@@ -0,0 +1,14 @@
+* compconstant - Returns 1 if `in` (expanded to binary array) > `ct`
+* aliascheck - check if `in` (expanded to binary array) oveflowed its 254 bits (<= -1)
+* babyjub - twisted Edwards curve 168700.x^2 + y^2 = 1 + 168696.x^2.y^2
+  * BabyAdd - (`xout`,`yout`) = (`x1`,`y1`) + (`x2`,`y2`)
+  * BabyDbl - (`xout`,`yout`) = 2*(`x`,`y`)
+  * BabyCheck - check that (`x`,`y`) is on the curve
+* binsub - binary subtraction
+* gates - logical gates
+* mimc - SNARK-friendly hash Minimal Multiplicative Complexity.
+  * https://eprint.iacr.org/2016/492.pdf
+  * zcash/zcash#2233
+* smt - Sparse Merkle Tree
+  * https://ethresear.ch/t/optimizing-sparse-merkle-trees/3751
+* montgomery https://en.wikipedia.org/wiki/Montgomery_curve

@@ -17,6 +17,9 @@ You should have received a copy of the GNU General Public License
     along with circom. If not, see <https://www.gnu.org/licenses/>.
 */
 
+include "bitify.circom";
+include "escalarmulfix.circom";
+
 template BabyAdd() {
     signal input x1;
     signal input y1;
@@ -77,3 +80,27 @@ y2 <== y*y;
 
     a*x2 + y2 === 1 + d*x2*y2;
 }
+
+// Extracts the public key from private key
+template BabyPbk() {
+    signal private input  in;
+    signal         output Ax;
+    signal         output Ay;
+
+    var BASE8 = [
+        17777552123799933955779906779655732241715742912184938656739573121738514868268,
+        2626589144620713026669568689430873010625803728049924121243784502389097019475
+    ];
+
+    component pvkBits = Num2Bits(253);
+    pvkBits.in <== in;
+
+    component mulFix = EscalarMulFix(253, BASE8);
+
+    var i;
+    for (i=0; i<253; i++) {
+        mulFix.e[i] <== pvkBits.out[i];
+    }
+    Ax  <== mulFix.out[0];
+    Ay  <== mulFix.out[1];
+}

@@ -90,12 +90,17 @@ success * (success -1) === 0;
 }
 
 
-template Multiplexor(wIn, nIn) {
+template Multiplexer(wIn, nIn) {
     signal input inp[nIn][wIn];
     signal input sel;
     signal output out[wIn];
-    component Decoder(nIn) dec;
-    component EscalarProduct(nIn) ep[wIn];
+    component dec = Decoder(nIn);
+    component ep[wIn];
+
+    for (var k=0; k<wIn; k++) {
+        ep[k] = EscalarProduct(nIn);
+    }
+
     sel ==> dec.inp;
     for (var j=0; j<wIn; j++) {
         for (var k=0; k<nIn; k++) {
@@ -106,7 +111,3 @@ ep[j].out ==> out[j];
     }
     dec.success === 1;
 }
-
-component Multiplexor(8,3) main;
-
-

