The Gronsfeld cipher, also known as the Bronckhorst cipher, was created by José de Bronckhorst (Count of Gronsfeld, hence the two names) around 1744. As a Belgian diplomat, it was important for him to ensure good confidentiality during exchanges.
The encryption itself is essentially a Caesar shift in which the shift distance is defined by a numerical key. One could say that this encryption is a variation of the Vigenere cipher in which the key is a series of numbers.
To encrypt using the Gronsfeld cipher, one takes each letter of the plaintext, and shifts it according to the key. For example, if the text to encrypt is "gronsfeld" and the key is 1234, the G is shifted by 1 position in the alphabet, becoming H, then the R is shifted by 2 positions, becoming T, and so on. For example:
Plain Text: gronsfeld
Encrypted Text: htrrthhpe
The key is repeated here to match the length of the text to be encrypted. It is evident that this encryption no longer offers any protection. However, it is more robust than the Caesar shift since it allows the use of a key, which, if long enough, will make brute-forcing difficult. The key should be sufficiently long; a simple 4-digit key offers only 9999 possibilities, which, coupled with a dictionary, is very easy to crack.
Frequency analysis, just like with the Vigenere cipher, can be used to break the Gronsfeld cipher. To do this, if you have a long enough text, you can identify repetitions in the text. These repetitions may result from encrypting the same letters of the text with the key. For example, the word "why" encrypted by the key "123". This analysis also allows guessing the length of the key. Then, compile all these sequences of identical letters and perform a frequency analysis to guess their components. Obviously, this assumes having a ciphertext of sufficient length.