diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index e81f1686d..c7079902b 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -86,20 +86,23 @@ public class BigInt internal constructor(
     public operator fun times(b: BigInt): BigInt = when {
         this.sign == 0.toByte() -> ZERO
         b.sign == 0.toByte() -> ZERO
-//          TODO: Karatsuba
+        b.magnitude.size == 1 -> this * b.magnitude[0] * b.sign.toInt()
+        this.magnitude.size == 1 -> b * this.magnitude[0] * this.sign.toInt()
         else -> BigInt((this.sign * b.sign).toByte(), multiplyMagnitudes(this.magnitude, b.magnitude))
     }
 
     public operator fun times(other: UInt): BigInt = when {
         sign == 0.toByte() -> ZERO
         other == 0U -> ZERO
+        other == 1U -> this
         else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
     }
 
-    public operator fun times(other: Int): BigInt = if (other > 0)
-        this * kotlin.math.abs(other).toUInt()
-    else
-        -this * kotlin.math.abs(other).toUInt()
+    public operator fun times(other: Int): BigInt = when {
+        other > 0 -> this * kotlin.math.abs(other).toUInt()
+        other != Int.MIN_VALUE -> -this * kotlin.math.abs(other).toUInt()
+        else -> times(other.toBigInt())
+    }
 
     public operator fun div(other: UInt): BigInt = BigInt(this.sign, divideMagnitudeByUInt(this.magnitude, other))
 
@@ -237,6 +240,7 @@ public class BigInt internal constructor(
         public const val BASE_SIZE: Int = 32
         public val ZERO: BigInt = BigInt(0, uintArrayOf())
         public val ONE: BigInt = BigInt(1, uintArrayOf(1u))
+        private const val KARATSUBA_THRESHOLD = 80
 
         private val hexMapping: HashMap<UInt, String> = hashMapOf(
             0U to "0", 1U to "1", 2U to "2", 3U to "3",
@@ -317,7 +321,16 @@ public class BigInt internal constructor(
             return stripLeadingZeros(result)
         }
 
-        private fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
+        internal fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude = when {
+            mag1.size + mag2.size < KARATSUBA_THRESHOLD || mag1.isEmpty() || mag2.isEmpty() -> naiveMultiplyMagnitudes(
+                mag1,
+                mag2
+            )
+            // TODO implement Fourier
+            else -> karatsubaMultiplyMagnitudes(mag1, mag2)
+        }
+
+        internal fun naiveMultiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
             val resultLength = mag1.size + mag2.size
             val result = Magnitude(resultLength)
 
@@ -336,6 +349,21 @@ public class BigInt internal constructor(
             return stripLeadingZeros(result)
         }
 
+        internal fun karatsubaMultiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude {
+            //https://en.wikipedia.org/wiki/Karatsuba_algorithm
+            val halfSize = min(mag1.size, mag2.size) / 2
+            val x0 = mag1.sliceArray(0 until halfSize).toBigInt(1)
+            val x1 = mag1.sliceArray(halfSize until mag1.size).toBigInt(1)
+            val y0 = mag2.sliceArray(0 until halfSize).toBigInt(1)
+            val y1 = mag2.sliceArray(halfSize until mag2.size).toBigInt(1)
+
+            val z0 = x0 * y0
+            val z2 = x1 * y1
+            val z1 = (x0 + x1) * (y1 + y0) - z0 - z2
+
+            return (z2.shl(2 * halfSize * BASE_SIZE) + z1.shl(halfSize * BASE_SIZE) + z0).magnitude
+        }
+
         private fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude {
             val resultLength = mag.size
             val result = Magnitude(resultLength)
@@ -426,7 +454,7 @@ private val hexChToInt: MutableMap<Char, Int> = hashMapOf(
 public fun String.parseBigInteger(): BigInt? {
     val sign: Int
     val sPositive: String
-
+    //TODO substring = O(n). Can be replaced by some drop that is O(1)
     when {
         this[0] == '+' -> {
             sign = +1
@@ -446,8 +474,10 @@ public fun String.parseBigInteger(): BigInt? {
     var digitValue = BigInt.ONE
     val sPositiveUpper = sPositive.uppercase()
 
-    if (sPositiveUpper.startsWith("0X")) {  // hex representation
+    if (sPositiveUpper.startsWith("0X")) {
+        // hex representation
         val sHex = sPositiveUpper.substring(2)
+        // TODO optimize O(n2) -> O(n)
 
         for (ch in sHex.reversed()) {
             if (ch == '_') continue
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt
index ae34dbc04..9f35f7a69 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntOperationsTest.kt
@@ -5,8 +5,9 @@
 
 package space.kscience.kmath.operations
 
-import kotlin.test.Test
-import kotlin.test.assertEquals
+import kotlin.random.Random
+import kotlin.random.nextUInt
+import kotlin.test.*
 
 @kotlin.ExperimentalUnsignedTypes
 class BigIntOperationsTest {
@@ -150,6 +151,18 @@ class BigIntOperationsTest {
         assertEquals(prod, res)
     }
 
+    @Test
+    fun testKaratsuba() {
+        val x = uintArrayOf(12U, 345U)
+        val y = uintArrayOf(6U, 789U)
+        assertContentEquals(BigInt.naiveMultiplyMagnitudes(x, y), BigInt.karatsubaMultiplyMagnitudes(x, y))
+        repeat(1000) {
+            val x1 = UIntArray(Random.nextInt(100, 1000)) { Random.nextUInt() }
+            val y1 = UIntArray(Random.nextInt(100, 1000)) { Random.nextUInt() }
+            assertContentEquals(BigInt.naiveMultiplyMagnitudes(x1, y1), BigInt.karatsubaMultiplyMagnitudes(x1, y1))
+        }
+    }
+
     @Test
     fun test_shr_20() {
         val x = 20.toBigInt()
@@ -383,4 +396,12 @@ class BigIntOperationsTest {
 
         return assertEquals(res, x % mod)
     }
+
+    @Test
+    fun testNotEqualsOtherTypeInstanceButButNotFails() = assertFalse(0.toBigInt().equals(""))
+
+    @Test
+    fun testIntAbsOverflow() {
+        assertEquals((-Int.MAX_VALUE.toLong().toBigInt() - 1.toBigInt()) * 2, 2.toBigInt() * Int.MIN_VALUE)
+    }
 }