Fixed issue #1 - gcd works incorrect with 0. Some extra sanitizing

README.md

@@ -173,6 +173,7 @@ An iterative implementation of the extended euclidean algorithm or extended grea
 Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
 
 **Kind**: global function  
+**Returns**: [<code>egcdReturn</code>](#egcdReturn) - A triple (g, x, y), such that ax + by = g = gcd(a, b).  
 
 | Param | Type |
 | --- | --- |
@@ -225,7 +226,7 @@ The least common multiple computed as abs(a*b)/gcd(a,b)
 Modular inverse.
 
 **Kind**: global function  
-**Returns**: <code>bigint</code> - the inverse modulo n  
+**Returns**: <code>bigint</code> - the inverse modulo n or NaN if it does not exist  
 
 | Param | Type | Description |
 | --- | --- | --- |

dist/bigint-crypto-utils-latest.browser.js

@@ -48,11 +48,14 @@ var bigintCryptoUtils = (function (exports) {
      * @param {number|bigint} a 
      * @param {number|bigint} b 
      * 
-     * @returns {egcdReturn}
+     * @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
      */
     function eGcd(a, b) {
         a = BigInt(a);
         b = BigInt(b);
+        if (a <= _ZERO | b <= _ZERO)
+            return NaN; // a and b MUST be positive
+
         let x = _ZERO;
         let y = _ONE;
         let u = _ONE;
@@ -88,6 +91,11 @@ var bigintCryptoUtils = (function (exports) {
     function gcd(a, b) {
         a = abs(a);
         b = abs(b);
+        if (a === _ZERO)
+            return b;
+        else if (b === _ZERO)
+            return a;
+
         let shift = _ZERO;
         while (!((a | b) & _ONE)) {
             a >>= _ONE;
@@ -154,6 +162,8 @@ var bigintCryptoUtils = (function (exports) {
     function lcm(a, b) {
         a = BigInt(a);
         b = BigInt(b);
+        if (a === _ZERO && b === _ZERO)
+            return _ZERO;
         return abs(a * b) / gcd(a, b);
     }
 
@@ -163,12 +173,15 @@ var bigintCryptoUtils = (function (exports) {
      * @param {number|bigint} a The number to find an inverse for
      * @param {number|bigint} n The modulo
      * 
-     * @returns {bigint} the inverse modulo n
+     * @returns {bigint} the inverse modulo n or NaN if it does not exist
      */
     function modInv(a, n) {
+        if (a == _ZERO | n <= _ZERO)
+            return NaN;
+
         let egcd = eGcd(toZn(a, n), n);
         if (egcd.b !== _ONE) {
-            return null; // modular inverse does not exist
+            return NaN; // modular inverse does not exist
         } else {
             return toZn(egcd.x, n);
         }
@@ -185,6 +198,9 @@ var bigintCryptoUtils = (function (exports) {
     function modPow(a, b, n) {
         // See Knuth, volume 2, section 4.6.3.
         n = BigInt(n);
+        if (n === _ZERO)
+            return NaN;
+
         a = toZn(a, n);
         b = BigInt(b);
         if (b < _ZERO) {
@@ -218,6 +234,8 @@ var bigintCryptoUtils = (function (exports) {
      * @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
      */
     function prime(bitLength, iterations = 16) {
+        if (bitLength < 1)
+            throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
         return new Promise((resolve) => {
             let workerList = [];
             const _onmessage = (msg, newWorker) => {
@@ -292,9 +310,12 @@ var bigintCryptoUtils = (function (exports) {
      * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
      */
     function randBits(bitLength, forceLength = false) {
+        if (bitLength < 1)
+            throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
+
         const byteLength = Math.ceil(bitLength / 8);
         let rndBytes = randBytesSync(byteLength, false);
-        // Fill with 0's the extra birs
+        // Fill with 0's the extra bits
         rndBytes[0] = rndBytes[0] & (2 ** (bitLength % 8) - 1);
         if (forceLength) {
             let mask = (bitLength % 8) ? 2 ** ((bitLength % 8) - 1) : 128;
@@ -312,6 +333,9 @@ var bigintCryptoUtils = (function (exports) {
      * @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
      */
     function randBytes(byteLength, forceLength = false) {
+        if (byteLength < 1)
+            throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
         let buf;
         { // browser
             return new Promise(function (resolve) {
@@ -331,6 +355,9 @@ var bigintCryptoUtils = (function (exports) {
      * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
      */
     function randBytesSync(byteLength, forceLength = false) {
+        if (byteLength < 1)
+            throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
         let buf;
         { // browser
             buf = new Uint8Array(byteLength);
@@ -351,6 +378,9 @@ var bigintCryptoUtils = (function (exports) {
      */
     function toZn(a, n) {
         n = BigInt(n);
+        if (n <= 0)
+            return NaN;
+
         a = BigInt(a) % n;
         return (a < 0) ? a + n : a;
     }

