From 4c2ccc0882471d67829667d28e778864d1cd6b64 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Fri, 12 Jul 2024 09:15:53 +0000
Subject: [PATCH 01/11] feat: Point::fromXandSign(...)

---
 .../ecc/curves/grumpkin/c_bind.cpp            |  8 +++++
 yarn-project/foundation/src/fields/fields.ts  |  8 +++++
 yarn-project/foundation/src/fields/point.ts   | 31 +++++++++++++++++++
 3 files changed, 47 insertions(+)

diff --git a/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp b/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
index 78bb4a04fc54..a989d45f5c6b 100644
--- a/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
+++ b/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
@@ -63,4 +63,12 @@ WASM_EXPORT void ecc_grumpkin__reduce512_buffer_mod_circuit_modulus(uint8_t* inp
     write(result, target_output.lo);
 }
 
+WASM_EXPORT void grumpkin_fr_sqrt(uint8_t const* field_buf, uint8_t* result)
+{
+    using serialize::write;
+    auto fr = from_buffer<grumpkin::fr>(field_buf);
+    auto [is_sqr, root] = fr.sqrt();
+    write(result, root);
+}
+
 // NOLINTEND(cert-dcl37-c, cert-dcl51-cpp, bugprone-reserved-identifier)
\ No newline at end of file
diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index 436003adbfda..587c590fef07 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -4,6 +4,7 @@ import { toBigIntBE, toBufferBE } from '../bigint-buffer/index.js';
 import { randomBytes } from '../crypto/random/index.js';
 import { BufferReader } from '../serialize/buffer_reader.js';
 import { TypeRegistry } from '../serialize/type_registry.js';
+import { BarretenbergSync } from '@aztec/bb.js';
 
 const ZERO_BUFFER = Buffer.alloc(32);
 
@@ -280,6 +281,13 @@ export class Fr extends BaseField {
     return new Fr(this.toBigInt() / rhs.toBigInt());
   }
 
+  sqrt() {
+    const wasm = BarretenbergSync.getSingleton().getWasm();
+    wasm.writeMemory(0, this.toBuffer());
+    wasm.call('grumpkin_fr_sqrt', 0, Fr.SIZE_IN_BYTES);
+    return Fr.fromBuffer(Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES, Fr.SIZE_IN_BYTES * 2)));
+  }
+
   toJSON() {
     return {
       type: 'Fr',
diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index 26c84d88ec06..846bed5bcc7e 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -78,6 +78,37 @@ export class Point {
     return new this(reader.readField(), reader.readField(), reader.readBoolean());
   }
 
+  /**
+   * Uses the x coordinate and isPositive flag (+/-) to reconstruct the point.
+   * @dev The y coordinate can be derived from the x coordinate and the sign flag by solving the grumpkin curve
+   * equation for y.
+   * @param x - The x coordinate of the point
+   * @param sign - The sign of the y coordinate
+   * @returns The point as an array of 2 fields
+   */
+  static fromXAndSign(x: Fr, sign: boolean) {
+    // Define the constant A for the Grumpkin curve equation (y^2 = x^3 - A)
+    const A = new Fr(17);
+
+    // Calculate y^2 = x^3 - 17
+    const ySquared = x.square().mul(x).sub(A)
+
+    // Calculate the square root of ySquared
+    const y = ySquared.sqrt();
+
+    // If y is null, the x-coordinate is not on the curve
+    if (y === null) {
+      throw new Error('The given x-coordinate is not on the Grumpkin curve');
+    }
+
+    // Choose the positive or negative root based on isPositive
+    // const finalY = sign ? y : y.neg();
+    const finalY = y;
+
+    // Create and return the new Point
+    return new this(x, finalY, false);
+  }
+
   /**
    * Returns the contents of the point as BigInts.
    * @returns The point as BigInts

From 3e7f425ccbc51a08d077d6bbf7ec37df2935ef87 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Fri, 12 Jul 2024 10:32:58 +0000
Subject: [PATCH 02/11] WIP

