concrete/docs/user/tutorial/ARITHMETIC_OPERATIONS.md

Arithmetic Operations

In this tutorial, we are going to go over all arithmetic operations available in Concrete. Please read Compiling and Executing before reading further to see how you can compile the functions below.

Addition

Static ClearScalar and EncryptedScalar

def f(x):
    return x + 42

or

def f(x):
    return 42 + x

where

• x = EncryptedScalar(UnsignedInteger(bits))

results in

circuit.run(3) == 45
circuit.run(0) == 42

Dynamic ClearScalar and EncryptedScalar

def f(x, y):
    return x + y

or

def f(x, y):
    return y + x

results in

circuit.run(6, 4) == 10
circuit.run(1, 1) == 2

where

• x = EncryptedScalar(UnsignedInteger(bits))
• y = ClearScalar(UnsignedInteger(bits))

EncryptedScalar and EncryptedScalar

def f(x, y):
    return x + y

where

• x = EncryptedScalar(UnsignedInteger(bits))
• y = EncryptedScalar(UnsignedInteger(bits))

results in

circuit.run(7, 7) == 14
circuit.run(3, 4) == 7

Subtraction

Static ClearScalar and EncryptedScalar

def f(x):
    return 3 - x

where

• x = EncryptedScalar(UnsignedInteger(bits))

results in

circuit.run(2) == 1
circuit.run(3) == 0

Dynamic ClearScalar and EncryptedScalar

def f(x, y):
    return y - x

where

• x = EncryptedScalar(UnsignedInteger(bits))
• y = ClearScalar(UnsignedInteger(bits))

results in

circuit.run(2, 4) == 2
circuit.run(1, 7) == 6

Multiplication

Static ClearScalar and EncryptedScalar

def f(x):
    return x * 2

or

def f(x):
    return 2 * x

where

• x = EncryptedScalar(UnsignedInteger(bits))

results in

circuit.run(2) == 4
circuit.run(5) == 10

Dynamic ClearScalar and EncryptedScalar

def f(x, y):
    return x * y

or

def f(x, y):
    return y * x

where

• x = EncryptedScalar(UnsignedInteger(bits))
• y = ClearScalar(UnsignedInteger(bits))

results in

circuit.run(2, 3) == 6
circuit.run(1, 7) == 7

Dot Product

Dynamic ClearTensor and EncryptedTensor

def f(x, y):
    return np.dot(x, y)

or

def f(x, y):
    return np.dot(y, x)

where

• x = EncryptedTensor(UnsignedInteger(bits), shape=(2,))
• y = ClearTensor(UnsignedInteger(bits), shape=(2,))

results in

circuit.run([1, 1], [2, 3]) == 5
circuit.run([2, 3], [2, 3]) == 13

Combining all together

def f(x, y, z):
    return 100 - (2 * (np.dot(x, y) + z))

where

• x = EncryptedTensor(UnsignedInteger(bits), shape=(2,))
• y = ClearTensor(UnsignedInteger(bits), shape=(2,))
• z = EncryptedScalar(UnsignedInteger(bits))

results in

circuit.run([1, 2], [4, 3], 10) == 60
circuit.run([2, 3], [3, 2], 5) == 66