@@ -2365,7 +2365,8 @@ },
             "bindings": {
               "version": "1.3.0",
               "resolved": "https://registry.npmjs.org/bindings/-/bindings-1.3.0.tgz",
-              "integrity": "sha512-DpLh5EzMR2kzvX1KIlVC0VkC3iZtHKTgdtZ0a3pglBZdaQFjt5S9g9xd1lE+YvXyfd6mtCeRnrUfOLYiTMlNSw=="
+              "integrity": "sha512-DpLh5EzMR2kzvX1KIlVC0VkC3iZtHKTgdtZ0a3pglBZdaQFjt5S9g9xd1lE+YvXyfd6mtCeRnrUfOLYiTMlNSw==",
+              "dev": true
             },
             "bip39": {
               "version": "2.5.0",
@@ -2384,6 +2385,7 @@ "bip66": {
               "version": "1.1.5",
               "resolved": "https://registry.npmjs.org/bip66/-/bip66-1.1.5.tgz",
               "integrity": "sha1-AfqHSHhcpwlV1QESF9GzE5lpyiI=",
+              "dev": true,
               "requires": {
                 "safe-buffer": "^5.0.1"
               }
@@ -2419,7 +2421,8 @@ },
             "bn.js": {
               "version": "4.11.8",
               "resolved": "https://registry.npmjs.org/bn.js/-/bn.js-4.11.8.tgz",
-              "integrity": "sha512-ItfYfPLkWHUjckQCk8xC+LwxgK8NYcXywGigJgSwOP8Y2iyWT4f2vsZnoOXTTbo+o5yXmIUJ4gn5538SO5S3gA=="
+              "integrity": "sha512-ItfYfPLkWHUjckQCk8xC+LwxgK8NYcXywGigJgSwOP8Y2iyWT4f2vsZnoOXTTbo+o5yXmIUJ4gn5538SO5S3gA==",
+              "dev": true
             },
             "body-parser": {
               "version": "1.18.3",
@@ -2464,12 +2467,14 @@ },
             "brorand": {
               "version": "1.1.0",
               "resolved": "https://registry.npmjs.org/brorand/-/brorand-1.1.0.tgz",
-              "integrity": "sha1-EsJe/kCkXjwyPrhnWgoM5XsiNx8="
+              "integrity": "sha1-EsJe/kCkXjwyPrhnWgoM5XsiNx8=",
+              "dev": true
             },
             "browserify-aes": {
               "version": "1.2.0",
               "resolved": "http://registry.npmjs.org/browserify-aes/-/browserify-aes-1.2.0.tgz",
               "integrity": "sha512-+7CHXqGuspUn/Sl5aO7Ea0xWGAtETPXNSAjHo48JfLdPWcMng33Xe4znFvQweqc/uzk5zSOI3H52CYnjCfb5hA==",
+              "dev": true,
               "requires": {
                 "buffer-xor": "^1.0.3",
                 "cipher-base": "^1.0.0",
@@ -2631,7 +2636,8 @@ },
             "buffer-xor": {
               "version": "1.0.3",
               "resolved": "https://registry.npmjs.org/buffer-xor/-/buffer-xor-1.0.3.tgz",
-              "integrity": "sha1-JuYe0UIvtw3ULm42cp7VHYVf6Nk="
+              "integrity": "sha1-JuYe0UIvtw3ULm42cp7VHYVf6Nk=",
+              "dev": true
             },
             "builtin-modules": {
               "version": "1.1.1",
@@ -2730,6 +2736,7 @@ "cipher-base": {
               "version": "1.0.4",
               "resolved": "https://registry.npmjs.org/cipher-base/-/cipher-base-1.0.4.tgz",
               "integrity": "sha512-Kkht5ye6ZGmwv40uUDZztayT2ThLQGfnj/T71N/XzeZeo3nf8foyW7zGTsPYkEya3m5f3cAypH+qe7YOrM1U2Q==",
+              "dev": true,
               "requires": {
                 "inherits": "^2.0.1",
                 "safe-buffer": "^5.0.1"
@@ -2896,6 +2903,7 @@ "create-hash": {
               "version": "1.2.0",
               "resolved": "http://registry.npmjs.org/create-hash/-/create-hash-1.2.0.tgz",
               "integrity": "sha512-z00bCGNHDG8mHAkP7CtT1qVu+bFQUPjYq/4Iv3C3kWjTFV10zIjfSoeqXo9Asws8gwSHDGj/hl2u4OGIjapeCg==",
+              "dev": true,
               "requires": {
                 "cipher-base": "^1.0.1",
                 "inherits": "^2.0.1",
@@ -2908,6 +2916,7 @@ "create-hmac": {
               "version": "1.1.7",
               "resolved": "http://registry.npmjs.org/create-hmac/-/create-hmac-1.1.7.tgz",
               "integrity": "sha512-MJG9liiZ+ogc4TzUwuvbER1JRdgvUFSB5+VR/g5h82fGaIRWMWddtKBHi7/sVhfjQZ6SehlyhvQYrcYkaUIpLg==",
+              "dev": true,
               "requires": {
                 "cipher-base": "^1.0.3",
                 "create-hash": "^1.1.0",
@@ -3212,6 +3221,7 @@ "drbg.js": {
               "version": "1.0.1",
               "resolved": "https://registry.npmjs.org/drbg.js/-/drbg.js-1.0.1.tgz",
               "integrity": "sha1-Pja2xCs3BDgjzbwzLVjzHiRFSAs=",
+              "dev": true,
