diff --git a/README.md b/README.md
index fac5167..9bdadcf 100644
--- a/README.md
+++ b/README.md
@@ -13,9 +13,6 @@ Audited & minimal JS implementation of elliptic curve cryptography.
   for encoding or hashing an arbitrary string to an elliptic curve point
 - 🧜‍♂️ Poseidon ZK-friendly hash
 
-Check out [Upgrading](#upgrading) if you've previously used single-feature noble
-packages. See [Resources](#resources) for articles and real-world software that uses curves.
-
 ### This library belongs to _noble_ crypto
 
 > **noble-crypto** — high-security, easily auditable set of contained cryptographic libraries and tools.
@@ -40,7 +37,6 @@ For [Deno](https://deno.land), ensure to use [npm specifier](https://deno.land/m
 For React Native, you may need a [polyfill for crypto.getRandomValues](https://github.com/LinusU/react-native-get-random-values).
 If you don't like NPM, a standalone [noble-curves.js](https://github.com/paulmillr/noble-curves/releases) is also available.
 
-- [Usage](#usage)
 - [Implementations](#implementations)
   - [ECDSA signature scheme](#ecdsa-signature-scheme)
   - [ECDSA public key recovery & extra entropy](#ecdsa-public-key-recovery--extra-entropy)
diff --git a/src/abstract/bls.ts b/src/abstract/bls.ts
index 282cbe7..fd56d6e 100644
--- a/src/abstract/bls.ts
+++ b/src/abstract/bls.ts
@@ -12,7 +12,7 @@
  * Some projects may prefer to swap this relation, it is not supported for now.
  */
 import { AffinePoint } from './curve.js';
-import { IField, hashToPrivateScalar } from './modular.js';
+import { IField, getMinHashLength, mapHashToField } from './modular.js';
 import { Hex, PrivKey, CHash, bitLen, bitGet, ensureBytes } from './utils.js';
 import * as htf from './hash-to-curve.js';
 import {
@@ -189,10 +189,8 @@ export function bls<Fp2, Fp6, Fp12>(
 
   const utils = {
     randomPrivateKey: (): Uint8Array => {
-      const bytesTaken = groupLen + Math.ceil(groupLen / 2); // e.g. 48b for 32b field
-      const rand = CURVE.randomBytes(bytesTaken);
-      const num = hashToPrivateScalar(rand, Fr.ORDER);
-      return Fr.toBytes(num);
+      const length = getMinHashLength(Fr.ORDER);
+      return mapHashToField(CURVE.randomBytes(length), Fr.ORDER);
     },
     calcPairingPrecomputes,
   };
diff --git a/src/abstract/modular.ts b/src/abstract/modular.ts
index b8cdbc7..285a6b3 100644
--- a/src/abstract/modular.ts
+++ b/src/abstract/modular.ts
@@ -409,16 +409,9 @@ export function FpSqrtEven<T>(Fp: IField<T>, elm: T) {
 
 /**
  * "Constant-time" private key generation utility.
- * Can take (n + 8) or more bytes of uniform input e.g. from CSPRNG or KDF
- * and convert them into private scalar, with the modulo bias being negligible.
- * Needs at least 40 bytes of input for 32-byte private key.
- * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
- * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final
- * hash-to-curve, https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-hashing-to-a-finite-field
- * @param hash hash output from SHA3 or a similar function
- * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)
- * @param isLE interpret hash bytes as LE num
- * @returns valid private scalar
+ * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).
+ * Which makes it slightly more biased, less secure.
+ * @deprecated use mapKeyToField instead
  */
 export function hashToPrivateScalar(
   hash: string | Uint8Array,
@@ -428,11 +421,43 @@ export function hashToPrivateScalar(
   hash = ensureBytes('privateHash', hash);
   const hashLen = hash.length;
   const minLen = nLength(groupOrder).nByteLength + 8; // 8b (64 bits) gives 2^-64 bias
-  // Small numbers aren't supported: need to understand their security / bias story first.
-  // Huge numbers aren't supported for security: it's easier to detect timings of their ops in JS.
   if (minLen < 24 || hashLen < minLen || hashLen > 1024)
     throw new Error(`expected ${minLen}-1024 bytes of input, got ${hashLen}`);
   const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
-  // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
   return mod(num, groupOrder - _1n) + _1n;
 }
+
+export function getFieldBytesLength(fieldOrder: bigint): number {
+  return nLength(fieldOrder).nByteLength;
+}
+
+export function getMinHashLength(fieldOrder: bigint): number {
+  const length = getFieldBytesLength(fieldOrder);
+  return length + Math.ceil(length / 2);
+}
+
+/**
+ * "Constant-time" private key generation utility.
+ * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF
+ * and convert them into private scalar, with the modulo bias being negligible.
+ * Needs at least 48 bytes of input for 32-byte private key.
+ * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
+ * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final
+ * hash-to-curve, https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-hashing-to-a-finite-field
+ * @param hash hash output from SHA3 or a similar function
+ * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)
+ * @param isLE interpret hash bytes as LE num
+ * @returns valid private scalar
+ */
+export function mapHashToField(key: Uint8Array, fieldOrder: bigint, isLE = false): Uint8Array {
+  const len = key.length;
+  const fieldLen = getFieldBytesLength(fieldOrder);
+  const minLen = getMinHashLength(fieldOrder);
+  // No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.
+  if (len < 16 || len < minLen || len > 1024)
+    throw new Error(`expected ${minLen}-1024 bytes of input, got ${len}`);
+  const num = isLE ? bytesToNumberBE(key) : bytesToNumberLE(key);
+  // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
+  const reduced = mod(num, fieldOrder - _1n) + _1n;
+  return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen)
+}
diff --git a/src/abstract/weierstrass.ts b/src/abstract/weierstrass.ts
index efa2fd0..492e35e 100644
--- a/src/abstract/weierstrass.ts
+++ b/src/abstract/weierstrass.ts
@@ -849,11 +849,8 @@ export function weierstrass(curveDef: CurveType): CurveFn {
      * (groupLen + ceil(groupLen / 2)) with modulo bias being negligible.
      */
     randomPrivateKey: (): Uint8Array => {
-      const groupLen = CURVE.nByteLength;
-      const bytesTaken = groupLen + Math.ceil(groupLen / 2); // e.g. 48b for 32b field
-      const rand = CURVE.randomBytes(bytesTaken);
-      const num = mod.hashToPrivateScalar(rand, CURVE_ORDER);
-      return ut.numberToBytesBE(num, groupLen);
+      const length = mod.getMinHashLength(CURVE.n);
+      return mod.mapHashToField(CURVE.randomBytes(length), CURVE.n);
     },
 
     /**