While encryption is a powerful tool for securing information, it does not ensure complete security on its own. There are several limitations and vulnerabilities in cryptographic systems that must be acknowledged.

One limitation is the potential for key compromise. If an attacker gains access to the cryptographic keys, the security of the encrypted data is compromised. This risk necessitates stringent key management practices, including secure storage, regular updates, and controlled access.

Another limitation is the strength of the encryption algorithm itself. Algorithms may have inherent weaknesses that can be exploited by attackers, especially as technology and computational power advance. This necessitates continuous evaluation and potential updates of cryptographic algorithms.

Furthermore, encryption does not protect against other types of security threats, such as social engineering attacks, where an attacker tricks someone into revealing sensitive information, or physical security breaches. It also does not inherently verify the authenticity or integrity of the data unless combined with other security measures like digital signatures or hash functions.

Lastly, encryption can be a double-edged sword. While it protects privacy and security, it can also be used for malicious purposes, such as in ransomware attacks where attackers encrypt victims' data and demand payment for the decryption key. Therefore, while encryption is a vital component of a comprehensive security strategy, it must be complemented with other security practices and measures.

Digital signatures in asymmetric cryptography are used to verify the authenticity and integrity of a message or document. They are akin to a digital equivalent of a handwritten signature or a stamped seal, but they offer far more inherent security. A digital signature is created using the private key of the signer and can be verified by anyone having the signer's public key, ensuring that the signature was created by the owner of the private key and that the message was not altered in transit.

The process involves creating a hash (a fixed-size string of bytes that uniquely represents the data) of the original message and then encrypting this hash with the signer's private key. This encrypted hash, along with the original message, forms the digital signature. When the recipient receives the message and its signature, they decrypt the hash using the signer's public key and generate a new hash from the received message. If both hashes match, it confirms that the message is authentic and hasn't been tampered with. Digital signatures are crucial in various online transactions and communications, providing a means of ensuring non-repudiation (the sender cannot deny sending the message) and data integrity.

Symmetric and asymmetric cryptography are used in various real-world applications, each suited to different scenarios based on their inherent properties.

Symmetric cryptography is typically used in scenarios where high-speed encryption and decryption of large volumes of data are required, and where secure key distribution can be managed. A common application is in securing data at rest, such as encrypting files on a hard drive or database entries. Symmetric encryption is also used in securing data in transit in many protocols, where a symmetric key can be securely exchanged using asymmetric cryptography and then used for the bulk encryption of data.

Asymmetric cryptography, with its capability for secure key distribution, is widely used in scenarios where secure communication needs to be established without prior sharing of keys. It's fundamental in digital certificates used in SSL/TLS for securing web communications, ensuring the authenticity of the communicating parties. Asymmetric cryptography is also used in digital signatures, providing authenticity and integrity to documents and software. Email encryption, such as PGP (Pretty Good Privacy), uses asymmetric cryptography to exchange the keys securely and then symmetric encryption for the actual message, combining the advantages of both methods.

Each type of cryptography has its specific use cases based on the trade-off between security needs, key management, and performance requirements. In many modern systems, symmetric and asymmetric cryptography are used together, leveraging the strengths of each to provide a robust security solution.

In cryptography, the algorithm and the key are two fundamental components, but they serve different purposes. The algorithm is a detailed step-by-step procedure or formula for encrypting and decrypting data. It's a public, well-known set of rules and processes that govern how the plain text is transformed into cipher text and vice versa. Algorithms like AES (Advanced Encryption Standard) for symmetric cryptography or RSA (Rivest-Shamir-Adleman) for asymmetric cryptography use mathematical operations to perform these transformations.

On the other hand, the key is a secret piece of information that the algorithm uses to alter its behaviour. Think of the algorithm as a lock, while the key is the actual key to that lock. The same algorithm can be used by many users, but each user will have a unique key. This separation between the algorithm and the key is fundamental in cryptography: the algorithm can be known to everyone, but the security of the encrypted data relies on the secrecy of the key. If the key is compromised, the security of the encrypted data is at risk, regardless of how robust the algorithm is. This is why the protection of cryptographic keys is of utmost importance in a security strategy.

Key length plays a crucial role in the security of a cryptographic system. The length of a key, measured in bits, determines the number of possible keys that can be generated, and consequently, the difficulty of a brute force attack, where an attacker tries every possible key. Longer keys provide a higher level of security. For instance, a 128-bit key offers significantly more possible combinations than a 64-bit key, making it exponentially more difficult for an attacker to crack the encryption. However, longer keys also require more processing power for encryption and decryption, which can impact performance. In symmetric cryptography, key lengths have increased over time to counteract advances in computing power and cryptanalysis techniques. For example, DES (Data Encryption Standard) with a 56-bit key was once considered secure but was later replaced by AES (Advanced Encryption Standard) which can use key lengths of 128, 192, or 256 bits. In asymmetric cryptography, key lengths are typically much longer due to the mathematical properties of the algorithms used, like RSA, which commonly uses keys of 1024 bits or longer. The choice of key length must balance security needs with performance requirements, and it's also influenced by the potential threat environment and the expected lifespan of the cryptographic system.