.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_autoexamples/Demo_3_Float_CKKS.py"
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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download__autoexamples_Demo_3_Float_CKKS.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr__autoexamples_Demo_3_Float_CKKS.py:


Fixed-point FHE with CKKS scheme
========================================

Fixed-point Demo for Pyfhel, operating with fixed point encoded values following
the CKKS scheme (https://eprint.iacr.org/2016/421.pdf)

.. GENERATED FROM PYTHON SOURCE LINES 10-23

1. CKKS context and key setup
-------------------------------
We take a look at the different parameters that can be set for the CKKS scheme.
A generally good strategy to choose `qi_sizes` (bitsize for each prime moduli) 
for the CKKS scheme is as follows:

1. Choose a 60-bit prime as the first prime in coeff_modulus. This will
   give the highest precision when decrypting;
2. Choose another 60-bit prime as the last element of coeff_modulus, as
   this will be used as the special prime and should be as large as the
   largest of the other primes;
3. Choose the intermediate primes to be close to each other.


.. GENERATED FROM PYTHON SOURCE LINES 23-44

.. code-block:: Python

    import numpy as np
    from Pyfhel import Pyfhel

    HE = Pyfhel()           # Creating empty Pyfhel object
    ckks_params = {
        'scheme': 'CKKS',   # can also be 'ckks'
        'n': 2**14,         # Polynomial modulus degree. For CKKS, n/2 values can be
                            #  encoded in a single ciphertext. 
                            #  Typ. 2^D for D in [10, 15]
        'scale': 2**30,     # All the encodings will use it for float->fixed point
                            #  conversion: x_fix = round(x_float * scale)
                            #  You can use this as default scale or use a different
                            #  scale on each operation (set in HE.encryptFrac)
        'qi_sizes': [60, 30, 30, 30, 60] # Number of bits of each prime in the chain. 
                            # Intermediate values should be  close to log2(scale)
                            # for each operation, to have small rounding errors.
    }
    HE.contextGen(**ckks_params)  # Generate context for ckks scheme
    HE.keyGen()             # Key Generation: generates a pair of public/secret keys
    HE.rotateKeyGen()








.. GENERATED FROM PYTHON SOURCE LINES 45-50

2. Float Array Encoding & Encryption
----------------------------------------
we will define two floating-point arrays, encode and encrypt them:
arr_x = [0.1, 0.2, -0.3] (length 3)
arr_y = [-1.5, 2.3, 4.7] (length 3)

.. GENERATED FROM PYTHON SOURCE LINES 50-68

.. code-block:: Python


    arr_x = np.array([0.1, 0.2, -0.3], dtype=np.float64)    # Always use type float64!
    arr_y = np.array([-1.5, 2.3, 4.7], dtype=np.float64)

    ptxt_x = HE.encodeFrac(arr_x)   # Creates a PyPtxt plaintext with the encoded arr_x
    ptxt_y = HE.encodeFrac(arr_y)   # plaintexts created from arrays shorter than 'n' are filled with zeros.

    ctxt_x = HE.encryptPtxt(ptxt_x) # Encrypts the plaintext ptxt_x and returns a PyCtxt
    ctxt_y = HE.encryptPtxt(ptxt_y) #  Alternatively you can use HE.encryptFrac(arr_y)

    # Otherwise, a single call to `HE.encrypt` would detect the data type,
    #  encode it and encrypt it
    #> ctxt_x = HE.encrypt(arr_x)

    print("\n2. Fixed-point Encoding & Encryption, ")
    print("->\tarr_x ", arr_x,'\n\t==> ptxt_x ', ptxt_x,'\n\t==> ctxt_x ', ctxt_x)
    print("->\tarr_y ", arr_y,'\n\t==> ptxt_y ', ptxt_y,'\n\t==> ctxt_y ', ctxt_y)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    2. Fixed-point Encoding & Encryption, 
    ->      arr_x  [ 0.1  0.2 -0.3] 
            ==> ptxt_x  <Pyfhel Plaintext at 0x7fecac0e4940, scheme=ckks, poly=?, is_ntt=Y, mod_level=0> 
            ==> ctxt_x  <Pyfhel Ciphertext at 0x7fecac0e2d60, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      arr_y  [-1.5  2.3  4.7] 
            ==> ptxt_y  <Pyfhel Plaintext at 0x7fecac0e4480, scheme=ckks, poly=?, is_ntt=Y, mod_level=0> 
            ==> ctxt_y  <Pyfhel Ciphertext at 0x7fecaf283f40, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>




.. GENERATED FROM PYTHON SOURCE LINES 69-74

3. Securely operating on encrypted fixed-point arrays
-------------------------------------------------------
We try all the operations supported by Pyfhel.
Note that, to operate, the ciphertexts/plaintexts must be built with the same
context. Internal checks prevent ops between ciphertexts of different contexts.

