diff --git a/src/kzg_basic_prover.js b/src/kzg_basic_prover.js
index 88a01a1..cb6fd1e 100644
--- a/src/kzg_basic_prover.js
+++ b/src/kzg_basic_prover.js
@@ -7,10 +7,7 @@ const readPTauHeader = require("./ptau_utils");
 module.exports = async function kzg_basic_prover(evalsBufferArray, pTauFilename, options) {
     const logger = options.logger;
 
-    if (logger) {
-        logger.info("> KZG BASIC PROVER STARTED");
-        logger.info("");
-    }
+    if (logger) logger.info("> KZG BASIC PROVER STARTED");
 
     const { fd: fdPTau, sections: pTauSections } = await readBinFile(pTauFilename, "ptau", 1, 1 << 22, 1 << 24);
     const { curve, power: nBitsPTau } = await readPTauHeader(fdPTau, pTauSections);
@@ -32,7 +29,6 @@ module.exports = async function kzg_basic_prover(evalsBufferArray, pTauFilename,
         throw new Error("Polynomial length must be power of two.");
     }
 
-
     // Ensure the powers of Tau file is sufficiently large
     if (nBitsPTau < nBits) {
         throw new Error("Powers of Tau has not enough values for this polynomial");
@@ -54,8 +50,6 @@ module.exports = async function kzg_basic_prover(evalsBufferArray, pTauFilename,
     let proof = {};
     let challenges = {};
 
-    // STEP 0. Get the settings and prepare the setup    
-    // Ensure all polynomials have the same length
     const pols = [];
     for (let i = 0; i < evalsBufferArray.length; i++) {
         // Convert the evaluations to Montgomery form
@@ -65,43 +59,39 @@ module.exports = async function kzg_basic_prover(evalsBufferArray, pTauFilename,
         pols[i] = await Polynomial.fromEvaluations(evals, curve, logger);
     }
 
-    // STEP 1. Generate the polynomial commitments of all polynomials
+    // STEP 1. Generate the polynomial commitments for all polynomials
     logger.info("> STEP 1. Compute polynomial commitments");
     proof.commitments = [];
     for(let i=0; i<pols.length; i++) {
         pols[i].coef = await curve.Fr.batchToMontgomery(pols[i].coef.slice(0, pols[i].coef.byteLength));
         proof.commitments[i] = await pols[i].multiExponentiation(PTau, `pol${i}`);
-        logger.info(`··· [p${i}(X)]_1 = `, curve.G1.toString(proof.commitments[i]));
+        logger.info(`··· [p${i}(X)]_1 =`, curve.G1.toString(proof.commitments[i]));
     }
 
-    // STEP 2. Get challenge xi from transcript
-    logger.info("> STEP 2. Get challenge xi");
+    // STEP 2. Compute opening evaluations
+    logger.info("> STEP 2. Compute opening evaluations");
+    // STEP 2.1 Compute challenge xi
     const transcript = new Keccak256Transcript(curve);
-    for(let i=0; i<pols.length; i++) {
-        transcript.addPolCommitment(proof.commitments[i]);
-    }
+    for(commitment of proof.commitments) transcript.addPolCommitment(commitment);
     challenges.xi = transcript.getChallenge();
-    logger.info("··· xi = ", curve.Fr.toString(challenges.xi));
+    logger.info("··· xi =", curve.Fr.toString(challenges.xi));
 
-    // STEP 3. Calculate the evaluations p(xi) = y for all polynomials
-    logger.info("> STEP 3. Calculate the opening p(xi) = y");
+    // STEP 2.2 Compute evaluations
     proof.evaluations = [];
     for(let i=0; i<pols.length; i++) {
         proof.evaluations[i] = pols[i].evaluate(challenges.xi);
-        logger.info(`··· y${i} = `, curve.Fr.toString(proof.evaluations[i]));
+        logger.info(`··· y${i} =`, curve.Fr.toString(proof.evaluations[i]));
     }
 
