Derive the time complexity of the following algorithm. Show your work.MULTIN : x and y, two n-bit binary numbers1 if b = 1if r = 1 A y = 123return 1else| return 06 (x1, T0) + (first [n/2] bits , last [n/2] bits ) of x7 (y1, Yo) + (first [n/2] bits , last [n/2] bits ) of y8 z1 + MULT(x1+x0, Y1+ Yo)MULT(r1,Y1)10 z3 + MULT(xo, yo)11 return z2 · 2" +(z1 – 22 – 23) · 2["/2] + z3OUT: The product of x and y59 z2 +Some details:•All additions and subtractions take O(n) time.•In the final return line, the multiplications by 2s0me power are actually bit shifts, and take O(n)time.•The base case takes O(1) time.

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Derive the time complexity of the following algorithm. Show your work. MULT IN : x and y, two n-bit binary numbers 1 if b= 1 if r = 1 A y = 1 |return 1 else |return 0 6 (x1, xo) + (first [n/2] bits , last |n/2| bits ) of x 7 (y1, Yo) + (first [n/2] bits , last [n/2] bits ) of y MULT(x1+xo, Y1 + Yo) 2 3 4 8 21 + 9 z2 + MULT(x1, Y1) 10 z3 + MULT(xo, yo) 11 return z2 · 2" + (z1 – z2 – z3) · 2 n/2] + z3 OUT: The product of x and y

Derive the time complexity of the following algorithm. Show your work. MULT IN : x and y, two n-bit binary numbers 1 if b= 1 if r = 1 A y = 1 |return 1 else |return 0 6 (x1, xo) + (first [n/2] bits , last |n/2| bits ) of x 7 (y1, Yo) + (first [n/2] bits , last [n/2] bits ) of y MULT(x1+xo, Y1 + Yo) 2 3 4 8 21 + 9 z2 + MULT(x1, Y1) 10 z3 + MULT(xo, yo) 11 return z2 · 2" + (z1 – z2 – z3) · 2 n/2] + z3 OUT: The product of x and y

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Derive the time complexity of the following algorithm. Show your work.
MULT
IN : x and y, two n-bit binary numbers
1 if b = 1
if r = 1 A y = 1
2
3
return 1
else
| return 0
6 (x1, T0) + (first [n/2] bits , last [n/2] bits ) of x
7 (y1, Yo) + (first [n/2] bits , last [n/2] bits ) of y
8 z1 + MULT(x1+x0, Y1+ Yo)
MULT(r1,Y1)
10 z3 + MULT(xo, yo)
11 return z2 · 2" +(z1 – 22 – 23) · 2["/2] + z3
OUT: The product of x and y
5
9 z2 +
Some details:
•All additions and subtractions take O(n) time.
•In the final return line, the multiplications by 2s0me power are actually bit shifts, and take O(n)
time.
•The base case takes O(1) time.

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In this problem we will work through a round of DES. For notational simplicity, assume it is the first round. Please enter all answers as strings of O's and 1's. The input is the 64 bit block 0000000000000100000000000100001000100000000000000000100000000000 Suppose that the subkey for the current round is this 48 bit number: 000000000000000010000000000000000000000000000000 What does the 64 bit state lok like after the IP transformation is applied to the input? Now find Ln and Ro, the left and right halves of the state. Lo =0 Ro = What is the result of applying the expansion box to Ro? E(Ro) = 0 What is the result of XORing the subkey with E(Ro)? k1 e E(Ro) = We now apply the S-box transformation. S(kı O E(Ro)) = Finally we apply the permutation box to complete the function f. f(Ro) = P(S(kı O E(Ro))) = We can now compute the state of DES going into the next round. L, =|| Rj =