               "requires": {
                 "browserify-aes": "^1.0.6",
                 "create-hash": "^1.1.2",
@@ -3252,6 +3262,7 @@ "elliptic": {
               "version": "6.4.1",
               "resolved": "https://registry.npmjs.org/elliptic/-/elliptic-6.4.1.tgz",
               "integrity": "sha512-BsXLz5sqX8OHcsh7CqBMztyXARmGQ3LWPtGjJi6DiJHq5C/qvi9P3OqgswKSDftbu8+IoI/QDTAm2fFnQ9SZSQ==",
+              "dev": true,
               "requires": {
                 "bn.js": "^4.4.0",
                 "brorand": "^1.0.1",
@@ -3546,17 +3557,8 @@ "resolved": "https://registry.npmjs.org/eth-sig-util/-/eth-sig-util-1.4.2.tgz",
                   "integrity": "sha1-jZWCAsftuq6Dlwf7pvCf8ydgYhA=",
                   "dev": true,
                   "requires": {
+                    "ethereumjs-abi": "git+https://github.com/ethereumjs/ethereumjs-abi.git",
                     "ethereumjs-util": "^5.1.1"
-                  },
-                  "dependencies": {
-                    "ethereumjs-abi": {
-                      "version": "git+https://github.com/ethereumjs/ethereumjs-abi.git#2863c40e0982acfc0b7163f0285d4c56427c7799",
-                      "from": "git+https://github.com/ethereumjs/ethereumjs-abi.git#2863c40e0982acfc0b7163f0285d4c56427c7799",
-                      "requires": {
-                        "bn.js": "^4.10.0",
-                        "ethereumjs-util": "^5.0.0"
-                      }
-                    }
                   }
                 },
                 "ethereum-common": {
@@ -3566,10 +3568,29 @@ "integrity": "sha512-XOnAR/3rntJgbCdGhqdaLIxDLWKLmsZOGhHdBKadEr6gEnJLH52k93Ou+TUdFaPN3hJc3isBZBal3U/XZ15abA==",
                   "dev": true
                 },
                 "ethereumjs-abi": {
-                  "version": "git+https://github.com/ethereumjs/ethereumjs-abi.git#2863c40e0982acfc0b7163f0285d4c56427c7799",
+                  "version": "git+https://github.com/ethereumjs/ethereumjs-abi.git#8431eab7b3384e65e8126a4602520b78031666fb",
                   "from": "git+https://github.com/ethereumjs/ethereumjs-abi.git",
+                  "dev": true,
                   "requires": {
-                    "bn.js": "^4.11.8"
+                    "bn.js": "^4.11.8",
+                    "ethereumjs-util": "^6.0.0"
+                  },
+                  "dependencies": {
+                    "ethereumjs-util": {
+                      "version": "6.1.0",
+                      "resolved": "https://registry.npmjs.org/ethereumjs-util/-/ethereumjs-util-6.1.0.tgz",
+                      "integrity": "sha512-URESKMFbDeJxnAxPppnk2fN6Y3BIatn9fwn76Lm8bQlt+s52TpG8dN9M66MLPuRAiAOIqL3dfwqWJf0sd0fL0Q==",
+                      "dev": true,
+                      "requires": {
+                        "bn.js": "^4.11.0",
+                        "create-hash": "^1.1.2",
+                        "ethjs-util": "0.1.6",
+                        "keccak": "^1.0.2",
+                        "rlp": "^2.0.0",
+                        "safe-buffer": "^5.1.1",
+                        "secp256k1": "^3.0.1"
+                      }
+                    }
                   }
                 },
                 "ethereumjs-block": {
@@ -3761,6 +3782,7 @@ "ethereumjs-util": {
               "version": "5.2.0",
               "resolved": "https://registry.npmjs.org/ethereumjs-util/-/ethereumjs-util-5.2.0.tgz",
               "integrity": "sha512-CJAKdI0wgMbQFLlLRtZKGcy/L6pzVRgelIZqRqNbuVFM3K9VEnyfbcvz0ncWMRNCe4kaHWjwRYQcYMucmwsnWA==",
+              "dev": true,
               "requires": {
                 "bn.js": "^4.11.0",
                 "create-hash": "^1.1.2",
@@ -3852,6 +3874,7 @@ "ethjs-util": {
               "version": "0.1.6",
               "resolved": "https://registry.npmjs.org/ethjs-util/-/ethjs-util-0.1.6.tgz",
               "integrity": "sha512-CUnVOQq7gSpDHZVVrQW8ExxUETWrnrvXYvYz55wOU8Uj4VCgw56XC2B/fVqQN+f7gmrnRHSLVnFAwsCuNwji8w==",
+              "dev": true,
               "requires": {
                 "is-hex-prefixed": "1.0.0",
                 "strip-hex-prefix": "1.0.0"
@@ -3874,6 +3897,7 @@ "evp_bytestokey": {