---
 yarn-project/foundation/src/fields/fields.ts    |  3 ++-
 .../foundation/src/fields/point.test.ts         | 17 +++++++++++++++++
 yarn-project/foundation/src/fields/point.ts     | 17 ++++++++++++++---
 3 files changed, 33 insertions(+), 4 deletions(-)
 create mode 100644 yarn-project/foundation/src/fields/point.test.ts

diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index 587c590fef07..54abae530133 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -1,10 +1,11 @@
+import { BarretenbergSync } from '@aztec/bb.js';
+
 import { inspect } from 'util';
 
 import { toBigIntBE, toBufferBE } from '../bigint-buffer/index.js';
 import { randomBytes } from '../crypto/random/index.js';
 import { BufferReader } from '../serialize/buffer_reader.js';
 import { TypeRegistry } from '../serialize/type_registry.js';
-import { BarretenbergSync } from '@aztec/bb.js';
 
 const ZERO_BUFFER = Buffer.alloc(32);
 
diff --git a/yarn-project/foundation/src/fields/point.test.ts b/yarn-project/foundation/src/fields/point.test.ts
new file mode 100644
index 000000000000..f71a2a1cbec2
--- /dev/null
+++ b/yarn-project/foundation/src/fields/point.test.ts
@@ -0,0 +1,17 @@
+import { Fr } from './fields.js';
+import { Point } from './point.js';
+
+describe('Point', () => {
+  it('converts to and from x and sign of y coordinate', () => {
+    const p = new Point(
+      new Fr(0x30426e64aee30e998c13c8ceecda3a77807dbead52bc2f3bf0eae851b4b710c1n),
+      new Fr(0x113156a068f603023240c96b4da5474667db3b8711c521c748212a15bc034ea6n),
+      false,
+    );
+
+    const [x, sign] = p.toXAndSign();
+    const p2 = Point.fromXAndSign(x, sign);
+
+    expect(p.equals(p2)).toBeTruthy();
+  });
+});
diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index 846bed5bcc7e..8faacd3fe0b9 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -91,7 +91,7 @@ export class Point {
     const A = new Fr(17);
 
     // Calculate y^2 = x^3 - 17
-    const ySquared = x.square().mul(x).sub(A)
+    const ySquared = x.square().mul(x).sub(A);
 
     // Calculate the square root of ySquared
     const y = ySquared.sqrt();
@@ -101,14 +101,25 @@ export class Point {
       throw new Error('The given x-coordinate is not on the Grumpkin curve');
     }
 
+    const yPositiveBigInt = y.toBigInt() > (Fr.MODULUS - 1n) / 2n ? Fr.MODULUS - y.toBigInt() : y.toBigInt();
+    const yNegativeBigInt = Fr.MODULUS - yPositiveBigInt;
+
     // Choose the positive or negative root based on isPositive
-    // const finalY = sign ? y : y.neg();
-    const finalY = y;
+    const finalY = sign ? new Fr(yPositiveBigInt) : new Fr(yNegativeBigInt);
 
     // Create and return the new Point
     return new this(x, finalY, false);
   }
 
+  /**
+   * Returns the x coordinate and the sign of the y coordinate.
+   * @dev The y sign can be determined by checking if the y coordinate is greater than half of the modulus.
+   * @returns The x coordinate and the sign of the y coordinate.
+   */
+  toXAndSign(): [Fr, boolean] {
+    return [this.x, this.y.toBigInt() <= (Fr.MODULUS - 1n) / 2n];
+  }
+
   /**
    * Returns the contents of the point as BigInts.
    * @returns The point as BigInts

From fb5aa8b1831d41f89e33b527ef216cf121e41d21 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Fri, 12 Jul 2024 11:23:34 +0000
Subject: [PATCH 03/11] WIP

---
 .../barretenberg/ecc/curves/grumpkin/c_bind.cpp   | 13 +++++++++----
 yarn-project/foundation/src/fields/fields.test.ts | 12 +++++++++++-
 yarn-project/foundation/src/fields/fields.ts      | 15 +++++++++++++--
 3 files changed, 33 insertions(+), 7 deletions(-)

diff --git a/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp b/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
index a989d45f5c6b..b206430a3f33 100644
--- a/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
+++ b/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
@@ -63,12 +63,17 @@ WASM_EXPORT void ecc_grumpkin__reduce512_buffer_mod_circuit_modulus(uint8_t* inp
     write(result, target_output.lo);
 }
 
-WASM_EXPORT void grumpkin_fr_sqrt(uint8_t const* field_buf, uint8_t* result)
+WASM_EXPORT void grumpkin_fr_sqrt(uint8_t const* input, uint8_t* result)
 {
     using serialize::write;
-    auto fr = from_buffer<grumpkin::fr>(field_buf);
-    auto [is_sqr, root] = fr.sqrt();
-    write(result, root);
+    auto input_fr = from_buffer<grumpkin::fr>(input);
+    auto [is_sqr, root] = input_fr.sqrt();
+
+    uint8_t* is_sqrt_result_ptr = result;
+    uint8_t* root_result_ptr = result + 1;
+
+    write(is_sqrt_result_ptr, is_sqr);
+    write(root_result_ptr, root);
 }
 