dist/bigint-crypto-utils-latest.browser.min.js

@@ -1 +1 @@
-var bigintCryptoUtils=function(a){'use strict';function c(b){return b=BigInt(b),b>=r?b:-b}function d(b){if(b=BigInt(b),b===s)return 1;let c=1;do c++;while((b>>=s)>s);return c}function e(c,d){c=BigInt(c),d=BigInt(d);let e=r,f=s,g=s,h=r;for(;c!==r;){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}}function f(d,e){d=c(d),e=c(e);let f=r;for(;!((d|e)&s);)d>>=s,e>>=s,f++;for(;!(d&s);)d>>=s;do{for(;!(e&s);)e>>=s;if(d>e){let a=d;d=e,e=a}e-=d}while(e);return d<<f}async function g(a,b=16){return"number"==typeof a&&(a=BigInt(a)),new Promise((c,d)=>{let e=new Worker(o());e.onmessage=a=>{e.terminate(),c(a.data.isPrime)},e.onmessageerror=a=>{d(a)},e.postMessage({rnd:a,iterations:b,id:0})})}function h(b,a){let c=e(m(b,a),a);return c.b===s?m(c.x,a):null}function i(d,e,f){if(f=BigInt(f),d=m(d,f),e=BigInt(e),e<r)return h(i(d,c(e),f),f);let g=s,j=d;for(;0<e;){var k=e%t;e/=t,k==s&&(g*=j,g%=f),j*=j,j%=f}return g}function j(a,b=s){if(a<=b)throw new Error("max must be > min");const c=a-b;let e,f=d(c);do{let a=k(f);e=n(a)}while(e>c);return e+b}function k(a,b=!1){var c=Math.ceil;const d=c(a/8);let e=l(d,!1);if(e[0]&=2**(a%8)-1,b){let b=a%8?2**(a%8-1):128;e[0]|=b}return e}function l(a,b=!1){let c;return c=new Uint8Array(a),self.crypto.getRandomValues(c),b&&(c[0]|=128),c}function m(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b}function n(a){let b=r;for(let c of a.values()){let a=BigInt(c);b=(b<<BigInt(8))+a}return b}function o(){let a=`'use strict';const _ZERO = BigInt(0);const _ONE = BigInt(1);const _TWO = BigInt(2);const eGcd = ${e.toString()};const modInv = ${h.toString()};const modPow = ${i.toString()};const toZn = ${m.toString()};const randBits = ${k.toString()};const randBytesSync = ${l.toString()};const randBetween = ${j.toString()};const isProbablyPrime = ${q.toString()};${d.toString()}${n.toString()}`;return a+=`onmessage = ${async function(a){const b=await g(a.data.rnd,a.data.iterations);postMessage({isPrime:b,value:a.data.rnd,id:a.data.id})}.toString()};`,p(a)}function p(a){a=`(() => {${a}})()`;var b=new Blob([a],{type:"text/javascript"});return window.URL.createObjectURL(b)}function q(c,b=16){if(c===t)return!0;if((c&s)===r||c===s)return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===r)return!1}let f=r,g=c-s;for(;g%t===r;)g/=t,++f;let h=(c-s)/t**f;loop:do{let