               "version": "1.0.3",
               "resolved": "https://registry.npmjs.org/evp_bytestokey/-/evp_bytestokey-1.0.3.tgz",
               "integrity": "sha512-/f2Go4TognH/KvCISP7OUsHn85hT9nUkxxA9BEWxFn+Oj9o8ZNLm/40hdlgSLyuOimsrTKLUMEorQexp/aPQeA==",
+              "dev": true,
               "requires": {
                 "md5.js": "^1.3.4",
                 "safe-buffer": "^5.1.1"
@@ -4301,6 +4325,7 @@ "hash-base": {
               "version": "3.0.4",
               "resolved": "https://registry.npmjs.org/hash-base/-/hash-base-3.0.4.tgz",
               "integrity": "sha1-X8hoaEfs1zSZQDMZprCj8/auSRg=",
+              "dev": true,
               "requires": {
                 "inherits": "^2.0.1",
                 "safe-buffer": "^5.0.1"
@@ -4310,6 +4335,7 @@ "hash.js": {
               "version": "1.1.5",
               "resolved": "https://registry.npmjs.org/hash.js/-/hash.js-1.1.5.tgz",
               "integrity": "sha512-eWI5HG9Np+eHV1KQhisXWwM+4EPPYe5dFX1UZZH7k/E3JzDEazVH+VGlZi6R94ZqImq+A3D1mCEtrFIfg/E7sA==",
+              "dev": true,
               "requires": {
                 "inherits": "^2.0.3",
                 "minimalistic-assert": "^1.0.1"
@@ -4337,6 +4363,7 @@ "hmac-drbg": {
               "version": "1.0.1",
               "resolved": "https://registry.npmjs.org/hmac-drbg/-/hmac-drbg-1.0.1.tgz",
               "integrity": "sha1-0nRXAQJabHdabFRXk+1QL8DGSaE=",
+              "dev": true,
               "requires": {
                 "hash.js": "^1.0.3",
                 "minimalistic-assert": "^1.0.0",
@@ -4508,7 +4535,8 @@ },
             "is-hex-prefixed": {
               "version": "1.0.0",
               "resolved": "https://registry.npmjs.org/is-hex-prefixed/-/is-hex-prefixed-1.0.0.tgz",
-              "integrity": "sha1-fY035q135dEnFIkTxXPggtd39VQ="
+              "integrity": "sha1-fY035q135dEnFIkTxXPggtd39VQ=",
+              "dev": true
             },
             "is-natural-number": {
               "version": "4.0.1",
@@ -4565,7 +4593,8 @@ },
             "is-typedarray": {
               "version": "1.0.0",
               "resolved": "https://registry.npmjs.org/is-typedarray/-/is-typedarray-1.0.0.tgz",
-              "integrity": "sha1-5HnICFjfDBsR3dppQPlgEfzaSpo="
+              "integrity": "sha1-5HnICFjfDBsR3dppQPlgEfzaSpo=",
+              "dev": true
             },
             "is-utf8": {
               "version": "0.2.1",
@@ -4712,6 +4741,7 @@ "keccak": {
               "version": "1.4.0",
               "resolved": "https://registry.npmjs.org/keccak/-/keccak-1.4.0.tgz",
               "integrity": "sha512-eZVaCpblK5formjPjeTBik7TAg+pqnDrMHIffSvi9Lh7PQgM1+hSzakUeZFCk9DVVG0dacZJuaz2ntwlzZUIBw==",
+              "dev": true,
               "requires": {
                 "bindings": "^1.2.1",
                 "inherits": "^2.0.3",
@@ -5012,6 +5042,7 @@ "md5.js": {
               "version": "1.3.5",
               "resolved": "https://registry.npmjs.org/md5.js/-/md5.js-1.3.5.tgz",
               "integrity": "sha512-xitP+WxNPcTTOgnTJcrhM0xvdPepipPSf3I8EIpGKeFLjt3PlJLIDG3u8EX53ZIubkb+5U2+3rELYpEhHhzdkg==",
+              "dev": true,
               "requires": {
                 "hash-base": "^3.0.0",
                 "inherits": "^2.0.1",
@@ -5176,12 +5207,14 @@ },
             "minimalistic-assert": {
               "version": "1.0.1",
               "resolved": "https://registry.npmjs.org/minimalistic-assert/-/minimalistic-assert-1.0.1.tgz",
-              "integrity": "sha512-UtJcAD4yEaGtjPezWuO9wC4nwUnVH/8/Im3yEHQP4b67cXlD/Qr9hdITCU1xDbSEXg2XKNaP8jsReV7vQd00/A=="
+              "integrity": "sha512-UtJcAD4yEaGtjPezWuO9wC4nwUnVH/8/Im3yEHQP4b67cXlD/Qr9hdITCU1xDbSEXg2XKNaP8jsReV7vQd00/A==",
+              "dev": true
             },
             "minimalistic-crypto-utils": {
               "version": "1.0.1",
               "resolved": "https://registry.npmjs.org/minimalistic-crypto-utils/-/minimalistic-crypto-utils-1.0.1.tgz",
-              "integrity": "sha1-9sAMHAsIIkblxNmd+4x8CDsrWCo="
+              "integrity": "sha1-9sAMHAsIIkblxNmd+4x8CDsrWCo=",
+              "dev": true
             },