 // NOLINTEND(cert-dcl37-c, cert-dcl51-cpp, bugprone-reserved-identifier)
\ No newline at end of file
diff --git a/yarn-project/foundation/src/fields/fields.test.ts b/yarn-project/foundation/src/fields/fields.test.ts
index 2f8686bb4c5b..d1a728e67d77 100644
--- a/yarn-project/foundation/src/fields/fields.test.ts
+++ b/yarn-project/foundation/src/fields/fields.test.ts
@@ -109,7 +109,7 @@ describe('Bn254 arithmetic', () => {
       expect(actual).toEqual(expected);
     });
 
-    it('High Bonudary', () => {
+    it('High Boundary', () => {
       // -1 - (-1) = 0
       const a = new Fr(Fr.MODULUS - 1n);
       const b = new Fr(Fr.MODULUS - 1n);
@@ -184,6 +184,16 @@ describe('Bn254 arithmetic', () => {
     });
   });
 
+  describe('Square root', () => {
+    it('Should return the correct square root', () => {
+      const a = new Fr(16);
+      const expected = new Fr(4);
+
+      const actual = a.sqrt();
+      expect(actual).toEqual(expected);
+    });
+  });
+
   describe('Comparison', () => {
     it.each([
       [new Fr(5), new Fr(10), -1],
diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index 54abae530133..a27b5fad26a3 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -282,11 +282,22 @@ export class Fr extends BaseField {
     return new Fr(this.toBigInt() / rhs.toBigInt());
   }
 
-  sqrt() {
+  /**
+   * Computes the square root of the field element.
+   * @returns The square root of the field element if it exists (undefined if not).
+   */
+  sqrt(): Fr | undefined {
     const wasm = BarretenbergSync.getSingleton().getWasm();
     wasm.writeMemory(0, this.toBuffer());
     wasm.call('grumpkin_fr_sqrt', 0, Fr.SIZE_IN_BYTES);
-    return Fr.fromBuffer(Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES, Fr.SIZE_IN_BYTES * 2)));
+    const isSqrtBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES, Fr.SIZE_IN_BYTES + 1));
+    const isSqrt = isSqrtBuf[0] === 1;
+    if (!isSqrt) {
+      return undefined;
+    }
+
+    const rootBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES + 1, Fr.SIZE_IN_BYTES * 2 + 1))
+    return Fr.fromBuffer(rootBuf);
   }
 
   toJSON() {

From 0f71bb70ba5d7fd6a10c00dfd4f4c84143e3cf50 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Fri, 12 Jul 2024 12:53:59 +0000
Subject: [PATCH 04/11] WIP

---
 yarn-project/foundation/src/fields/fields.ts | 7 ++++---
 yarn-project/foundation/src/fields/point.ts  | 5 +----
 2 files changed, 5 insertions(+), 7 deletions(-)

diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index a27b5fad26a3..7718d9d0abc4 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -284,16 +284,17 @@ export class Fr extends BaseField {
 
   /**
    * Computes the square root of the field element.
-   * @returns The square root of the field element if it exists (undefined if not).
+   * @returns The square root of the field element (null if it does not exist).
    */
-  sqrt(): Fr | undefined {
+  sqrt(): Fr | null {
     const wasm = BarretenbergSync.getSingleton().getWasm();
     wasm.writeMemory(0, this.toBuffer());
     wasm.call('grumpkin_fr_sqrt', 0, Fr.SIZE_IN_BYTES);
     const isSqrtBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES, Fr.SIZE_IN_BYTES + 1));
     const isSqrt = isSqrtBuf[0] === 1;
     if (!isSqrt) {
-      return undefined;
+      // Field element is not a quadratic residue mod p so it has no square root.
+      return null;
     }
 
     const rootBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES + 1, Fr.SIZE_IN_BYTES * 2 + 1))
diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index 8faacd3fe0b9..4d42af83795f 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -87,11 +87,8 @@ export class Point {
    * @returns The point as an array of 2 fields
    */
   static fromXAndSign(x: Fr, sign: boolean) {
-    // Define the constant A for the Grumpkin curve equation (y^2 = x^3 - A)
-    const A = new Fr(17);
-
     // Calculate y^2 = x^3 - 17
-    const ySquared = x.square().mul(x).sub(A);
+    const ySquared = x.square().mul(x).sub(new Fr(17));
 
     // Calculate the square root of ySquared
     const y = ySquared.sqrt();