.. GENERATED FROM PYTHON SOURCE LINES 74-117

.. code-block:: Python


    # Ciphertext-ciphertext ops:
    ccSum = ctxt_x + ctxt_y       # Calls HE.add(ctxt_x, ctxt_y, in_new_ctxt=True)
                                #  `ctxt_x += ctxt_y` for inplace operation
    ccSub = ctxt_x - ctxt_y       # Calls HE.sub(ctxt_x, ctxt_y, in_new_ctxt=True)
                                #  `ctxt_x -= ctxt_y` for inplace operation
    ccMul = ctxt_x * ctxt_y       # Calls HE.multiply(ctxt_x, ctxt_y, in_new_ctxt=True)
                                #  `ctxt_x *= ctxt_y` for inplace operation
    cSq   = ctxt_x**2            # Calls HE.square(ctxt_x, in_new_ctxt=True)
                                #  `ctxt_x **= 2` for inplace operation
    cNeg  = -ctxt_x              # Calls HE.negate(ctxt_x, in_new_ctxt=True)
                                # 
    # cPow  = ctxt_x**3          # pow Not supported in CKKS
    cRotR = ctxt_x >> 2          # Calls HE.rotate(ctxt_x, k=2, in_new_ctxt=True)
                                #  `ctxt_x >>= 2` for inplace operation
    cRotL = ctxt_x << 2          # Calls HE.rotate(ctxt_x, k=-2, in_new_ctxt=True)
                                #  `ctxt_x <<= 2` for inplace operation

    # Ciphetext-plaintext ops
    cpSum = ctxt_x + ptxt_y       # Calls HE.add_plain(ctxt_x, ptxt_y, in_new_ctxt=True)
                                # `ctxt_x += ctxt_y` for inplace operation
    cpSub = ctxt_x - ptxt_y       # Calls HE.sub_plain(ctxt_x, ptxt_y, in_new_ctxt=True)
                                # `ctxt_x -= ctxt_y` for inplace operation
    cpMul = ctxt_x * ptxt_y       # Calls HE.multiply_plain(ctxt_x, ptxt_y, in_new_ctxt=True)
                                # `ctxt_x *= ctxt_y` for inplace operation


    print("3. Secure operations")
    print(" Ciphertext-ciphertext: ")
    print("->\tctxt_x + ctxt_y = ccSum: ", ccSum)
    print("->\tctxt_x - ctxt_y = ccSub: ", ccSub)
    print("->\tctxt_x * ctxt_y = ccMul: ", ccMul)
    print(" Single ciphertext: ")
    print("->\tctxt_x**2      = cSq  : ", cSq  )
    print("->\t- ctxt_x       = cNeg : ", cNeg )
    print("->\tctxt_x >> 4    = cRotR: ", cRotR)
    print("->\tctxt_x << 4    = cRotL: ", cRotL)
    print(" Ciphertext-plaintext: ")
    print("->\tctxt_x + ptxt_y = cpSum: ", cpSum)
    print("->\tctxt_x - ptxt_y = cpSub: ", cpSub)
    print("->\tctxt_x * ptxt_y = cpMul: ", cpMul)

          




