weierstrass, edwards: get rid of bigint literals. Closes gh-22

src/abstract/edwards.ts

@@ -5,11 +5,9 @@ import * as ut from './utils.js';
 import { ensureBytes, FHash, Hex } from './utils.js';
 import { Group, GroupConstructor, wNAF, BasicCurve, validateBasic, AffinePoint } from './curve.js';
 
-// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
+// Be friendly to bad ECMAScript parsers by not using bigint literals
-const _0n = BigInt(0);
+// prettier-ignore
-const _1n = BigInt(1);
+const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _8n = BigInt(8);
-const _2n = BigInt(2);
-const _8n = BigInt(8);
 
 // Edwards curves must declare params a & d.
 export type CurveType = BasicCurve<bigint> & {
@@ -111,7 +109,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       if (ctx.length || phflag) throw new Error('Contexts/pre-hash are not supported');
       return data;
     }); // NOOP
-  const inBig = (n: bigint) => typeof n === 'bigint' && 0n < n; // n in [1..]
+  const inBig = (n: bigint) => typeof n === 'bigint' && _0n < n; // n in [1..]
   const inRange = (n: bigint, max: bigint) => inBig(n) && inBig(max) && n < max; // n in [1..max-1]
   const in0MaskRange = (n: bigint) => n === _0n || inRange(n, MASK); // n in [0..MASK-1]
   function assertInRange(n: bigint, max: bigint) {

src/abstract/modular.ts

@@ -275,7 +275,7 @@ export function FpPow<T>(f: IField<T>, num: T, power: bigint): T {
   while (power > _0n) {
     if (power & _1n) p = f.mul(p, d);
     d = f.sqr(d);
-    power >>= 1n;
+    power >>= _1n;
   }
   return p;
 }

src/abstract/weierstrass.ts

@@ -176,9 +176,9 @@ const DER = {
   },
 };
 
-// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
+// Be friendly to bad ECMAScript parsers by not using bigint literals
-const _0n = BigInt(0);
+// prettier-ignore
-const _1n = BigInt(1);
+const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3), _4n = BigInt(4);
 
 export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
   const CURVE = validatePointOpts(opts);
@@ -365,7 +365,7 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
     // Cost: 8M + 3S + 3*a + 2*b3 + 15add.
     double() {
       const { a, b } = CURVE;
-      const b3 = Fp.mul(b, 3n);
+      const b3 = Fp.mul(b, _3n);
       const { px: X1, py: Y1, pz: Z1 } = this;
       let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore
       let t0 = Fp.mul(X1, X1); // step 1
@@ -412,7 +412,7 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
       const { px: X2, py: Y2, pz: Z2 } = other;
       let X3 = Fp.ZERO, Y3 = Fp.ZERO, Z3 = Fp.ZERO; // prettier-ignore
       const a = CURVE.a;
-      const b3 = Fp.mul(CURVE.b, 3n);
+      const b3 = Fp.mul(CURVE.b, _3n);
       let t0 = Fp.mul(X1, X2); // step 1
       let t1 = Fp.mul(Y1, Y2);
       let t2 = Fp.mul(Z1, Z2);
@@ -1078,15 +1078,15 @@ export function weierstrass(curveDef: CurveType): CurveFn {
 export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
   // Generic implementation
   const q = Fp.ORDER;
-  let l = 0n;
+  let l = _0n;
-  for (let o = q - 1n; o % 2n === 0n; o /= 2n) l += 1n;
+  for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
   const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
-  const c2 = (q - 1n) / 2n ** c1; // 2. c2 = (q - 1) / (2^c1)        # Integer arithmetic
+  const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1)        # Integer arithmetic
-  const c3 = (c2 - 1n) / 2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
+  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
-  const c4 = 2n ** c1 - 1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic
+  const c4 = _2n ** c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic
-  const c5 = 2n ** (c1 - 1n); // 5. c5 = 2^(c1 - 1)              # Integer arithmetic
+  const c5 = _2n ** (c1 - _1n); // 5. c5 = 2^(c1 - 1)              # Integer arithmetic
   const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2
-  const c7 = Fp.pow(Z, (c2 + 1n) / 2n); // 7. c7 = Z^((c2 + 1) / 2)
+  const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)
   let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {
     let tv1 = c6; // 1. tv1 = c6
     let tv2 = Fp.pow(v, c4); // 2. tv2 = v^c4
@@ -1106,7 +1106,7 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
     tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)
     // 17. for i in (c1, c1 - 1, ..., 2):
     for (let i = c1; i > 1; i--) {
-      let tv5 = 2n ** (i - 2n); // 18.    tv5 = i - 2;    19.    tv5 = 2^tv5
+      let tv5 = _2n ** (i - _2n); // 18.    tv5 = i - 2;    19.    tv5 = 2^tv5
       let tvv5 = Fp.pow(tv4, tv5); // 20.    tv5 = tv4^tv5
       const e1 = Fp.eql(tvv5, Fp.ONE); // 21.    e1 = tv5 == 1
       tv2 = Fp.mul(tv3, tv1); // 22.    tv2 = tv3 * tv1
@@ -1117,9 +1117,9 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
     }
     return { isValid: isQR, value: tv3 };
   };
-  if (Fp.ORDER % 4n === 3n) {
+  if (Fp.ORDER % _4n === _3n) {
     // sqrt_ratio_3mod4(u, v)
-    const c1 = (Fp.ORDER - 3n) / 4n; // 1. c1 = (q - 3) / 4     # Integer arithmetic
+    const c1 = (Fp.ORDER - _3n) / _4n; // 1. c1 = (q - 3) / 4     # Integer arithmetic
     const c2 = Fp.sqrt(Fp.neg(Z)); // 2. c2 = sqrt(-Z)
     sqrtRatio = (u: T, v: T) => {
       let tv1 = Fp.sqr(v); // 1. tv1 = v^2
@@ -1135,7 +1135,7 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
     };
   }
   // No curves uses that
-  // if (Fp.ORDER % 8n === 5n) // sqrt_ratio_5mod8
+  // if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8
   return sqrtRatio;
 }
 // From draft-irtf-cfrg-hash-to-curve-16