             "minimatch": {
               "version": "3.0.4",
@@ -5233,7 +5266,8 @@ },
             "ms": {
               "version": "2.0.0",
               "resolved": "https://registry.npmjs.org/ms/-/ms-2.0.0.tgz",
-              "integrity": "sha1-VgiurfwAvmwpAd9fmGF4jeDVl8g="
+              "integrity": "sha1-VgiurfwAvmwpAd9fmGF4jeDVl8g=",
+              "dev": true
             },
             "mz": {
               "version": "2.7.0",
@@ -5250,7 +5284,8 @@ },
             "nan": {
               "version": "2.10.0",
               "resolved": "http://registry.npmjs.org/nan/-/nan-2.10.0.tgz",
-              "integrity": "sha512-bAdJv7fBLhWC+/Bls0Oza+mvTaNQtP+1RyhhhvD95pgUJz6XM5IzgmxOkItJ9tkoCiplvAnXI1tNmmUD/eScyA=="
+              "integrity": "sha512-bAdJv7fBLhWC+/Bls0Oza+mvTaNQtP+1RyhhhvD95pgUJz6XM5IzgmxOkItJ9tkoCiplvAnXI1tNmmUD/eScyA==",
+              "dev": true
             },
             "nano-json-stream-parser": {
               "version": "0.1.2",
@@ -5935,6 +5970,7 @@ "ripemd160": {
               "version": "2.0.2",
               "resolved": "https://registry.npmjs.org/ripemd160/-/ripemd160-2.0.2.tgz",
               "integrity": "sha512-ii4iagi25WusVoiC4B4lq7pbXfAp3D9v5CwfkY33vffw2+pkDjY1D8GaN7spsxvCSx8dkPqOZCEZyfxcmJG2IA==",
+              "dev": true,
               "requires": {
                 "hash-base": "^3.0.0",
                 "inherits": "^2.0.1"
@@ -5944,6 +5980,7 @@ "rlp": {
               "version": "2.1.0",
               "resolved": "https://registry.npmjs.org/rlp/-/rlp-2.1.0.tgz",
               "integrity": "sha512-93U7IKH5j7nmXFVg19MeNBGzQW5uXW1pmCuKY8veeKIhYTE32C2d0mOegfiIAfXcHOKJjjPlJisn8iHDF5AezA==",
+              "dev": true,
               "requires": {
                 "safe-buffer": "^5.1.1"
               }
@@ -5957,7 +5994,8 @@ },
             "safe-buffer": {
               "version": "5.1.2",
               "resolved": "https://registry.npmjs.org/safe-buffer/-/safe-buffer-5.1.2.tgz",
-              "integrity": "sha512-Gd2UZBJDkXlY7GbJxfsE8/nvKkUEU1G38c1siN6QP6a9PT9MmHB8GnpscSmMJSoF8LOIrt8ud/wPtojys4G6+g=="
+              "integrity": "sha512-Gd2UZBJDkXlY7GbJxfsE8/nvKkUEU1G38c1siN6QP6a9PT9MmHB8GnpscSmMJSoF8LOIrt8ud/wPtojys4G6+g==",
+              "dev": true
             },
             "safe-event-emitter": {
               "version": "1.0.1",
@@ -6009,6 +6047,7 @@ "secp256k1": {
               "version": "3.5.2",
               "resolved": "https://registry.npmjs.org/secp256k1/-/secp256k1-3.5.2.tgz",
               "integrity": "sha512-iin3kojdybY6NArd+UFsoTuapOF7bnJNf2UbcWXaY3z+E1sJDipl60vtzB5hbO/uquBu7z0fd4VC4Irp+xoFVQ==",
+              "dev": true,
               "requires": {
                 "bindings": "^1.2.1",
                 "bip66": "^1.1.3",
@@ -6146,6 +6185,7 @@ "sha.js": {
               "version": "2.4.11",
               "resolved": "http://registry.npmjs.org/sha.js/-/sha.js-2.4.11.tgz",
               "integrity": "sha512-QMEp5B7cftE7APOjk5Y6xgrbWu+WkLVQwk8JNjZ8nKRciZaByEW6MubieAiToS7+dwvrjGhH8jRXz3MVd0AYqQ==",
+              "dev": true,
               "requires": {
                 "inherits": "^2.0.1",
                 "safe-buffer": "^5.0.1"
@@ -6360,6 +6400,7 @@ "strip-hex-prefix": {
               "version": "1.0.0",
               "resolved": "https://registry.npmjs.org/strip-hex-prefix/-/strip-hex-prefix-1.0.0.tgz",
               "integrity": "sha1-DF8VX+8RUTczd96du1iNoFUA428=",
+              "dev": true,
               "requires": {
                 "is-hex-prefixed": "1.0.0"
               }
@@ -6609,6 +6650,7 @@ "typedarray-to-buffer": {
               "version": "3.1.5",
               "resolved": "https://registry.npmjs.org/typedarray-to-buffer/-/typedarray-to-buffer-3.1.5.tgz",
               "integrity": "sha512-zdu8XMNEDepKKR+XYOXAVPtWui0ly0NtohUscw+UmaHiAWT8hrV1rr//H6V+0DvJ3OQ19S979M0laLfX8rm82Q==",
+              "dev": true,
               "requires": {
                 "is-typedarray": "^1.0.0"
               }
@@ -7071,24 +7113,34 @@ "resolved": "https://registry.npmjs.org/eth-sig-util/-/eth-sig-util-1.4.2.tgz",
                   "integrity": "sha1-jZWCAsftuq6Dlwf7pvCf8ydgYhA=",