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    3. Secure operations
     Ciphertext-ciphertext: 
    ->      ctxt_x + ctxt_y = ccSum:  <Pyfhel Ciphertext at 0x7fecac563a90, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      ctxt_x - ctxt_y = ccSub:  <Pyfhel Ciphertext at 0x7fecac12a900, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      ctxt_x * ctxt_y = ccMul:  <Pyfhel Ciphertext at 0x7fecac12a220, scheme=ckks, size=3/3, scale_bits=60, mod_level=1>
     Single ciphertext: 
    ->      ctxt_x**2      = cSq  :  <Pyfhel Ciphertext at 0x7fecaf3eb360, scheme=ckks, size=3/3, scale_bits=60, mod_level=1>
    ->      - ctxt_x       = cNeg :  <Pyfhel Ciphertext at 0x7fecaf833090, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      ctxt_x >> 4    = cRotR:  <Pyfhel Ciphertext at 0x7fecaf833d60, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      ctxt_x << 4    = cRotL:  <Pyfhel Ciphertext at 0x7fecaf2a3130, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
     Ciphertext-plaintext: 
    ->      ctxt_x + ptxt_y = cpSum:  <Pyfhel Ciphertext at 0x7fecaf2a3720, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      ctxt_x - ptxt_y = cpSub:  <Pyfhel Ciphertext at 0x7fecaf2a32c0, scheme=ckks, size=2/2, scale_bits=30, mod_level=0>
    ->      ctxt_x * ptxt_y = cpMul:  <Pyfhel Ciphertext at 0x7fecaf2a3400, scheme=ckks, size=2/2, scale_bits=60, mod_level=1>




.. GENERATED FROM PYTHON SOURCE LINES 118-128

4. CKKS relinearization: What, why, when
-----------------------------------------
Ciphertext-ciphertext multiplications increase the size of the polynoms 
representing the resulting ciphertext. To prevent this growth, the 
relinearization technique is used (typically right after each c-c mult) to 
reduce the size of a ciphertext back to the minimal size (two polynoms c0 & c1).
For this, a special type of public key called Relinearization Key is used.

In Pyfhel, you can either generate a relin key with HE.RelinKeyGen() or skip it
and call HE.relinearize() directly, in which case a warning is issued.

.. GENERATED FROM PYTHON SOURCE LINES 128-135

.. code-block:: Python


    print("\n4. Relinearization-> Right after each multiplication.")
    print(f"ccMul before relinearization (size {ccMul.size()}): {ccMul}")
    HE.relinKeyGen()
    ~ccMul    # Equivalent to HE.relinearize(ccMul). Relin always happens in-place.
    print(f"ccMul after relinearization (size {ccMul.size()}): {ccMul}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    4. Relinearization-> Right after each multiplication.
    ccMul before relinearization (size 3): <Pyfhel Ciphertext at 0x7fecac12a220, scheme=ckks, size=3/3, scale_bits=60, mod_level=1>
    ccMul after relinearization (size 2): <Pyfhel Ciphertext at 0x7fecac12a220, scheme=ckks, size=2/3, scale_bits=60, mod_level=1>




.. GENERATED FROM PYTHON SOURCE LINES 136-161

5. Rescaling & Mod Switching
-------------------------------
More complex operations with CKKS require keeping track of the CKKS scale. 
Operating with two CKKS ciphertexts (or a ciphertext and a plaintext) requires
them to have the same scale and the same modulus level. 

-> Scale: Multiplications yield a new scale, which is the product of the scales
 of the two operands. To scale down a ciphertext, the HE.rescale_to_next(ctxt)
 function is used, which switches the modulus to the next one in the qi chain
 and divides the ciphertext by the previous modulus.#  Since this is the only
 scale-down operation, it is advised to use `scale_bits` with the same size as 
 the intermediate moduli sizes in HE.qi_sizes. 
-> Mod Switching: Switches to the next modulus in the qi chain, but without
 rescaling. This is achieved by the HE.mod_switch_to_next(ctxt) function.

To ease the life of the user, Pyfhel provides `HE.align_mod_n_scale(this, other)`,
which automatically does the rescaling and mod switching. All the 2-input
overloaded operators (+, -, \*, /) of PyCtxt automatically call this function.
The respective HE.add, HE.sub, HE.multiply don't.

