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93 [10] Note that the solution to this problem is useful in the efficient implementation of the RSA algorithm, which is used widely for

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93 [10] Note that the solution to this problem is useful in the efficient implementation of the RSA algorithm, which is used widely for encryption. For integers X and Y design an efficient (log Y time) iterative algo- rithm to compute XY. Complete the following proof outline {x=X^y=Y>0} ? {z = XY} You should assume that variables x, y, and z hold mathematical inte- gers-thus there is no overflow- and that the operations assignment, +, -, x, , 'odd', and 'even' each take 1 unit of time, as do any compar- isons. Be sure to state the invariant of your loop.

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