a=j(c-s,t),b=i(a,h,c);if(b===s||b===c-s)continue;for(let a=1;a<f;a++){if(b=i(b,t,c),b===c-s)continue loop;if(b===s)break}return!1}while(--b);return!0}const r=BigInt(0),s=BigInt(1),t=BigInt(2);return a.abs=c,a.bitLength=d,a.eGcd=e,a.gcd=f,a.isProbablyPrime=g,a.lcm=function(d,e){return d=BigInt(d),e=BigInt(e),c(d*e)/f(d,e)},a.modInv=h,a.modPow=i,a.prime=function(a,b=16){return new Promise(c=>{let d=[];const e=(e,f)=>{if(e.isPrime){for(let a=0;a<d.length;a++)d[a].terminate();for(;d.length;)d.pop();c(e.value)}else{let c=k(a,!0),d=n(c);try{f.postMessage({rnd:d,iterations:b,id:e.id})}catch(a){}}};{let a=o();for(let b,c=0;c<self.navigator.hardwareConcurrency;c++)b=new Worker(a),b.onmessage=a=>e(a.data,b),d.push(b)}for(let e=0;e<d.length;e++){let c=k(a,!0),f=n(c);d[e].postMessage({rnd:f,iterations:b,id:e})}})},a.randBetween=j,a.randBits=k,a.randBytes=function(a,b=!1){let c;return new Promise(function(b){c=new Uint8Array(a),self.crypto.getRandomValues(c),b(c)})},a.randBytesSync=l,a.toZn=m,a}({});
+var bigintCryptoUtils=function(a){'use strict';function c(b){return b=BigInt(b),b>=r?b:-b}function d(b){if(b=BigInt(b),b===s)return 1;let c=1;do c++;while((b>>=s)>s);return c}function e(c,d){if(c=BigInt(c),d=BigInt(d),c<=r|d<=r)return NaN;let e=r,f=s,g=s,h=r;for(;c!==r;){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}}function f(d,e){if(d=c(d),e=c(e),d===r)return e;if(e===r)return d;let f=r;for(;!((d|e)&s);)d>>=s,e>>=s,f++;for(;!(d&s);)d>>=s;do{for(;!(e&s);)e>>=s;if(d>e){let a=d;d=e,e=a}e-=d}while(e);return d<<f}async function g(a,b=16){return"number"==typeof a&&(a=BigInt(a)),new Promise((c,d)=>{let e=new Worker(o());e.onmessage=a=>{e.terminate(),c(a.data.isPrime)},e.onmessageerror=a=>{d(a)},e.postMessage({rnd:a,iterations:b,id:0})})}function h(b,a){if(b==r|a<=r)return NaN;let c=e(m(b,a),a);return c.b===s?m(c.x,a):NaN}function i(d,e,f){if(f=BigInt(f),f===r)return NaN;if(d=m(d,f),e=BigInt(e),e<r)return h(i(d,c(e),f),f);let g=s,j=d;for(;0<e;){var k=e%t;e/=t,k==s&&(g*=j,g%=f),j*=j,j%=f}return g}function j(a,b=s){if(a<=b)throw new Error("max must be > min");const c=a-b;let e,f=d(c);do{let a=k(f);e=n(a)}while(e>c);return e+b}function k(a,b=!1){var c=Math.ceil;if(1>a)throw new RangeError(`bitLength MUST be > 0 and it is ${a}`);const d=c(a/8);let e=l(d,!1);if(e[0]&=2**(a%8)-1,b){let b=a%8?2**(a%8-1):128;e[0]|=b}return e}function