fix crypto formatting (#39)

Author: knightron0

problems/ecc-point-negation/problem.md

@@ -37,24 +37,23 @@ $$
 E: y^2 \equiv x^3 + 7 \pmod{p}, \quad p = 2^{61} - 1.
 $$
 
-For each input point \($x_i, y_i$\):
+For each input point $(x_i, y_i)$:
 
 $$
 (x_i, y_i) \mapsto (x_i,\; (p - y_i) \bmod p).
 $$
 
+
 ## Input
 
-- Arrays `xs[i]`, `ys[i]` of length \(N\), each element in \([0, p)\).
-- Prime modulus $p = 2^{61} - 1$.
-- Batch size \(N\).
+- Arrays `xs[i]`, `ys[i]` of length $N$, each element in $[0, p)$
+- Prime modulus $p = 2^{61} - 1$
+- Batch size $N$
+
+Your kernel must produce the exact negation for every point in the batch.
 
 ## Output
 
-- A single array `out_xy` of length \(2N\), storing the results as pairs:
+- A single array `out_xy` of length $2N$, storing the results as pairs:
   - `out_xy[2*i] = xs[i]`
   - `out_xy[2*i + 1] = (p - ys[i]) % p`
-
-## Correctness
-
-Your kernel must produce the exact negation for every point in the batch.

problems/poly-multiply-ff/problem.md

@@ -51,8 +51,6 @@ $$
 c_k = \sum_{i+j=k} a_i \, b_j \pmod{p}
 $$
 
----
-
 ## Input
 
 - Two arrays `d_input1`, `d_input2` of length $n$, with values in $[0, p)$.
@@ -62,9 +60,7 @@ $$
 
 - Array `d_output` of length $2n - 1$ with coefficients of $c(x)$ modulo $p$.
 
----
-
-## Example
+## Notes
 
 For small $n=3$:
 
@@ -81,14 +77,11 @@ $$
 
 So:
 
-a = [1, 2, 3]
-b = [4, 5, 6]
-→ c = [4, 13, 28, 27, 18]
-
----
-
-## Naive Baseline
+- $a = [1, 2, 3]$
+- $b = [4, 5, 6]$
+- $c = [4, 13, 28, 27, 18]$
 
+A naive implementation:
 ```cpp
 const uint32_t P = 2147483647u;
 
@@ -102,15 +95,9 @@ static __host__ __device__ inline uint32_t mul_mod(uint32_t a, uint32_t b) {
     return (uint32_t)(prod % P);
 }
 
-for (size_t i = 0; i < n; ++i)
-  for (size_t j = 0; j < n; ++j)
+for (size_t i = 0; i < n; ++i) {
+  for (size_t j = 0; j < n; ++j) {
     d_output[i + j] = add_mod(d_output[i + j], mul_mod(d_input1[i], d_input2[j]));
-```
-
-## Optimizations to Explore
-
-Shared memory tiling or register blocking for the naive $O(n^2)$ method.
-
-Two-phase accumulation (local tile sums, then global merge).
-
-(Advanced) NTT over moduli with large roots of unity, combined with CRT back to $p$.
+  }
+}
+```

problems/vector-multiply-ff/problem.md

@@ -38,51 +38,22 @@ $$
 p = 2^{31} - 1 = 2147483647
 $$
 
----
-
 ## Input
-
 - Vectors `a` and `b` of length $n$, with each element in $[0, p)$.
 
 ## Output
-
 - Vector `c` of length $n$ such that:
   $$
   c_i = a_i \cdot b_i \bmod p
   $$
-
----
-
-## Constraints
-
+  
+## Notes
 - $1 \le n \le 2^{30}$
 - Inputs and outputs are 32-bit unsigned integers.
 - Intermediate products must be reduced modulo $p$.
-
----
-
-## Baseline Implementation
-
-A simple (correct) implementation:
-
-```cpp
-const uint32_t P = 2147483647u;
-uint64_t prod = (uint64_t)a[i] * (uint64_t)b[i];
-c[i] = (uint32_t)(prod % P);
-
-
-```
-
-## Optimizations to explore
-
-Optimizations to Explore
-
-- Use Mersenne-friendly reduction for $p = 2^{31} - 1$:
-
-- exploit $2^{31} \equiv 1 \pmod p$ to fold high bits instead of %
-
-- Inline your helpers with **forceinline**
-
-- Fuse multiply-and-reduce to minimize temporaries
-
-- Tune block/thread sizing for occupancy
+- A simple (correct) implementation:
+  ```cpp
+  const uint32_t P = 2147483647u;
+  uint64_t prod = (uint64_t)a[i] * (uint64_t)b[i];
+  c[i] = (uint32_t)(prod % P);
+  ```