                   "dev": true,
                   "requires": {
+                    "ethereumjs-abi": "git+https://github.com/ethereumjs/ethereumjs-abi.git",
                     "ethereumjs-util": "^5.1.1"
+                  }
+                },
+                "ethereumjs-abi": {
+                  "version": "git+https://github.com/ethereumjs/ethereumjs-abi.git#8431eab7b3384e65e8126a4602520b78031666fb",
+                  "from": "git+https://github.com/ethereumjs/ethereumjs-abi.git",
+                  "dev": true,
+                  "requires": {
+                    "bn.js": "^4.11.8",
+                    "ethereumjs-util": "^6.0.0"
                   },
                   "dependencies": {
-                    "ethereumjs-abi": {
-                      "version": "git+https://github.com/ethereumjs/ethereumjs-abi.git#2863c40e0982acfc0b7163f0285d4c56427c7799",
-                      "from": "git+https://github.com/ethereumjs/ethereumjs-abi.git#2863c40e0982acfc0b7163f0285d4c56427c7799",
+                    "ethereumjs-util": {
+                      "version": "6.1.0",
+                      "resolved": "https://registry.npmjs.org/ethereumjs-util/-/ethereumjs-util-6.1.0.tgz",
+                      "integrity": "sha512-URESKMFbDeJxnAxPppnk2fN6Y3BIatn9fwn76Lm8bQlt+s52TpG8dN9M66MLPuRAiAOIqL3dfwqWJf0sd0fL0Q==",
+                      "dev": true,
                       "requires": {
-                        "bn.js": "^4.10.0",
-                        "ethereumjs-util": "^5.0.0"
+                        "bn.js": "^4.11.0",
+                        "create-hash": "^1.1.2",
+                        "ethjs-util": "0.1.6",
+                        "keccak": "^1.0.2",
+                        "rlp": "^2.0.0",
+                        "safe-buffer": "^5.1.1",
+                        "secp256k1": "^3.0.1"
                       }
                     }
-                  }
-                },
-                "ethereumjs-abi": {
-                  "version": "git+https://github.com/ethereumjs/ethereumjs-abi.git#2863c40e0982acfc0b7163f0285d4c56427c7799",
-                  "from": "git+https://github.com/ethereumjs/ethereumjs-abi.git",
-                  "requires": {
-                    "bn.js": "^4.11.8"
                   }
                 },
                 "ws": {
@@ -7133,20 +7185,25 @@ "dev": true,
               "optional": true,
               "requires": {
                 "underscore": "1.8.3",
-                "web3-core-helpers": "1.0.0-beta.35"
+                "web3-core-helpers": "1.0.0-beta.35",
+                "websocket": "git://github.com/frozeman/WebSocket-Node.git#browserifyCompatible"
               },
               "dependencies": {
                 "debug": {
                   "version": "2.6.9",
                   "resolved": "https://registry.npmjs.org/debug/-/debug-2.6.9.tgz",
                   "integrity": "sha512-bC7ElrdJaJnPbAP+1EotYvqZsb3ecl5wi6Bfi6BJTUcNowp6cvspg0jXznRTKDjm/E7AdgFBVeAPVMNcKGsHMA==",
+                  "dev": true,
+                  "optional": true,
                   "requires": {
                     "ms": "2.0.0"
                   }
                 },
                 "websocket": {
                   "version": "git://github.com/frozeman/WebSocket-Node.git#6c72925e3f8aaaea8dc8450f97627e85263999f2",
-                  "from": "git://github.com/frozeman/WebSocket-Node.git#6c72925e3f8aaaea8dc8450f97627e85263999f2",
+                  "from": "git://github.com/frozeman/WebSocket-Node.git#browserifyCompatible",
+                  "dev": true,
+                  "optional": true,
                   "requires": {
                     "debug": "^2.2.0",
                     "nan": "^2.3.3",
@@ -7332,7 +7389,8 @@ },
             "yaeti": {
               "version": "0.0.6",
               "resolved": "https://registry.npmjs.org/yaeti/-/yaeti-0.0.6.tgz",
-              "integrity": "sha1-8m9ITXJoTPQr7ft2lwqhYI+/lXc="
+              "integrity": "sha1-8m9ITXJoTPQr7ft2lwqhYI+/lXc=",
+              "dev": true
             },
             "yargs": {
               "version": "4.8.1",