l(a,b=!1){if(1>a)throw new RangeError(`byteLength MUST be > 0 and it is ${a}`);let c;return c=new Uint8Array(a),self.crypto.getRandomValues(c),b&&(c[0]|=128),c}function m(b,c){return(c=BigInt(c),0>=c)?NaN:(b=BigInt(b)%c,0>b?b+c:b)}function n(a){let b=r;for(let c of a.values()){let a=BigInt(c);b=(b<<BigInt(8))+a}return b}function o(){let a=`'use strict';const _ZERO = BigInt(0);const _ONE = BigInt(1);const _TWO = BigInt(2);const eGcd = ${e.toString()};const modInv = ${h.toString()};const modPow = ${i.toString()};const toZn = ${m.toString()};const randBits = ${k.toString()};const randBytesSync = ${l.toString()};const randBetween = ${j.toString()};const isProbablyPrime = ${q.toString()};${d.toString()}${n.toString()}`;return a+=`onmessage = ${async function(a){const b=await g(a.data.rnd,a.data.iterations);postMessage({isPrime:b,value:a.data.rnd,id:a.data.id})}.toString()};`,p(a)}function p(a){a=`(() => {${a}})()`;var b=new Blob([a],{type:"text/javascript"});return window.URL.createObjectURL(b)}function q(c,b=16){if(c===t)return!0;if((c&s)===r||c===s)return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===r)return!1}let f=r,g=c-s;for(;g%t===r;)g/=t,++f;let h=(c-s)/t**f;loop:do{let a=j(c-s,t),b=i(a,h,c);if(b===s||b===c-s)continue;for(let a=1;a<f;a++){if(b=i(b,t,c),b===c-s)continue loop;if(b===s)break}return!1}while(--b);return!0}const r=BigInt(0),s=BigInt(1),t=BigInt(2);return a.abs=c,a.bitLength=d,a.eGcd=e,a.gcd=f,a.isProbablyPrime=g,a.lcm=function(d,e){return d=BigInt(d),e=BigInt(e),d===r&&e===r?r:c(d*e)/f(d,e)},a.modInv=h,a.modPow=i,a.prime=function(a,b=16){if(1>a)throw new RangeError(`bitLength MUST be > 0 and it is ${a}`);return new Promise(c=>{let d=[];const e=(e,f)=>{if(e.isPrime){for(let a=0;a<d.length;a++)d[a].terminate();for(;d.length;)d.pop();c(e.value)}else{let c=k(a,!0),d=n(c);try{f.postMessage({rnd:d,iterations:b,id:e.id})}catch(a){}}};{let a=o();for(let b,c=0;c<self.navigator.hardwareConcurrency;c++)b=new Worker(a),b.onmessage=a=>e(a.data,b),d.push(b)}for(let e=0;e<d.length;e++){let c=k(a,!0),f=n(c);d[e].postMessage({rnd:f,iterations:b,id:e})}})},a.randBetween=j,a.randBits=k,a.randBytes=function(a,b=!1){if(1>a)throw new RangeError(`byteLength MUST be > 0 and it is ${a}`);let c;return new Promise(function(b){c=new Uint8Array(a),self.crypto.getRandomValues(c),b(c)})},a.randBytesSync=l,a.toZn=m,a}({});

