Improve the sentence structure and flow of the following text to be more readable while fixing the math notation into proper LaTeX:


"The authors propose using NAME_1 operator theory to analyze the security of public-key cryptographic protocols like Diffie-Hellman key exchange. They transform the nonlinear modulo operation into a linear system for easier analysis but acknowledge that this method does not significantly reduce computational complexity of brute-force attacks. The paper presents a fresh viewpoint on traditional cryptographic algorithms and connects them with chaotic dynamics. Notations include definitions of natural numbers, integers, nonnegative integers, ranges of integers, symbols \(A^\dagger\) and \(\ln(z)\), complex exponential function, and polar forms. The equation z=exp(w)=exp(w+i2πℓ) holds for all ℓ∈ℤ and implies that if z is given in polar form r⋅exp(iθ) with r>0 and θ∈ℝ, then all complex logarithms of z are of the form ln(r)+i(θ+2πℓ). An integer m is called a quadratic residue modulo p (abbreviated by mRp) if there exists an integer x such that m=x^2 mod p. Two integers p1,p2 are relatively prime or coprime if their greatest common divisor is equal to 1. All integers from {1,...,p} which are relatively prime to p form the multiplicative group Zp* of integers modulo p. Additionally, we use γ1��2 as an abbreviation of γ1≡γ2modp. A number m is a primitive root modulo p if for any integer c coprime to p there exists an exponent k∈ℕ such that m^k��. Equivalently, m is called a generator of Zp*."


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