Does concept "Collision Resistance" and "Binding Commitment" in cryptography similar?

Question

I found there are two perplexing and related concept "Collision Resistance" and "Computation Binding in Commitment" in cryptography. I found the wikipedia's explanation is confusing. And no resources clarify their difference

Especially, I found I can't differentiate the two concepts' common ideas which is given certain inputs, there is no more than one output for a particular Hash function.

Answer 1

They are related but according to the adversary and the scheme;

Hash commits

• If you are malicious and make a hash commitment. then $commit = H(c)$ then you may seek a collision of two commits $c_1$ and $c_2$ such that $commit = H(c_1) = H(c_2)$. This can be easy with MD5 and SHA-1 but hard with SHA-2, SHA-3, BLAKE2, etc.

  You may be a secretary and give $c_1$ to your boss to commit and later claim that the commit $c_2$ where your advantage on $c_2$ is higher than $c_1$.

• If you are malicious and someone gave you a hash commitment. $commit = H(c)$ and you want to have an advantage, then you have to see another $c'$ such that $commit = H(c) = H(c')$. This is the second pre-image attack on the hash functions.

Keyed Hash Commits

If one uses a key $k$ to commit like $commit = HMAC(k,c)$ then the collision resistance of the hash function is no more problem since HMAC doesn't rely on the collision resistance of the underlying hash function, only PRF is enough.

• If you are malicious and make a keyed hash commitment. Then again collision; you need to find two messages that have the same HMAC value under the same key.

• If you are malicious and someone gave you a hash commitment. This time your attack is brute-forcing the key then finding the second-pre-image under the same key.

Answer 2

According to Wikipedia:

Collision Resistance:

a property of cryptographic hash functions: a hash function H is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs a and b where a≠b but H(a) =H(b).

Commitment Binding
Let open be chosen from a set of size $2^k$ i.e., it can be represented as a k bit string, and let $\text { Commit }_{k}$ be the corresponding commitment scheme. As the size of k determines the security of the commitment scheme it is called the security parameter.
Then for all non-uniform probabilistic polynomial time algorithms that output and of increasing length k, the probability that and $x \neq x^{\prime}$ and $\operatorname{Commit}_{k}(x$, open $)=\operatorname{Commit}_{k}\left(x^{\prime}\right.$, open $\left.^{\prime}\right)$ is a negligible function in k.