From 606e3af2d16d631aab74d3827209378958d6e2e3 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 10:30:01 +0000
Subject: [PATCH 05/11] WIP

---
 .../barretenberg/ecc/curves/bn254/c_bind.cpp  | 33 +++++++++++++++++++
 .../ecc/curves/grumpkin/c_bind.cpp            | 13 --------
 .../foundation/src/fields/fields.test.ts      | 20 +++++++----
 yarn-project/foundation/src/fields/fields.ts  | 31 ++++++++++++++---
 4 files changed, 74 insertions(+), 23 deletions(-)
 create mode 100644 barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp

diff --git a/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp b/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp
new file mode 100644
index 000000000000..85070ee080f1
--- /dev/null
+++ b/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp
@@ -0,0 +1,33 @@
+#include "../bn254/fq.hpp"
+#include "../bn254/fr.hpp"
+#include "barretenberg/common/wasm_export.hpp"
+
+using namespace bb;
+
+WASM_EXPORT void bn254_fr_sqrt(uint8_t const* input, uint8_t* result)
+{
+    using serialize::write;
+    auto input_fr = from_buffer<bb::fr>(input);
+    auto [is_sqr, root] = input_fr.sqrt();
+
+    uint8_t* is_sqrt_result_ptr = result;
+    uint8_t* root_result_ptr = result + 1;
+
+    write(is_sqrt_result_ptr, is_sqr);
+    write(root_result_ptr, root);
+}
+
+WASM_EXPORT void bn254_fq_sqrt(uint8_t const* input, uint8_t* result)
+{
+    using serialize::write;
+    auto input_fq = from_buffer<bb::fq>(input);
+    auto [is_sqr, root] = input_fq.sqrt();
+
+    uint8_t* is_sqrt_result_ptr = result;
+    uint8_t* root_result_ptr = result + 1;
+
+    write(is_sqrt_result_ptr, is_sqr);
+    write(root_result_ptr, root);
+}
+
+// NOLINTEND(cert-dcl37-c, cert-dcl51-cpp, bugprone-reserved-identifier)
\ No newline at end of file
diff --git a/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp b/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
index b206430a3f33..78bb4a04fc54 100644
--- a/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
+++ b/barretenberg/cpp/src/barretenberg/ecc/curves/grumpkin/c_bind.cpp
@@ -63,17 +63,4 @@ WASM_EXPORT void ecc_grumpkin__reduce512_buffer_mod_circuit_modulus(uint8_t* inp
     write(result, target_output.lo);
 }
 
-WASM_EXPORT void grumpkin_fr_sqrt(uint8_t const* input, uint8_t* result)
-{
-    using serialize::write;
-    auto input_fr = from_buffer<grumpkin::fr>(input);
-    auto [is_sqr, root] = input_fr.sqrt();
-
-    uint8_t* is_sqrt_result_ptr = result;
-    uint8_t* root_result_ptr = result + 1;
-
-    write(is_sqrt_result_ptr, is_sqr);
-    write(root_result_ptr, root);
-}
-
 // NOLINTEND(cert-dcl37-c, cert-dcl51-cpp, bugprone-reserved-identifier)
\ No newline at end of file
diff --git a/yarn-project/foundation/src/fields/fields.test.ts b/yarn-project/foundation/src/fields/fields.test.ts
index d1a728e67d77..bd31319bcc83 100644
--- a/yarn-project/foundation/src/fields/fields.test.ts
+++ b/yarn-project/foundation/src/fields/fields.test.ts
@@ -1,4 +1,4 @@
-import { Fr, GrumpkinScalar } from './fields.js';
+import { Fq, Fr, GrumpkinScalar } from './fields.js';
 
 describe('GrumpkinScalar Serialization', () => {
   // Test case for GrumpkinScalar.fromHighLow
@@ -185,12 +185,20 @@ describe('Bn254 arithmetic', () => {
   });
 
   describe('Square root', () => {
-    it('Should return the correct square root', () => {
-      const a = new Fr(16);
-      const expected = new Fr(4);
+    it('Should return the correct square root for Fr', () => {
+      const a = Fr.random();
+      const squared = a.mul(a);
 
-      const actual = a.sqrt();
-      expect(actual).toEqual(expected);
+      const actual = squared.sqrt();
+      expect(actual!.mul(actual!)).toEqual(squared);
+    });
+
+    it('Should return the correct square root for Fq', () => {
+      const a = Fq.random();
+      const squared = a.mul(a);
+
+      const actual = squared.sqrt();
+      expect(actual!.mul(actual!)).toEqual(squared);
     });
   });
 
diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index 7718d9d0abc4..c84b547cf3ef 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -283,13 +283,13 @@ export class Fr extends BaseField {
   }
 