@@ -26,6 +26,7 @@ "license": "GPL-3.0",
   "dependencies": {
     "blake-hash": "^1.1.0",
     "snarkjs": "0.1.11",
+    "typedarray-to-buffer": "^3.1.5",
     "web3": "^1.0.0-beta.36"
   },
   "devDependencies": {

@@ -22,8 +22,14 @@ const cta = bigInt("168700");
     const d = bigInt("168696");
 
     const res = [];
-    res[0] = bigInt((a[0]*b[1] + b[0]*a[1]) *  bigInt(bigInt("1") + d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
+
+    /* does the equivalent of:
+     res[0] = bigInt((a[0]*b[1] + b[0]*a[1]) *  bigInt(bigInt("1") + d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
     res[1] = bigInt((a[1]*b[1] - cta*a[0]*b[0]) * bigInt(bigInt("1") - d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
+    */
+    res[0] = bigInt((bigInt(a[0]).mul(b[1]).add(bigInt(b[0]).mul(a[1]))).mul(bigInt(bigInt("1").add(d.mul(a[0]).mul(b[0]).mul(a[1]).mul(b[1]))).inverse(q))).affine(q);
+    res[1] = bigInt((bigInt(a[1]).mul(b[1]).sub(cta.mul(a[0]).mul(b[0]))).mul(bigInt(bigInt("1").sub(d.mul(a[0]).mul(b[0]).mul(a[1]).mul(b[1]))).inverse(q))).affine(q);
+
     return res;
 }
 

