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quiz1_fall2006

# quiz1_fall2006 - Fa'I'i 2006 Csc349 Quiz#1 dosed books...

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Unformatted text preview: Fa'I'i 2006 Csc349 Quiz #1 dosed books, c'losed notes Poss'bia 4mm 13 PtS 15 minutes 5&549 1) —1-_Given is the number 18. Specify two different numbers, ’ both different from 18, and not greater than 50 that are congruent to 18 (mod 13). 3} gas] / 2) —1— Are the numbers 24 and 51 co ruent (mod 17)? Yes dirk?) / In the next two questions write just one number (not an expression). 3) —1- what 15 the inverse of 1 mod 50'? 1 l449me< 1/ £2335 4) —1- what is the inverse of 49 mod 50'?ng one .c ' 1/ S) —1— How many numbers smaHer than 10 have an inverse (mod 50)?/9/e/\$/ :4: 1+ has a. aprrme, a-s—sxso Any number no+a a. e 79 mM-Hw'p/e o-F seams Ham {0, W459; .m-f— l {3) —1- Assume that a and b have inverses (mod N) and a l b. Does"’°“k 1t fo‘ﬂow that the invgejare aiso different? Yes No / v?) +~le If N is chosen as the product of 2 primes, p and q, what - ll / 15 the totient of N? ‘ ~ __ «-1)-( —:L (PM , 7 (P 7’ ) #8) —1— S ecif¥7the totient of 77. @{7’2} =(7-1) {ll—1): é-lo 2 690 -H c . 4‘ N . Z PPM: Prune 9)_ —1— Write the congruence 3014 ~= 5467 (mod N) as an equation WTth N and k- "gaze—5997; N»/< / // 9"”th «10) —2- Someone chooses the modui us N for an RSA encryption, 1_et + t be the totient of N. The person chooses e (< t) as the pubhc encryption key. _ 4+ 3.) with which a'lgorithm does s/he compute the gaaryptlion key d? 3 Farmer buck-deaf Eucirbi"°t"l ﬂclaorri‘hwm 'fc-e+:yv%:16«dolﬁ—) / ﬁ/ 13) Write the reiation that e and d must fuiFiH. 9‘ ‘J‘A 0‘50 ' ) "2 we _ I 5 v‘ 11) —1— what is the totient of 71? (consider prima'lity) , 43171).- a?” r 2 C, ...
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