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So now we use the extended Euclid’s algorithm to find the multiplicative inverse of e. EXTENDED EUCLID (Ф(n), e) 1. (A1, A2, A3) ← (1, 0, m); (B1, B2, B3) ← (0, 1, b) 2. if B3 = 0 return A3 = gcd(Ф(n), e); no inverse. 3. if B3 = 1 return B3 = gcd(Ф(n), e); B2 = e-1 mod m. 4. Q = [A3/B3] 5. (T1, T2, T3) ← (A1 - QB1, A2 - QB2, A3 - QB3) 6.
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[DOCX File]B. V. V. Sangha’s
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The sender knows the value of e, and only receiver knows the value of d. Thus, this is a public-key encryption algorithm with a public key of KU={e,n}, and a private key of KR={d,n}. For this algorithm to be satisfactory for public-key encryption, the following requirements must be met: Description of the Algorithm (Cont 1)
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THIS MEMORANDUM OF UNDERSTANDING is made this day …
Use Extended Euclid’s algorithm to find the private key.(13) K3 Apply 13 (i) User A and B use Diffie-Hellman key exchange a common prime q=71 and a primitive root a=7.Calculate the following. If user A has private key XA=5, what is A’s public key YA. If user A has private key XB=12, what is B’s public key YB and what is shared secret key?
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[DOC File]Proof That Euclid’s Algorithm Works
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b) Using the Extended Euclidean Algorithm find all pairs of integers x and y that satisfy the equation 427x + 154y = gcd(427, 154). 35 - 2(14) = 7, (6) which is obtained by writing (4) backwards. We know that 14 = 119 - 3(35) from (3), so now substitute for 14 into (6):
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Extended Euclidean algorithm - Wikipedia
Furthermore, the Extended Euclidean Algorithm can be used to find values of x and y to satisfy the equation above. The algorithm will look similar to the proof in some manner. Consider writing down the steps of Euclid's algorithm: a = q1b + r1, where 0 < r < b. b = q2r1 + r2, where 0 < r2 < r1. r1 = q3r2 + r3, where 0 < r3 < r2..
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[DOC File]SOLUTIONS MANUAL - National Tsing Hua University
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Design and write a program to implement Extended Euclid’s algorithm to compute the, greatest. common divisor . of integers . a . and . b, also the coefficients of Bézout's identity, which are integers . x . and . y . such that ax+ by= gcd (a,b).
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[DOC File]To calculate d, we have to 1st calculate Ф(n)
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To see that algorithm correctly returns gcd(m,b), note that if we equate A and B in Euclid’s algorithm with A3 and B3 in the extended Euclid’s algorithm, then the treatment of the two variables is identical. Note also that if gcd(m,b)=1, then on the final step we would have B3=0 and A3 =1. Therefore, on the preceding step, B3=1.
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[DOC File]FINITE FIELDS OF THE FORM GF(p)
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EUCLIDEAN ALGORITHM. Eulidean algorithm (Euclid’s algorithm) is an algorithm to determine the greatest common divisor (GCD or gcd ) of two integers by repeatedly dividing the two numbers and the remainder in turns. Description of the algorithm. Given two natural numbers m and n, check if n = 0. If yes, m is the gcd.
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[DOC File]WordPress.com
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b. Euclid's algorithm requires a "long division" at each step whereas the Stein algorithm only requires division by 2, which is a simple operation in binary arithmetic. 4.18 a. If An and Bn are both even, then 2 gcd(An+1, Bn+1) = gcd(An, Bn). But …
the extended euclidean algorithm

[DOC File]COT 3100 Quiz #9: Euclid's Algorithm 3/23/05
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The Extended Euclidian Algorithm. Donald Knuth describes Euclid’s algorithm as, “the granddaddy of all algorithms, because it is the oldest nontrivial algorithm that has survived to …
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Euclid s extended algorithm