src/ed25519.ts

@@ -204,7 +204,7 @@ function map_to_curve_elligator2_curve25519(u: bigint) {
   let y = Fp.cmov(y2, y1, e3);  //  36.   y = CMOV(y2, y1, e3)    # If e3, y = y1, else y = y2
   let e4 = Fp.isOdd(y);         //  37.  e4 = sgn0(y) == 1        # Fix sign of y
   y = Fp.cmov(y, Fp.neg(y), e3 !== e4); //  38.   y = CMOV(y, -y, e3 XOR e4)
-  return { xMn: xn, xMd: xd, yMn: y, yMd: 1n }; //  39. return (xn, xd, y, 1)
+  return { xMn: xn, xMd: xd, yMn: y, yMd: _1n }; //  39. return (xn, xd, y, 1)
 }
 
 const ELL2_C1_EDWARDS = FpSqrtEven(Fp, Fp.neg(BigInt(486664))); // sgn0(c1) MUST equal 0

src/ed448.ts

@@ -54,6 +54,7 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
 }
 
 const Fp = Field(ed448P, 456, true);
+const _4n = BigInt(4);
 
 const ED448_DEF = {
   // Param: a
@@ -195,10 +196,10 @@ function map_to_curve_elligator2_edwards448(u: bigint) {
   xEn = Fp.mul(xEn, xd2); // 9.  xEn = xEn * xd2
   xEn = Fp.mul(xEn, yd); // 10. xEn = xEn * yd
   xEn = Fp.mul(xEn, yn); // 11. xEn = xEn * yn
-  xEn = Fp.mul(xEn, 4n); // 12. xEn = xEn * 4
+  xEn = Fp.mul(xEn, _4n); // 12. xEn = xEn * 4
   tv2 = Fp.mul(tv2, xn2); // 13. tv2 = tv2 * xn2
   tv2 = Fp.mul(tv2, yd2); // 14. tv2 = tv2 * yd2
-  let tv3 = Fp.mul(yn2, 4n); // 15. tv3 = 4 * yn2
+  let tv3 = Fp.mul(yn2, _4n); // 15. tv3 = 4 * yn2
   let tv1 = Fp.add(tv3, yd2); // 16. tv1 = tv3 + yd2
   tv1 = Fp.mul(tv1, xd4); // 17. tv1 = tv1 * xd4
   let xEd = Fp.add(tv1, tv2); // 18. xEd = tv1 + tv2

src/secp256k1.ts

@@ -131,7 +131,7 @@ function lift_x(x: bigint): PointType<bigint> {
   const xx = modP(x * x);
   const c = modP(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
   let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.
-  if (y % 2n !== 0n) y = modP(-y); // Return the unique point P such that x(P) = x and
+  if (y % _2n !== _0n) y = modP(-y); // Return the unique point P such that x(P) = x and
   const p = new Point(x, y, _1n); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
   p.assertValidity();
   return p;