How Can We Efficiently Generate All Possible Passwords of a Given Length?

Efficiently Generating All Possible Passwords of a Given Length

When attempting to brute-force crack passwords, it's essential to generate all possible combinations efficiently. To achieve this, we'll explore an approach that avoids storing all passwords in memory simultaneously and allows for variable password lengths.

N-ary Cartesian Product

The task at hand involves generating the n-ary Cartesian product of a set with itself. Consider the problem of generating all 3-character passwords using characters 'a' and 'b' with n = 3.

Iterative Construction

We can iteratively construct the desired product by first obtaining the n-1 product, then adding each element of the initial set to each product.

Example with Two Characters

To illustrate this concept, let's consider the process of generating all 3-character passwords from the set {a, b}:

• 2-character product: {ab}
• 3-character product: {(a,a,a),(a,a,b),(a,b,a),(a,b,b),(b,a,a),(b,a,b),(b,b,a),(b,b,b)}

Implementation in Go

The following Go function implements the iterative construction technique:

func NAryProduct(input string, n int) []string {
    if n <= 0 {
        return nil
    }

    prod := make([]string, len(input))
    for i, char := range input {
        prod[i] = string(char)
    }

    for i := 1; i < n; i++ {
        next := make([]string, 0, len(input)*len(prod))
        for _, word := range prod {
            for _, char := range input {
                next = append(next, word + string(char))
            }
        }
        prod = next
    }

    return prod
}

Performance Optimization

The presented solution has room for improvement if generating passwords of various lengths is required. To avoid recalculation, you could modify the code to take an arbitrary (n-m)ary product and derive the n-ary product recursively.

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