dist/bigint-crypto-utils-latest.browser.mod.js

@@ -45,11 +45,14 @@ function bitLength(a) {
  * @param {number|bigint} a 
  * @param {number|bigint} b 
  * 
- * @returns {egcdReturn}
+ * @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
  */
 function eGcd(a, b) {
     a = BigInt(a);
     b = BigInt(b);
+    if (a <= _ZERO | b <= _ZERO)
+        return NaN; // a and b MUST be positive
+
     let x = _ZERO;
     let y = _ONE;
     let u = _ONE;
@@ -85,6 +88,11 @@ function eGcd(a, b) {
 function gcd(a, b) {
     a = abs(a);
     b = abs(b);
+    if (a === _ZERO)
+        return b;
+    else if (b === _ZERO)
+        return a;
+
     let shift = _ZERO;
     while (!((a | b) & _ONE)) {
         a >>= _ONE;
@@ -151,6 +159,8 @@ async function isProbablyPrime(w, iterations = 16) {
 function lcm(a, b) {
     a = BigInt(a);
     b = BigInt(b);
+    if (a === _ZERO && b === _ZERO)
+        return _ZERO;
     return abs(a * b) / gcd(a, b);
 }
 
@@ -160,12 +170,15 @@ function lcm(a, b) {
  * @param {number|bigint} a The number to find an inverse for
  * @param {number|bigint} n The modulo
  * 
- * @returns {bigint} the inverse modulo n
+ * @returns {bigint} the inverse modulo n or NaN if it does not exist
  */
 function modInv(a, n) {
+    if (a == _ZERO | n <= _ZERO)
+        return NaN;
+
     let egcd = eGcd(toZn(a, n), n);
     if (egcd.b !== _ONE) {
-        return null; // modular inverse does not exist
+        return NaN; // modular inverse does not exist
     } else {
         return toZn(egcd.x, n);
     }
@@ -182,6 +195,9 @@ function modInv(a, n) {
 function modPow(a, b, n) {
     // See Knuth, volume 2, section 4.6.3.
     n = BigInt(n);
+    if (n === _ZERO)
+        return NaN;
+
     a = toZn(a, n);
     b = BigInt(b);
     if (b < _ZERO) {
@@ -215,6 +231,8 @@ function modPow(a, b, n) {
  * @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
  */
 function prime(bitLength, iterations = 16) {
+    if (bitLength < 1)
+        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
     return new Promise((resolve) => {
         let workerList = [];
         const _onmessage = (msg, newWorker) => {
@@ -289,9 +307,12 @@ function randBetween(max, min = _ONE) {
  * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
  */
 function randBits(bitLength, forceLength = false) {
+    if (bitLength < 1)
+        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
+
     const byteLength = Math.ceil(bitLength / 8);
     let rndBytes = randBytesSync(byteLength, false);
-    // Fill with 0's the extra birs
+    // Fill with 0's the extra bits
     rndBytes[0] = rndBytes[0] & (2 ** (bitLength % 8) - 1);
     if (forceLength) {
         let mask = (bitLength % 8) ? 2 ** ((bitLength % 8) - 1) : 128;
@@ -309,6 +330,9 @@ function randBits(bitLength, forceLength = false) {
  * @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
  */
 function randBytes(byteLength, forceLength = false) {
+    if (byteLength < 1)
+        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
     let buf;
     { // browser
         return new Promise(function (resolve) {
@@ -328,6 +352,9 @@ function randBytes(byteLength, forceLength = false) {
  * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
  */
 function randBytesSync(byteLength, forceLength = false) {
+    if (byteLength < 1)
+        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
     let buf;
     { // browser
         buf = new Uint8Array(byteLength);
@@ -348,6 +375,9 @@ function randBytesSync(byteLength, forceLength = false) {
  */
 function toZn(a, n) {
     n = BigInt(n);
+    if (n <= 0)
+        return NaN;
+
     a = BigInt(a) % n;
     return (a < 0) ? a + n : a;
 }

dist/bigint-crypto-utils-latest.node.js

@@ -49,11 +49,14 @@ function bitLength(a) {
  * @param {number|bigint} a 
  * @param {number|bigint} b 
  * 
- * @returns {egcdReturn}
+ * @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
  */
 function eGcd(a, b) {
     a = BigInt(a);
     b = BigInt(b);
+    if (a <= _ZERO | b <= _ZERO)
+        return NaN; // a and b MUST be positive
+
     let x = _ZERO;
     let y = _ONE;
     let u = _ONE;
@@ -89,6 +92,11 @@ function eGcd(a, b) {
 function gcd(a, b) {
     a = abs(a);
     b = abs(b);
+    if (a === _ZERO)
+        return b;
+    else if (b === _ZERO)
+        return a;
+
     let shift = _ZERO;
     while (!((a | b) & _ONE)) {
         a >>= _ONE;
@@ -161,6 +169,8 @@ async function isProbablyPrime(w, iterations = 16) {
 function lcm(a, b) {
     a = BigInt(a);
     b = BigInt(b);
+    if (a === _ZERO && b === _ZERO)
+        return _ZERO;
     return abs(a * b) / gcd(a, b);
 }
 
