Commitments

When we think about commitments, we think about couples making commitment to their relationship, group of talented and enthusiastic people committed to bringing power to the morden consumers, or a country pledged to land a man to the moon and return him safely on earth. It is an obligation of being dedicated to a cause, activity or entity; a process of focusing on something with neccessary resources at the expense of oppurtunity cost. It is what transforms a promise into reality.

I always have this mental image when I think about commitment: a bigger, fluffier and unstructured space being mapped to a smaller, clearer and structured space. It is about less, not more. It is about making specific, irrevocable choices instead of leaving the options open. Even though commitment takes hard work and perseverance, many studies seem to suggest that it is a major factor for happiness. Actually, being happy itself is something that we can commit to as well.

As programmers, we must be the subset of human beings that has the most intimacy towards the concept of commitments since we do git commit basically everyday. When we commit code, knowledge from a much larger and fluid space are transformed to a specific format stored on disk. We even get an id for this, called a commit id. The commit id is an SHA-1 hash, which is in fact a crypographic commitment to a bunch of things, such as the content of the file, commit date, commit message, id of the previous commit, etc. When the hash is being created, information from a much larger space is mapped to a space with only 160 bits, which is still really, really huge, but theoretically speaking there exists infinite number of preimages for any hash values.

The trick of a “good” hash function is to make sure that the likelihood of finding another preimage that can be hashed to the same value is astronomically low, otherwise the cryptographic commitment is broken. This property is called collision resistence. If we are being objective, isn’t that the case for all types of commitments? Last time I checked, 50% of the marriages in the United States will end in divorce. As much as we want to romanticize it, it doesn’t change the fact that commitment is a game of probabilities.

In cryptography, hash function can be thought of as a member in a bigger family called commitment scheme, which “allows one to commit to a chosen value (or chosen statement) while keeping it hidden to others, with the ability to reveal the committed value later.” Hash can be thought of as one way to commit to static information. As it turns out, we can create commitment to dynamic program as well, for example, using polynomial commitment. This allows verifier who has this commitment to check if a claimed evaluation of original program is valid. Under the hood, it is the same probabilities game. Even though theoretically there might be infinite number of programs that could produce the same commitment, the likelihood of you happen to convince the verifier with another program is astronomically small. Polynomial commitment at the core of many Zero knowledge proofs (ZKP) systems, which has the potential to really help us improve our current privacy situation.

Hash is my favourite cryptographic primitives. From user’s perspective, it is simple, it is post quantum resistant, it is easy to use. To the extent where people just take it for granted. I have a strong believe that ZKP will make a great impact in the years to come. It is fair to say that crypographic commitment makes the world a better place and improve the collective happiness of human beings, just like any other commitment we made in our lives.

Written on September 1, 2020