   /**
-   * Computes the square root of the field element.
-   * @returns The square root of the field element (null if it does not exist).
+   * Computes a square root of the field element.
+   * @returns A square root of the field element (null if it does not exist).
    */
   sqrt(): Fr | null {
     const wasm = BarretenbergSync.getSingleton().getWasm();
     wasm.writeMemory(0, this.toBuffer());
-    wasm.call('grumpkin_fr_sqrt', 0, Fr.SIZE_IN_BYTES);
+    wasm.call('bn254_fr_sqrt', 0, Fr.SIZE_IN_BYTES);
     const isSqrtBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES, Fr.SIZE_IN_BYTES + 1));
     const isSqrt = isSqrtBuf[0] === 1;
     if (!isSqrt) {
@@ -297,7 +297,7 @@ export class Fr extends BaseField {
       return null;
     }
 
-    const rootBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES + 1, Fr.SIZE_IN_BYTES * 2 + 1))
+    const rootBuf = Buffer.from(wasm.getMemorySlice(Fr.SIZE_IN_BYTES + 1, Fr.SIZE_IN_BYTES * 2 + 1));
     return Fr.fromBuffer(rootBuf);
   }
 
@@ -380,6 +380,29 @@ export class Fq extends BaseField {
     return new Fq((high.toBigInt() << Fq.HIGH_SHIFT) + low.toBigInt());
   }
 
+  mul(rhs: Fq) {
+    return new Fq((this.toBigInt() * rhs.toBigInt()) % Fq.MODULUS);
+  }
+
+  /**
+   * Computes a square root of the field element.
+   * @returns A square root of the field element (null if it does not exist).
+   */
+  sqrt(): Fq | null {
+    const wasm = BarretenbergSync.getSingleton().getWasm();
+    wasm.writeMemory(0, this.toBuffer());
+    wasm.call('bn254_fq_sqrt', 0, Fq.SIZE_IN_BYTES);
+    const isSqrtBuf = Buffer.from(wasm.getMemorySlice(Fq.SIZE_IN_BYTES, Fq.SIZE_IN_BYTES + 1));
+    const isSqrt = isSqrtBuf[0] === 1;
+    if (!isSqrt) {
+      // Field element is not a quadratic residue mod p so it has no square root.
+      return null;
+    }
+
+    const rootBuf = Buffer.from(wasm.getMemorySlice(Fq.SIZE_IN_BYTES + 1, Fq.SIZE_IN_BYTES * 2 + 1));
+    return Fq.fromBuffer(rootBuf);
+  }
+
   toJSON() {
     return {
       type: 'Fq',

From 35b69c9c39558fea8a359e8a9a6ffb0c90083f06 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 10:41:24 +0000
Subject: [PATCH 06/11] cleanup

---
 .../barretenberg/ecc/curves/bn254/c_bind.cpp  | 14 -----------
 .../foundation/src/fields/fields.test.ts      | 12 ++--------
 yarn-project/foundation/src/fields/fields.ts  | 23 -------------------
 3 files changed, 2 insertions(+), 47 deletions(-)

diff --git a/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp b/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp
index 85070ee080f1..bf0807a4e68e 100644
--- a/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp
+++ b/barretenberg/cpp/src/barretenberg/ecc/curves/bn254/c_bind.cpp
@@ -1,4 +1,3 @@
-#include "../bn254/fq.hpp"
 #include "../bn254/fr.hpp"
 #include "barretenberg/common/wasm_export.hpp"
 
@@ -17,17 +16,4 @@ WASM_EXPORT void bn254_fr_sqrt(uint8_t const* input, uint8_t* result)
     write(root_result_ptr, root);
 }
 
-WASM_EXPORT void bn254_fq_sqrt(uint8_t const* input, uint8_t* result)
-{
-    using serialize::write;
-    auto input_fq = from_buffer<bb::fq>(input);
-    auto [is_sqr, root] = input_fq.sqrt();
-
-    uint8_t* is_sqrt_result_ptr = result;
-    uint8_t* root_result_ptr = result + 1;
-
-    write(is_sqrt_result_ptr, is_sqr);
-    write(root_result_ptr, root);
-}
-
 // NOLINTEND(cert-dcl37-c, cert-dcl51-cpp, bugprone-reserved-identifier)
\ No newline at end of file
diff --git a/yarn-project/foundation/src/fields/fields.test.ts b/yarn-project/foundation/src/fields/fields.test.ts
index bd31319bcc83..2813be152a02 100644
--- a/yarn-project/foundation/src/fields/fields.test.ts
+++ b/yarn-project/foundation/src/fields/fields.test.ts
@@ -1,4 +1,4 @@
-import { Fq, Fr, GrumpkinScalar } from './fields.js';
+import { Fr, GrumpkinScalar } from './fields.js';
 
