Progress has brought increased vulnerability to currently used cryptographic mechanisms that serve as security measures for data and messages. For such algorithms as RSA and ECC, based on NP problems, specific mathematical problems, such as integer factorization and discrete logarithms, are most at risk in the face of quantum algorithms such as Shor’s and Grover’s. This paper considers a new approach to cryptography that is relatively new but will become increasingly important soon. Post-quantum cryptography, assumed to protect data from classical and quantum hacking Try different post quantum cryptography algorithms such as. This analysis is then followed by an evaluation of the mathematical characteristics and security of lattice-based, hash-based, and other post-quantum cryptographic algorithms. Traditional and quantum-safe algorithms’ computational complexity, key lengths, and encryption/decryption times were analyzed using an elaborate experimental design that included tools like Python libraries such as PyCrypto and liboqs. Outcomes of these experiments show that algorithms for quantum-safe cryptography, especially lattice technique, perform well in terms of security but have higher complexity costs due to large size of keys and computations. Hash based schemes however show simplicity and efficiency in digital signatures and are a key building block of future cryptographic systems. To assess the vulnerabilities of the traditional systems, quantum-based simulations of attacks employing Grover’s and Shor’s algorithms were performed. Grover’s algorithm showed the capability of searching through symmetric key more efficiently than brute force and Shor’s algorithm very effectively implemented factoring of RSA keys, which proved that classical cryptographic system is vulnerable to quantum threats. Additional graphical presentations of encryption-decryption time, scalability of key size, and probability of success for quantum attacks reinforced the observation that it is about time to move to post-quantize solutions. The research also offers theoretical contributions to the nature and robustness of quantum-safe algorithms in lattice-based cryptography, it depends on the difficulty of lattice problems such as SVP hash-based cryptography, on the other hand, guarantees no collisions.