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This lecture explores Coppersmith's method to find small roots of polynomials modulo N efficiently, reducing the problem to root finding over ZCR. The instructor demonstrates the application of this method, such as attacking RSA encryption, by efficiently computing all roots. The lecture covers the theorem, proof, and idea behind Coppersmith's method, emphasizing the reduction of the problem to root finding. Various examples and applications are discussed, including the consideration of multiples of f(x) and the use of numerical methods like Newton's method.