@@ -170,12 +180,15 @@ function lcm(a, b) {
  * @param {number|bigint} a The number to find an inverse for
  * @param {number|bigint} n The modulo
  * 
- * @returns {bigint} the inverse modulo n
+ * @returns {bigint} the inverse modulo n or NaN if it does not exist
  */
 function modInv(a, n) {
+    if (a == _ZERO | n <= _ZERO)
+        return NaN;
+
     let egcd = eGcd(toZn(a, n), n);
     if (egcd.b !== _ONE) {
-        return null; // modular inverse does not exist
+        return NaN; // modular inverse does not exist
     } else {
         return toZn(egcd.x, n);
     }
@@ -192,6 +205,9 @@ function modInv(a, n) {
 function modPow(a, b, n) {
     // See Knuth, volume 2, section 4.6.3.
     n = BigInt(n);
+    if (n === _ZERO)
+        return NaN;
+
     a = toZn(a, n);
     b = BigInt(b);
     if (b < _ZERO) {
@@ -225,6 +241,9 @@ function modPow(a, b, n) {
  * @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
  */
 function prime(bitLength, iterations = 16) {
+    if (bitLength < 1)
+        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
+
     if (!_useWorkers) {
         let rnd = _ZERO;
         do {
@@ -307,9 +326,12 @@ function randBetween(max, min = _ONE) {
  * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
  */
 function randBits(bitLength, forceLength = false) {
+    if (bitLength < 1)
+        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
+
     const byteLength = Math.ceil(bitLength / 8);
     let rndBytes = randBytesSync(byteLength, false);
-    // Fill with 0's the extra birs
+    // Fill with 0's the extra bits
     rndBytes[0] = rndBytes[0] & (2 ** (bitLength % 8) - 1);
     if (forceLength) {
         let mask = (bitLength % 8) ? 2 ** ((bitLength % 8) - 1) : 128;
@@ -327,6 +349,9 @@ function randBits(bitLength, forceLength = false) {
  * @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
  */
 function randBytes(byteLength, forceLength = false) {
+    if (byteLength < 1)
+        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
     let buf;
     {  // node
         const crypto = require('crypto');
@@ -349,6 +374,9 @@ function randBytes(byteLength, forceLength = false) {
  * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
  */
 function randBytesSync(byteLength, forceLength = false) {
+    if (byteLength < 1)
+        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
     let buf;
     {  // node
         const crypto = require('crypto');
@@ -370,6 +398,9 @@ function randBytesSync(byteLength, forceLength = false) {
  */
 function toZn(a, n) {
     n = BigInt(n);
+    if (n <= 0)
+        return NaN;
+
     a = BigInt(a) % n;
     return (a < 0) ? a + n : a;
 }

src/main.js

@@ -47,11 +47,14 @@ export function bitLength(a) {
  * @param {number|bigint} a 
  * @param {number|bigint} b 
  * 
- * @returns {egcdReturn}
+ * @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
  */
 export function eGcd(a, b) {
     a = BigInt(a);
     b = BigInt(b);
+    if (a <= _ZERO | b <= _ZERO)
+        return NaN; // a and b MUST be positive
+
     let x = _ZERO;
     let y = _ONE;
     let u = _ONE;
@@ -87,6 +90,11 @@ export function eGcd(a, b) {
 export function gcd(a, b) {
     a = abs(a);
     b = abs(b);
+    if (a === _ZERO)
+        return b;
+    else if (b === _ZERO)
+        return a;
+
     let shift = _ZERO;
     while (!((a | b) & _ONE)) {
         a >>= _ONE;
@@ -178,6 +186,8 @@ export async function isProbablyPrime(w, iterations = 16) {
 export function lcm(a, b) {
     a = BigInt(a);
     b = BigInt(b);
+    if (a === _ZERO && b === _ZERO)
+        return _ZERO;
     return abs(a * b) / gcd(a, b);
 }
 
