Hashing can be used for secure data storage, but with certain considerations. In the context of security, hashing serves two main purposes:

• Data Integrity: Hash functions can verify the integrity of data. By storing the hash of data alongside the data itself, one can later re-hash the data and compare it to the stored hash to ensure it hasn't been altered.
• Secure Password Storage: Instead of storing passwords in plaintext, systems store the hash of a password. When a user logs in, the system hashes the entered password and compares it to the stored hash. This way, even if the data storage is compromised, the actual passwords remain secure.

However, for these purposes, cryptographic hash functions are used. These are designed to be secure against attacks such as finding two different inputs that produce the same hash (collision resistance) and determining the original input from a hash value (pre-image resistance). Additionally, techniques like salting (adding random data to each password before hashing) are used to enhance security.

In summary, while hashing is a fundamental tool in secure data storage, it requires the use of specialised cryptographic hash functions and additional strategies like salting to ensure robust security.

Double hashing is a technique used in open addressing to resolve collisions in a hash table. It uses two distinct hash functions: the first to determine the initial position and the second to calculate the interval of probing in case of collisions. The key steps in double hashing are:

• Initial Position: Determine the initial position using the first hash function.
• Collision Resolution: If a collision occurs, use the second hash function to calculate the probe interval.
• Probe Sequence: Continue probing at intervals determined by the second hash function until an empty slot is found.

This method improves upon other techniques like linear or quadratic probing in several ways:

• Reduced Clustering: Double hashing greatly reduces the issue of clustering (both primary and secondary) common in linear and quadratic probing.
• Better Distribution: It provides a better distribution of keys, as the interval between probes is not constant but determined by another hash function.
• Customisable: By choosing appropriate hash functions, double hashing can be adapted to suit specific needs and data distributions.

Despite these advantages, double hashing can be more complex to implement and requires careful selection of both hash functions to ensure effectiveness.

The choice of a hash function significantly impacts the performance of a hash table. An ideal hash function should:

• Uniformly Distribute Keys: It should distribute keys evenly across the hash table. This reduces collisions and ensures that the table is utilised efficiently.
• Minimise Collision Probability: While collisions are inevitable, a good hash function minimises their occurrence. This reduces the need for complex collision resolution techniques, thereby speeding up data access times.
• Be Fast to Compute: The hash function should be quick to execute, as it is computed every time a data lookup or insertion is performed.
• Avoid Patterns: It should not produce predictable patterns that might align with patterns in the key set, as this can lead to clustering.
• Fit the Data Set and Usage Pattern: Different types of data may require different hash functions. For example, a function well-suited for string data might not be efficient for numerical data.

Poorly chosen hash functions can lead to high collision rates, causing performance degradation as more time is spent in collision resolution. This is particularly problematic in applications requiring rapid data retrieval and updates.

Hashing facilitates faster search operations compared to traditional search methods like linear or binary search through its ability to compute the position of a data item rather than having to search for it.

• Direct Access: Hashing transforms the search problem into a computation problem. By using a hash function to compute the index where a data item is stored, it provides direct access to the data, bypassing the need for a sequential or binary search.
• Constant Time Complexity: Ideally, hashing achieves a time complexity of O(1) for search operations. This means that the time taken to find a data item is constant, regardless of the size of the data set.
• Efficiency in Large Datasets: While traditional search methods become slower as the dataset grows (linear search has a time complexity of O(n) and binary search has O(log n)), the performance of hashing remains relatively unaffected by the size of the data set.
• Minimised Comparisons: Hashing minimises the number of comparisons needed to find a data item. Instead of comparing the search key with elements of the dataset, it directly computes the position.

However, this efficiency relies heavily on a good hash function and effective collision resolution techniques. In cases of high collision rates, the efficiency can degrade, approaching that of linear search methods.

Linear probing and quadratic probing are both methods used in open addressing for collision resolution in hash tables.

• Linear Probing: In linear probing, when a collision occurs, the hash table checks the next slot sequentially until it finds an empty slot. While simple to implement, it can lead to a problem known as clustering, where a group of consecutive slots gets filled, leading to longer search times.
• Quadratic Probing: Quadratic probing, on the other hand, addresses this issue of clustering. Instead of searching sequentially, it jumps to the square of the distance from the original position (1st, 4th, 9th position, and so on). This method spreads out the keys more uniformly, reducing the clustering effect. However, it can be more complex to implement and requires careful consideration to ensure that all slots can be probed and that the probe sequence covers the entire table.

Both methods aim to optimise the efficiency of the hash table, but the choice between them depends on the specific requirements and constraints of the application, such as the expected load factor, the distribution of key values, and the complexity the system can handle.