 describe('GrumpkinScalar Serialization', () => {
   // Test case for GrumpkinScalar.fromHighLow
@@ -185,21 +185,13 @@ describe('Bn254 arithmetic', () => {
   });
 
   describe('Square root', () => {
-    it('Should return the correct square root for Fr', () => {
+    it('Should return the correct square root', () => {
       const a = Fr.random();
       const squared = a.mul(a);
 
       const actual = squared.sqrt();
       expect(actual!.mul(actual!)).toEqual(squared);
     });
-
-    it('Should return the correct square root for Fq', () => {
-      const a = Fq.random();
-      const squared = a.mul(a);
-
-      const actual = squared.sqrt();
-      expect(actual!.mul(actual!)).toEqual(squared);
-    });
   });
 
   describe('Comparison', () => {
diff --git a/yarn-project/foundation/src/fields/fields.ts b/yarn-project/foundation/src/fields/fields.ts
index c84b547cf3ef..5fa3c9cac295 100644
--- a/yarn-project/foundation/src/fields/fields.ts
+++ b/yarn-project/foundation/src/fields/fields.ts
@@ -380,29 +380,6 @@ export class Fq extends BaseField {
     return new Fq((high.toBigInt() << Fq.HIGH_SHIFT) + low.toBigInt());
   }
 
-  mul(rhs: Fq) {
-    return new Fq((this.toBigInt() * rhs.toBigInt()) % Fq.MODULUS);
-  }
-
-  /**
-   * Computes a square root of the field element.
-   * @returns A square root of the field element (null if it does not exist).
-   */
-  sqrt(): Fq | null {
-    const wasm = BarretenbergSync.getSingleton().getWasm();
-    wasm.writeMemory(0, this.toBuffer());
-    wasm.call('bn254_fq_sqrt', 0, Fq.SIZE_IN_BYTES);
-    const isSqrtBuf = Buffer.from(wasm.getMemorySlice(Fq.SIZE_IN_BYTES, Fq.SIZE_IN_BYTES + 1));
-    const isSqrt = isSqrtBuf[0] === 1;
-    if (!isSqrt) {
-      // Field element is not a quadratic residue mod p so it has no square root.
-      return null;
-    }
-
-    const rootBuf = Buffer.from(wasm.getMemorySlice(Fq.SIZE_IN_BYTES + 1, Fq.SIZE_IN_BYTES * 2 + 1));
-    return Fq.fromBuffer(rootBuf);
-  }
-
   toJSON() {
     return {
       type: 'Fq',

From 918cebc45a07da550da527e7eaef8137f4a4ab51 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 10:56:55 +0000
Subject: [PATCH 07/11] fixing Point.random

---
 yarn-project/foundation/src/crypto/random/index.ts | 9 +++++++++
 yarn-project/foundation/src/fields/point.test.ts   | 4 ++++
 yarn-project/foundation/src/fields/point.ts        | 5 ++---
 3 files changed, 15 insertions(+), 3 deletions(-)

diff --git a/yarn-project/foundation/src/crypto/random/index.ts b/yarn-project/foundation/src/crypto/random/index.ts
index a64dc4f4a957..76ee5a9a6a9b 100644
--- a/yarn-project/foundation/src/crypto/random/index.ts
+++ b/yarn-project/foundation/src/crypto/random/index.ts
@@ -74,3 +74,12 @@ export const randomBigInt = (max: bigint) => {
   const randomBigInt = BigInt(`0x${randomBuffer.toString('hex')}`); // Convert buffer to a large integer.
   return randomBigInt % max; // Use modulo to ensure the result is less than max.
 };
+
+/**
+ * Generate a random boolean value.
+ * @returns A random boolean value.
+ */
+export const randomBoolean = () => {
+  const randomByte = randomBytes(1)[0]; // Generate a single random byte.
+  return randomByte % 2 === 0; // Use modulo to determine if the byte is even or odd.
+};
diff --git a/yarn-project/foundation/src/fields/point.test.ts b/yarn-project/foundation/src/fields/point.test.ts
index f71a2a1cbec2..48d452a16ade 100644
--- a/yarn-project/foundation/src/fields/point.test.ts
+++ b/yarn-project/foundation/src/fields/point.test.ts
@@ -14,4 +14,8 @@ describe('Point', () => {
 