@@ -187,12 +197,15 @@ export function lcm(a, b) {
  * @param {number|bigint} a The number to find an inverse for
  * @param {number|bigint} n The modulo
  * 
- * @returns {bigint} the inverse modulo n
+ * @returns {bigint} the inverse modulo n or NaN if it does not exist
  */
 export function modInv(a, n) {
+    if (a == _ZERO | n <= _ZERO)
+        return NaN;
+
     let egcd = eGcd(toZn(a, n), n);
     if (egcd.b !== _ONE) {
-        return null; // modular inverse does not exist
+        return NaN; // modular inverse does not exist
     } else {
         return toZn(egcd.x, n);
     }
@@ -209,6 +222,9 @@ export function modInv(a, n) {
 export function modPow(a, b, n) {
     // See Knuth, volume 2, section 4.6.3.
     n = BigInt(n);
+    if (n === _ZERO)
+        return NaN;
+
     a = toZn(a, n);
     b = BigInt(b);
     if (b < _ZERO) {
@@ -242,6 +258,9 @@ export function modPow(a, b, n) {
  * @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
  */
 export function prime(bitLength, iterations = 16) {
+    if (bitLength < 1)
+        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
+
     if (!process.browser && !_useWorkers) {
         let rnd = _ZERO;
         do {
@@ -331,9 +350,12 @@ export function randBetween(max, min = _ONE) {
  * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
  */
 export function randBits(bitLength, forceLength = false) {
+    if (bitLength < 1)
+        throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`);
+
     const byteLength = Math.ceil(bitLength / 8);
     let rndBytes = randBytesSync(byteLength, false);
-    // Fill with 0's the extra birs
+    // Fill with 0's the extra bits
     rndBytes[0] = rndBytes[0] & (2 ** (bitLength % 8) - 1);
     if (forceLength) {
         let mask = (bitLength % 8) ? 2 ** ((bitLength % 8) - 1) : 128;
@@ -351,6 +373,9 @@ export function randBits(bitLength, forceLength = false) {
  * @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
  */
 export function randBytes(byteLength, forceLength = false) {
+    if (byteLength < 1)
+        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
     let buf;
     if (!process.browser) {  // node
         const crypto = require('crypto');
@@ -379,6 +404,9 @@ export function randBytes(byteLength, forceLength = false) {
  * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
  */
 export function randBytesSync(byteLength, forceLength = false) {
+    if (byteLength < 1)
+        throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`);
+
     let buf;
     if (!process.browser) {  // node
         const crypto = require('crypto');
@@ -403,6 +431,9 @@ export function randBytesSync(byteLength, forceLength = false) {
  */
 export function toZn(a, n) {
     n = BigInt(n);
+    if (n <= 0)
+        return NaN;
+
     a = BigInt(a) % n;
     return (a < 0) ? a + n : a;
 }

test/browser/tests.js

@@ -78,6 +78,21 @@ const inputs$2 = [
         b: BigInt(1),
         gcd: BigInt(1)
     },
+    {
+        a: BigInt(0),
+        b: BigInt(189),
+        gcd: BigInt(189)
+    },
+    {
+        a: BigInt(189),
+        b: BigInt(0),
+        gcd: BigInt(189)
+    },
+    {
+        a: BigInt(0),
+        b: BigInt(0),
+        gcd: BigInt(0)
+    },
     {
         a: BigInt(1),
         b: BigInt('14546149867129487614601346814'),
@@ -244,16 +259,22 @@ const inputs$4 = [
         a: BigInt(-2),
         n: BigInt(5),
         modInv: BigInt(2)
+    },
+    {
+        a: BigInt(2),
+        n: BigInt(4),
+        modInv: NaN
     }
 ];
 
 describe('modInv', function () {
-    for (const input of inputs$4) {
     let ret;
+    for (const input of inputs$4) {
         describe(`modInv(${input.a}, ${input.n})`, function () {
             it(`should return ${input.modInv}`, function () {
                 ret = bigintCryptoUtils.modInv(input.a, input.n);
-                chai.expect(ret).to.equal(input.modInv);
+                // chai.assert( String(ret) === String(input.modInv) );
+                chai.expect(String(ret)).to.be.equal(String(input.modInv));
             });
         });
     }

test/gcd.js

@@ -11,6 +11,21 @@ const inputs = [
         b: BigInt(1),
         gcd: BigInt(1)
     },
+    {
+        a: BigInt(0),
+        b: BigInt(189),
+        gcd: BigInt(189)
+    },
+    {
+        a: BigInt(189),
+        b: BigInt(0),
+        gcd: BigInt(189)
+    },
+    {
+        a: BigInt(0),
+        b: BigInt(0),
+        gcd: BigInt(0)
+    },
     {
         a: BigInt(1),
         b: BigInt('14546149867129487614601346814'),

test/modInv.js

@@ -20,16 +20,22 @@ const inputs = [
         a: BigInt(-2),
         n: BigInt(5),
         modInv: BigInt(2)
+    },
+    {
+        a: BigInt(2),
+        n: BigInt(4),
+        modInv: NaN
     }
 ];
 
 describe('modInv', function () {
-    for (const input of inputs) {
     let ret;
+    for (const input of inputs) {
         describe(`modInv(${input.a}, ${input.n})`, function () {
             it(`should return ${input.modInv}`, function () {
                 ret = bigintCryptoUtils.modInv(input.a, input.n);
-                chai.expect(ret).to.equal(input.modInv);
+                // chai.assert( String(ret) === String(input.modInv) );
+                chai.expect(String(ret)).to.be.equal(String(input.modInv));
             });
         });
     }