@@ -3,10 +3,12 @@ const path = require("path");
 const snarkjs = require("snarkjs");
 const compiler = require("circom");
 
-const assert = chai.assert;
+const createBlakeHash = require("blake-hash");
+const eddsa = require("../src/eddsa.js");
 
-const bigInt = require("big-integer");
+const assert = chai.assert;
 
+const bigInt = require("snarkjs").bigInt;
 
 describe("Baby Jub test", function () {
     let circuitAdd;
@@ -22,6 +24,11 @@
         const cirDefTest = await compiler(path.join(__dirname, "circuits", "babycheck_test.circom"));
         circuitTest = new snarkjs.Circuit(cirDefTest);
         console.log("NConstrains BabyTest: " + circuitTest.nConstraints);
+
+        const cirDefPbk = await compiler(path.join(__dirname, "circuits", "babypbk_test.circom"));
+        circuitPbk = new snarkjs.Circuit(cirDefPbk);
+        console.log("NConstrains BabyPbk: " + circuitPbk.nConstraints);
+
     });
 
     it("Should add point (0,1) and (0,1)", async () => {
@@ -95,6 +102,24 @@ assert(false, "Should be a valid point");
         } catch(err) {
             assert.equal(err.message, "Constraint doesn't match: 168700 != 1");
         }
+    });
+
+    it("Should extract the public key from the private one", async () => {    
+
+        const rawpvk = Buffer.from("0001020304050607080900010203040506070809000102030405060708090021", "hex");
+        const pvk    = eddsa.pruneBuffer(createBlakeHash("blake512").update(rawpvk).digest().slice(0,32));
+        const S      = bigInt.leBuff2int(pvk).shr(3);
+
+        const A      = eddsa.prv2pub(rawpvk);
+
+        const input = {
+            in : S,
+            Ax : A[0],
+            Ay : A[1]
+        }
+
+        const w = circuitPbk.calculateWitness(input);
+        assert(circuitPbk.checkWitness(w));
     });
 
 });

@@ -0,0 +1,3 @@
+include "../../circuits/babyjub.circom";
+
+component main = BabyPbk();