     expect(p.equals(p2)).toBeTruthy();
   });
+
+  it('creates a valid random point', () => {
+    expect(Point.random().isOnGrumpkin()).toBeTruthy();
+  });
 });
diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index 4d42af83795f..faf5fbb7efad 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -1,4 +1,4 @@
-import { poseidon2Hash } from '../crypto/index.js';
+import { poseidon2Hash, randomBoolean } from '../crypto/index.js';
 import { BufferReader, FieldReader, serializeToBuffer } from '../serialize/index.js';
 import { Fr } from './fields.js';
 
@@ -37,8 +37,7 @@ export class Point {
    * @returns A randomly generated Point instance.
    */
   static random() {
-    // TODO make this return an actual point on curve.
-    return new Point(Fr.random(), Fr.random(), false);
+    return Point.fromXAndSign(Fr.random(), randomBoolean());
   }
 
   /**

From 26cbf19eaedb456d5609432715f0f542bdf99ced Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 12:36:29 +0000
Subject: [PATCH 08/11] WIP

---
 .../foundation/src/fields/point.test.ts       | 14 ++++++++
 yarn-project/foundation/src/fields/point.ts   | 33 ++++++++++++++++++-
 2 files changed, 46 insertions(+), 1 deletion(-)

diff --git a/yarn-project/foundation/src/fields/point.test.ts b/yarn-project/foundation/src/fields/point.test.ts
index 48d452a16ade..6fa64160b414 100644
--- a/yarn-project/foundation/src/fields/point.test.ts
+++ b/yarn-project/foundation/src/fields/point.test.ts
@@ -18,4 +18,18 @@ describe('Point', () => {
   it('creates a valid random point', () => {
     expect(Point.random().isOnGrumpkin()).toBeTruthy();
   });
+
+  it('converts to and from buffer', () => {
+    const p = Point.random();
+    const p2 = Point.fromBuffer(p.toBuffer());
+
+    expect(p.equals(p2)).toBeTruthy();
+  });
+
+  it('converts to and from compressed buffer', () => {
+    const p = Point.random();
+    const p2 = Point.fromCompressedBuffer(p.toCompressedBuffer());
+
+    expect(p.equals(p2)).toBeTruthy();
+  });
 });
diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index faf5fbb7efad..3c4d197d617d 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -10,6 +10,7 @@ import { Fr } from './fields.js';
 export class Point {
   static ZERO = new Point(Fr.ZERO, Fr.ZERO, false);
   static SIZE_IN_BYTES = Fr.SIZE_IN_BYTES * 2;
+  static COMPRESSED_SIZE_IN_BYTES = Fr.SIZE_IN_BYTES + 1;
 
   /** Used to differentiate this class from AztecAddress */
   public readonly kind = 'point';
@@ -37,7 +38,17 @@ export class Point {
    * @returns A randomly generated Point instance.
    */
   static random() {
-    return Point.fromXAndSign(Fr.random(), randomBoolean());
+    while (true) {
+      try {
+        return Point.fromXAndSign(Fr.random(), randomBoolean());
+      } catch (e: any) {
+        if (e.message !== 'The given x-coordinate is not on the Grumpkin curve') {
+          throw e;
+        }
+        // The random point is not on the curve - we try again
+        continue;
+      }
+    }
   }
 
   /**
@@ -52,6 +63,18 @@ export class Point {
     return new this(Fr.fromBuffer(reader), Fr.fromBuffer(reader), false);
   }
 
+  /**
+   * Create a Point instance from a compressed buffer.
+   * The input 'buffer' should have exactly 33 bytes representing the x coordinate and the sign of the y coordinate.
+   *
+   * @param buffer - The buffer containing the x coordinate and the sign of the y coordinate.
+   * @returns A Point instance.
+   */
+  static fromCompressedBuffer(buffer: Buffer | BufferReader) {
+    const reader = BufferReader.asReader(buffer);
+    return this.fromXAndSign(Fr.fromBuffer(reader), reader.readBoolean());
+  }
+
   /**
    * Create a Point instance from a hex-encoded string.
    * The input 'address' should be prefixed with '0x' or not, and have exactly 128 hex characters representing the x and y coordinates.
@@ -149,6 +172,14 @@ export class Point {
     return buf;
   }
 
