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216 lines
2.8 KiB
Markdown
216 lines
2.8 KiB
Markdown
# Arithmetic Operations
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In this tutorial, we are going to go over all arithmetic operations available in **concrete**. Please read [Compiling and Executing](../howto/COMPILING_AND_EXECUTING.md) before reading further to see how you can compile the functions below.
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## Addition
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### Static ClearScalar and EncryptedScalar
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```python
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def f(x):
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return x + 42
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```
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or
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```python
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def f(x):
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return 42 + x
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run(3) == 45
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engine.run(0) == 42
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```
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### Dynamic ClearScalar and EncryptedScalar
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```python
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def f(x, y):
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return x + y
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```
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or
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```python
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def f(x, y):
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return y + x
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```
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results in
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```python
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engine.run(6, 4) == 10
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engine.run(1, 1) == 2
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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- `y = ClearScalar(UnsignedInteger(bits))`
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### EncryptedScalar and EncryptedScalar
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```python
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def f(x, y):
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return x + y
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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- `y = EncryptedScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run(7, 7) == 14
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engine.run(3, 4) == 7
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```
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## Subtraction
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### Static ClearScalar and EncryptedScalar
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```python
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def f(x):
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return 3 - x
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run(2) == 1
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engine.run(3) == 0
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```
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### Dynamic ClearScalar and EncryptedScalar
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```python
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def f(x, y):
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return y - x
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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- `y = ClearScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run(2, 4) == 2
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engine.run(1, 7) == 6
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```
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## Multiplication
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### Static ClearScalar and EncryptedScalar
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```python
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def f(x):
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return x * 2
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```
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or
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```python
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def f(x):
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return 2 * x
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run(2) == 4
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engine.run(5) == 10
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```
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### Dynamic ClearScalar and EncryptedScalar
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```python
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def f(x, y):
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return x * y
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```
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or
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```python
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def f(x, y):
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return y * x
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(bits))`
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- `y = ClearScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run(2, 3) == 6
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engine.run(1, 7) == 7
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```
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## Dot Product
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### Dynamic ClearTensor and EncryptedTensor
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```python
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def f(x, y):
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return np.dot(x, y)
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```
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or
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```python
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def f(x, y):
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return np.dot(y, x)
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```
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where
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- `x = EncryptedTensor(UnsignedInteger(bits), shape=(2,))`
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- `y = ClearTensor(UnsignedInteger(bits), shape=(2,))`
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results in
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```python
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engine.run([1, 1], [2, 3]) == 5
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engine.run([2, 3], [2, 3]) == 13
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```
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## Combining all together
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```python
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def f(x, y, z):
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return 100 - (2 * (np.dot(x, y) + z))
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```
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where
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- `x = EncryptedTensor(UnsignedInteger(bits), shape=(2,))`
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- `y = ClearTensor(UnsignedInteger(bits), shape=(2,))`
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- `z = EncryptedScalar(UnsignedInteger(bits))`
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results in
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```python
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engine.run([1, 2], [4, 3], 10) == 60
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engine.run([2, 3], [3, 2], 5) == 66
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```
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