## 4 Results  
Table 7 and Figures 2-4 show a wide range of performance benchmarks, providing an extensive analysis of the effectiveness and efficiency of three well-known cryptographic schemes: CRYSTALS-Kyber, CRYSTALS-Dilithium, and Falcon. These resources move beyond simple comparisons, delving into the details of major generation times, and exposing insights critical for informed decision making. The evident pattern of increasing key generation times with increasing security levels gives meaningful information about the challenging balancing of security robustness and computational needs. This discovery highlights the dynamic nature of cryptographic algorithms and how they respond to increased security needs. The shift from Dilithium to Falcon is particularly notable as large alterations in key generation times become apparent. This highlights the different structural complexities built into each signature method. Such detailed information helps administrators to navigate the complicated field of cryptographic options, and it also offers a mindful selection that meets not just severe security requirements but also realistic performance limitations. In Figure 5, signature sizes, we have a comparison of the sizes of cryptographic signatures for different algorithms and configurations. The x-axis represents our various cryptographic algorithms and their key sizes, including Falcon 256, Falcon 512, Falcon 1024, Dilithium 2, Dilithium 3, and Dilithium 5. The y-axis represents the size of the signatures in bytes. Falcon 256 has the smallest signature size at 356 bytes, followed by Falcon 512 at 666 bytes, and Falcon 1024 with the largest signature size at 1280 bytes. On the other hand, the Dilithium signature sizes, which are Dilithium 2, Dilithium 3, and Dilithium 5, are larger, beginning with 2420 to 4595 bytes. This figure provides the efficiency of different signature schemes in terms of signature size. As the security level increases, the size increases as well. Figure 6, ciphertext sizes for CRYSTALS-Kyber configurations, represents  
Figure 4: Comparison of Falcon key generation time and sizes. Figure 3: Comparison of CRYSTALS-Dilithium key generation time and sizes. Figure 2: Comparison of CRYSTALS-Kyber key generation time and sizes. the sizes of ciphertexts generated by all three security levels of the CRYSTALS-Kyber cryptographic algorithm including Kyber 512, Kyber 768, and Kyber 1024. Examining these data, we can see that Kyber 512 generates ciphertexts of size 768 bytes, Kyber 768 produces ciphertexts of size 1088 bytes, and Kyber 1024 results in ciphertexts of size 1568 bytes. This figure illustrates how the choice of Kyber security level impacts the size of ciphertexts, which is essential for assessing the trade-off between security and efficiency in cryptographic applications. Significant differences in key size, cipher size, and signature size among algorithms arise from their principles and design. In CRYSTALS-Kyber, the public key consists of a matrix and some random values used in the encryption process. This public key size is quite large. The ciphertext is generated during the encryption process and includes some compressed values derived from the public key and the message. Compression techniques are used to reduce the size of these values, which makes the ciphertext smaller than the public key. CRYSTALS-Dilithium also uses lattice-based cryptography. It achieves a lower signature size than the key size by using structured lattices. Falcon is based on the NTRU lattice problem and uses the FFT for optimization. This allows Falcon to achieve very compact signatures and smaller key sizes compared to other lattice-based algorithms. Figures 7-9 provide a detailed examination of the encapsulation time of CRYSTALS-Kyber across various signing algorithms. These figures illustrate the time, measured in milliseconds, needed to encapsulate data for different security levels. It is important to observe that as security levels increase, the time required for this operation also increases.