed, internal wirings of rototsfor each 26 possible positions for each rotor, there are 6 ways to place these rotors = 26^3 x 6; operator picks message key = 3 letters -> how you set key for next messageFunctions