-    // STEP 4. Get challenge alpha from transcript
-    logger.info("> STEP 4. Get challenge alpha");
+    // STEP 3. Calculate the polynomial q(X)
+    logger.info("> STEP 3. Calculate the polynomial q(X)");
+    // STEP 3.1 Compute challenge alpha
     transcript.reset();
-    for(let i=0; i<pols.length; i++) {
-        transcript.addEvaluation(proof.evaluations[i]);
-    }
+    for(evaluation of proof.evaluations) transcript.addEvaluation(evaluation);
     challenges.alpha = transcript.getChallenge();
-    logger.info("··· alpha = ", curve.Fr.toString(challenges.alpha));
+    logger.info("··· alpha =", curve.Fr.toString(challenges.alpha));
 
-    // STEP 5. Calculate the polynomial q(X)
-    logger.info("> STEP 5. Calculate the polynomial q(X)");
+    // STEP 3.1 Calculate the polynomial q(X)
     let polQ = new Polynomial(new Uint8Array(curve.Fr.n8 * polLen), curve, logger);
 
     let currentAlpha = curve.Fr.one;
@@ -115,12 +105,9 @@ module.exports = async function kzg_basic_prover(evalsBufferArray, pTauFilename,
     }
 
     proof.commitQ = await polQ.multiExponentiation(PTau, "Q");
-    logger.info("··· [q(X)]_1 = ", curve.G1.toString(proof.commitQ));
+    logger.info("··· [q(X)]_1 =", curve.G1.toString(proof.commitQ));
 
-    if (logger) {
-        logger.info("");
-        logger.info("> KZG BASIC PROVER FINISHED");
-    }
+    if (logger) logger.info("> KZG BASIC PROVER FINISHED");
 
     await fdPTau.close();
 
diff --git a/src/kzg_basic_verifier.js b/src/kzg_basic_verifier.js
index 30539b3..ca953af 100644
--- a/src/kzg_basic_verifier.js
+++ b/src/kzg_basic_verifier.js
@@ -5,10 +5,7 @@ const readPTauHeader = require("./ptau_utils");
 module.exports = async function kzg_basic_verifier(proof, pTauFilename, options) {
     const logger = options.logger;
 
-    if (logger) {
-        logger.info("> KZG BASIC VERIFIER STARTED");
-        logger.info("");
-    }
+    if (logger) logger.info("> KZG BASIC VERIFIER STARTED");
 
     const { fd: fdPTau, sections: pTauSections } = await readBinFile(pTauFilename, "ptau", 1, 1 << 22, 1 << 24);
     const { curve } = await readPTauHeader(fdPTau, pTauSections);
@@ -31,7 +28,7 @@ module.exports = async function kzg_basic_verifier(proof, pTauFilename, options)
         transcript.addPolCommitment(proof.commitments[i]);
     }
     challenges.xi = transcript.getChallenge();
-    logger.info("··· xi = ", curve.Fr.toString(challenges.xi));
+    logger.info("··· xi =", curve.Fr.toString(challenges.xi));
 
     // STEP 2. Calculate challenge alpha from transcript
     logger.info("> STEP 2. Compute challenge alpha");
@@ -40,7 +37,7 @@ module.exports = async function kzg_basic_verifier(proof, pTauFilename, options)
         transcript.addEvaluation(proof.evaluations[i]);
     }
     challenges.alpha = transcript.getChallenge();
-    logger.info("··· alpha = ", curve.Fr.toString(challenges.alpha));
+    logger.info("··· alpha =", curve.Fr.toString(challenges.alpha));
     
     // STEP 3. Compute [F]_1
     let currentAlpha = curve.Fr.one;
@@ -82,10 +79,7 @@ module.exports = async function kzg_basic_verifier(proof, pTauFilename, options)
         }
     }
 
-    if (logger) {
-        logger.info("");
-        logger.info("> KZG BASIC VERIFIER FINISHED");
-    }
+    if (logger) logger.info("");
 
     await fdPTau.close();