feat(entropy): add protocol explanation for callbacks + latex formulas

next.config.js

@@ -19,6 +19,7 @@ const withNextra = require("nextra")({
         }),
     },
   },
+  latex: true,
 });
 
 // Use this array as a shorter way to specify redirect URLs so we can write down a lot of them.

pages/entropy/protocol-design.mdx

@@ -3,47 +3,61 @@
 The Entropy protocol is an extension of a classical commit/reveal protocol.
 The original version has the following steps:
 
-1. Two parties A and B each draw secret random numbers, `x_A` and `x_B`.
-2. A and B hash their random numbers and share the hashes, `h_A = hash(x_A)` and `h_B = hash(x_B)`
-3. A and B reveal `x_A` and `x_B`
-4. Both parties verify that `hash(x_A) == h_A` and `hash(x_B) == h_B`
-5. The random number `r = hash(x_A, x_B)`
+1. Two parties A and B each draw secret random numbers, $x_A$ and $x_B$.
+2. A and B hash their random numbers and share the hashes, $h_A = \mathrm{hash}(x_A)$ and $h_B = \mathrm{hash}(x_B)$
+3. A and B reveal $x_A$ and $x_B$
+4. Both parties verify that $\mathrm{hash}(x_A) = h_A$ and $\mathrm{hash}(x_B) = h_B$
+5. The random number $r = \mathrm{hash}(x_A, x_B)$
 
 This protocol has the property that the result is random as long as either A or B are honest.
 Thus, neither party needs to trust the other -- as long as they are themselves honest, they can
-ensure that the result `r` is random.
+ensure that the result $r$ is random.
 
 Entropy implements a version of this protocol that is optimized for on-chain usage. The
 key difference is that one of the participants (the provider) commits to a sequence of random numbers
 up-front using a hash chain. Users of the protocol then simply grab the next random number in the sequence.
 
-**Setup**: The provider P computes a sequence of `N` random numbers, `x_i` for `(i = 0...N-1)`:
+**Setup**: The provider P computes a sequence of $N$ random numbers, $x_i$ for $0 \leq i \leq N-1$:
 
-- `x_{N-1} = random()`
-- `x_i = hash(x_{i + 1})`
+- $x_{N-1} = \mathrm{random}()$
+- $x_i = \mathrm{hash}(x_{i + 1})$
 
-The provider commits to `x_0` by posting it to the Entropy contract.
-Each random number in the sequence can then be verified against the previous one in the sequence by hashing it, i.e., `hash(x_i) == x_{i - 1}`
+The provider commits to $x_0$ by posting it to the Entropy contract.
+Each random number in the sequence can then be verified against the previous one in the sequence by hashing it, i.e., $\mathrm{hash}(x_i) = x_{i - 1}$
 
 **Request**: To produce a random number, the following steps occur.
 
-1. The user U draws a random number `x_U`, and submits `h_U = hash(x_U)` to the contract
-2. The contract remembers `h_U` and assigns it an incrementing sequence number `i`, representing which
+1. The user U draws a random number $x_U$, and submits $h_U = \mathrm{hash}(x_U)$ to the contract
+2. The contract remembers $h_U$ and assigns it an incrementing sequence number $i$, representing which
    of the provider's random numbers the user will receive.
-3. The user submits an off-chain request (e.g. via HTTP) to the provider to reveal the `i`'th random number.
-4. The provider checks the on-chain sequence number and ensures it is > `i`. If it is not, the provider
+3. The user submits an off-chain request (e.g. via HTTP) to the provider to reveal the $i$'th random number.
+4. The provider checks the on-chain sequence number and ensures it is > $i$. If it is not, the provider
    refuses to reveal the ith random number. The provider should wait for a sufficient number of block confirmations
    to ensure that the request does not get re-orged out of the blockchain.
-5. The provider reveals `x_i` to the user.
-6. The user submits both the provider's revealed number `x_i` and their own `x_U` to the contract.
-7. The contract verifies `hash(x_i) == x_{i-1}` to prove that `x_i` is the `i`'th random number. The contract also checks that `hash(x_U) == h_U`.
-   The contract stores `x_i` as the `i`'th random number to reuse for future verifications.
-8. If both of the above conditions are satisfied, the random number `r = hash(x_i, x_U)`.
+5. The provider reveals $x_i$ to the user.
+6. The user submits both the provider's revealed number $x_i$ and their own $x_U$ to the contract.
+7. The contract verifies $\mathrm{hash}(x_i) = x_{i-1}$ to prove that $x_i$ is the $i$'th random number. The contract also checks that $\mathrm{hash}(x_U) = h_U$.
+   The contract stores $x_i$ as the $i$'th random number to reuse for future verifications.
+8. If both of the above conditions are satisfied, the random number $r = \mathrm{hash}(x_i, x_U)$.
    As an added security mechanism, this step can incorporate the blockhash of the block that the
-   request transaction landed in: `r = hash(x_i, x_U, blockhash)`.
+   request transaction landed in: $r = \mathrm{hash}(x_i, x_U, \mathrm{blockhash})$.
 
 This protocol has the same security properties as the 2-party randomness protocol above: as long as either
-the provider or user is honest, the number `r` is random. Honesty here means that the participant keeps their
-random number `x` a secret until the revelation phase (step 5) of the protocol. Note that providers need to
+the provider or user is honest, the number $r$ is random. Honesty here means that the participant keeps their
+random number $x$ a secret until the revelation phase (step 5) of the protocol. Note that providers need to
 be careful to ensure their off-chain service isn't compromised to reveal the random numbers -- if this occurs,
-then users will be able to influence the random number `r`.
+then users will be able to influence the random number $r$.
+
+With automatic callbacks the flow is simplified:
+
+1. The user U draws a random number $x_U$, and submits **both** $x_U$ and $h_U = \mathrm{hash}(x_U)$ to the contract
+2. The contract remembers $h_U$ and assigns it an incrementing sequence number $i$, representing which
+   of the provider's random numbers the user will receive. $x_U$ is recorded in the event logs.
+3. After sufficient block confirmations, the provider submits a reveal transaction with $x_i$ and $x_U$ to the contract.
+4. The contract verifies $\mathrm{hash}(x_U) = h_U$ and $\mathrm{hash}(x_i) = x_{i-1}$ to prove that $x_i$ is the $i$'th random number.
+5. If both of the above conditions are satisfied,
+   the random number $r = \mathrm{hash}(x_i, x_U)$ is generated and a callback is made to the requesting contract.
+
+In this flow, providers can refuse revealing $x_i$ if the final random number $r$ is not in their favor, or
+they may be able to access $x_U$ before on-chain submission (e.g. via mempool) and rotate their commitments to influence the random number $r$.
+Of course, both of these behaviors are detectable and protocols can blacklist providers that exhibit them.