+  /**
+   * Converts the Point instance to a compressed Buffer representation of the coordinates.
+   * @returns A Buffer representation of the Point instance
+   */
+  toCompressedBuffer() {
+    return serializeToBuffer(this.toXAndSign());
+  }
+
   /**
    * Convert the Point instance to a hexadecimal string representation.
    * The output string is prefixed with '0x' and consists of exactly 128 hex characters,

From 18fdcc822d387b69a54ee6f6e634c6db17be3184 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 12:38:47 +0000
Subject: [PATCH 09/11] WIP

---
 yarn-project/foundation/src/fields/point.ts | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index 3c4d197d617d..d8be2ae78c63 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -42,7 +42,7 @@ export class Point {
       try {
         return Point.fromXAndSign(Fr.random(), randomBoolean());
       } catch (e: any) {
-        if (e.message !== 'The given x-coordinate is not on the Grumpkin curve') {
+        if (!(e instanceof NotOnCurveError)) {
           throw e;
         }
         // The random point is not on the curve - we try again
@@ -117,7 +117,7 @@ export class Point {
 
     // If y is null, the x-coordinate is not on the curve
     if (y === null) {
-      throw new Error('The given x-coordinate is not on the Grumpkin curve');
+      throw new NotOnCurveError();
     }
 
     const yPositiveBigInt = y.toBigInt() > (Fr.MODULUS - 1n) / 2n ? Fr.MODULUS - y.toBigInt() : y.toBigInt();
@@ -263,3 +263,10 @@ export function isPoint(obj: object): obj is Point {
   const point = obj as Point;
   return point.kind === 'point' && point.x !== undefined && point.y !== undefined;
 }
+
+class NotOnCurveError extends Error {
+  constructor() {
+    super('The given x-coordinate is not on the Grumpkin curve');
+    this.name = 'NotOnCurveError';
+  }
+}

From 140429af51828f9ddab603ec16e22b1a33c44bd2 Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 18:26:40 +0000
Subject: [PATCH 10/11] more tests

---
 .../foundation/src/fields/fields.test.ts         | 16 +++++++++++++++-
 1 file changed, 15 insertions(+), 1 deletion(-)

diff --git a/yarn-project/foundation/src/fields/fields.test.ts b/yarn-project/foundation/src/fields/fields.test.ts
index 2813be152a02..f07db9fe8992 100644
--- a/yarn-project/foundation/src/fields/fields.test.ts
+++ b/yarn-project/foundation/src/fields/fields.test.ts
@@ -185,7 +185,21 @@ describe('Bn254 arithmetic', () => {
   });
 
   describe('Square root', () => {
-    it('Should return the correct square root', () => {
+    it.each([
+      [new Fr(0), 0n],
+      [new Fr(4), 2n],
+      [new Fr(9), 3n],
+      [new Fr(16), 4n],
+    ])('Should return the correct square root for %p', (input, expected) => {
+      const actual = input.sqrt()!.toBigInt();
+
+      // The square root can be either the expected value or the modulus - expected value
+      const isValid = actual == expected || actual == Fr.MODULUS - expected;
+
+      expect(isValid).toBeTruthy();
+    });
+
+    it('Should return the correct square root for random value', () => {
       const a = Fr.random();
       const squared = a.mul(a);
 

From 46db3deafc5247e627e79cf19d5572cfd6dd071c Mon Sep 17 00:00:00 2001
From: benesjan <janbenes1234@gmail.com>
Date: Mon, 15 Jul 2024 18:29:28 +0000
Subject: [PATCH 11/11] more docs

---
 yarn-project/foundation/src/fields/point.ts | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/yarn-project/foundation/src/fields/point.ts b/yarn-project/foundation/src/fields/point.ts
index d8be2ae78c63..3bcf4a00ede1 100644
--- a/yarn-project/foundation/src/fields/point.ts
+++ b/yarn-project/foundation/src/fields/point.ts
@@ -102,10 +102,11 @@ export class Point {
 
   /**
    * Uses the x coordinate and isPositive flag (+/-) to reconstruct the point.
-   * @dev The y coordinate can be derived from the x coordinate and the sign flag by solving the grumpkin curve
+   * @dev The y coordinate can be derived from the x coordinate and the "sign" flag by solving the grumpkin curve
    * equation for y.
    * @param x - The x coordinate of the point
-   * @param sign - The sign of the y coordinate
+   * @param sign - The "sign" of the y coordinate - note that this is not a sign as is known in integer arithmetic.
+   * Instead it is a boolean flag that determines whether the y coordinate is <= (Fr.MODULUS - 1) / 2
    * @returns The point as an array of 2 fields
    */
   static fromXAndSign(x: Fr, sign: boolean) {