match benchmarks with table

README.md

@@ -4,29 +4,41 @@ This library implements all necessary arguments of cryptobazaar: auctioneer, bid
 
 ## Benchmarks
 
-We have defined six benchmarks to evaluate key areas of the library:
+We have defined six benchmarks to evaluate key areas of the library that should match numbers displayed in `Table 1` of the paper:
 
-1. **Benchmark 1: `auctioneer`**
-    - Measures the performance of the auctioneer given number of bidders and price range
-    - Run with ``cargo bench --bench auctioneer``
-
-2. **Benchmark 2: `encode`**
-    - Measures the speed of bid encoding
-    - Run with ``cargo bench --bench encode``
-
-3. **Benchmark 3: `ipa`**
-    - Measures the performance of inner product argument that is used in the second round of the protocol
-    - Run with ``cargo bench --bench ipa``
+1. **Benchmark 1: `veceq`**
+    - Measures the speed of proving that KZG committed vector is equal to vector committed behind array of elliptic curve points 
+    - Matches $\pi_{x_i}$ of the `Table 1` part `(a)`
+    - Run with ``cargo bench --bench veceq``
 
-4. **Benchmark 4: `lderivative`**
+2. **Benchmark 2: `nonzero`**
+    - Measures the speed of proving that committed vector has non zero entires
+    - Matches $\pi_{r_i}$ of the `Table 1` part `(a)`
+    - Run with ``cargo bench --bench nonzero``
+
+3. **Benchmark 3: `lderivative`**
     - Measures the speed of log derivative argument for proving that bid is a valid unary encoded vector
+    - Matches $\pi_{b_i}$ of the `Table 1` part `(a)`
     - Run with ``cargo bench --bench lderivative``
 
-5. **Benchmark 5: `nonzero`**
-    - Measures the speed of proving that committed vector has non zero entires
-    - Run with ``cargo bench --bench nonzero``
-◊
-6. **Benchmark 6: `veceq`**
-    - Measures the speed of proving that KZG committed vector is equal to vector committed behind array of elliptic curve points 
-    - Run with ``cargo bench --bench veceq``
+4. **Benchmark 4: `ipa`**
+    - Measures the performance of computing the bidder's second round output 
+    - Matches $\pi_{Z_i}$ of the `Table 1` part `(a)`
+    - Run with ``cargo bench --bench ipa``
+
+5. **Benchmark 5: `auctioneer_r1`**
+    - Measures the performance of the auctioneer to compute AV matrix Y given number of bidders and price range
+    - Matches `Table 1` part `(b)` 
+    - Run with ``cargo bench --bench auctioneer``
+
+6. **Benchmark 6: `auctioneer_r2`**
+    - Measures the performance of the auctioneer to compute results vector R
+    - Matches `Table 1` part `(c)` 
+    - Run with ``cargo bench --bench auctioneer``
+
+
+
+
+
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