NOTE: For more information, check the SEAL example #4_ccks_basics.cpp

In this example we will compute the mean squared error, treating the average of
the two ciphertexts as the true distribution. We check the scale and mod-level
step by step:

.. GENERATED FROM PYTHON SOURCE LINES 161-179

.. code-block:: Python


    #  1. Mean
    c_mean = (ctxt_x + ctxt_y) / 2
    #  2. MSE
    c_mse_1 = ~((ctxt_x - c_mean)**2)
    c_mse_2 = (~(ctxt_y - c_mean)**2)
    c_mse = (c_mse_1 + c_mse_2)/ 3
    #  3. Cumulative sum
    c_mse += (c_mse << 1)
    c_mse += (c_mse << 2)  # element 0 contains the result
    print("\n5. Rescaling & Mod Switching.")
    print("->\tMean: ", c_mean)
    print("->\tMSE_1: ", c_mse_1)
    print("->\tMSE_2: ", c_mse_2)
    print("->\tMSE: ", c_mse)







.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    5. Rescaling & Mod Switching.
    ->      Mean:  <Pyfhel Ciphertext at 0x7fecac13db30, scheme=ckks, size=2/2, scale_bits=60, mod_level=1>
    ->      MSE_1:  <Pyfhel Ciphertext at 0x7fecaf283ea0, scheme=ckks, size=2/3, scale_bits=60, mod_level=2>
    ->      MSE_2:  <Pyfhel Ciphertext at 0x7fecac12abd0, scheme=ckks, size=2/3, scale_bits=60, mod_level=2>
    ->      MSE:  <Pyfhel Ciphertext at 0x7fecac12ad60, scheme=ckks, size=2/3, scale_bits=60, mod_level=3>




.. GENERATED FROM PYTHON SOURCE LINES 180-185

6. Decrypt & Decode results
------------------------------
Time to decrypt results! We use HE.decryptFrac for this. 
 HE.decrypt() could also be used, in which case the decryption type would be
 inferred from the ciphertext metadata. 

.. GENERATED FROM PYTHON SOURCE LINES 185-223

.. code-block:: Python

    r_x    = HE.decryptFrac(ctxt_x)
    r_y    = HE.decryptFrac(ctxt_y)
    rccSum = HE.decryptFrac(ccSum)
    rccSub = HE.decryptFrac(ccSub)
    rccMul = HE.decryptFrac(ccMul)
    rcSq   = HE.decryptFrac(cSq  )
    rcNeg  = HE.decryptFrac(cNeg )
    rcRotR = HE.decryptFrac(cRotR)
    rcRotL = HE.decryptFrac(cRotL)
    rcpSum = HE.decryptFrac(cpSum)
    rcpSub = HE.decryptFrac(cpSub)
    rcpMul = HE.decryptFrac(cpMul)
    rmean  = HE.decryptFrac(c_mean)
    rmse   = HE.decryptFrac(c_mse)

    # Note: results are approximate! if you increase the decimals, you will notice
    #  the errors
    _r = lambda x: np.round(x, decimals=3)
    print("6. Decrypting results")
    print(" Original ciphertexts: ")
    print("   ->\tctxt_x --(decr)--> ", _r(r_x))
    print("   ->\tctxt_y --(decr)--> ", _r(r_y))
    print(" Ciphertext-ciphertext Ops: ")
    print("   ->\tctxt_x + ctxt_y = ccSum --(decr)--> ", _r(rccSum))
    print("   ->\tctxt_x - ctxt_y = ccSub --(decr)--> ", _r(rccSub))
    print("   ->\tctxt_x * ctxt_y = ccMul --(decr)--> ", _r(rccMul))
    print(" Single ciphertext: ")
    print("   ->\tctxt_x**2      = cSq   --(decr)--> ", _r(rcSq  ))
    print("   ->\t- ctxt_x       = cNeg  --(decr)--> ", _r(rcNeg ))
    print("   ->\tctxt_x >> 4    = cRotR --(decr)--> ", _r(rcRotR))
    print("   ->\tctxt_x << 4    = cRotL --(decr)--> ", _r(rcRotL))
    print(" Ciphertext-plaintext ops: ")
    print("   ->\tctxt_x + ptxt_y = cpSum --(decr)--> ", _r(rcpSum))
    print("   ->\tctxt_x - ptxt_y = cpSub --(decr)--> ", _r(rcpSub))
    print("   ->\tctxt_x * ptxt_y = cpMul --(decr)--> ", _r(rcpMul))
    print(" Mean Squared error: ")
    print("   ->\tmean(ctxt_x, ctxt_y) = c_mean --(decr)--> ", _r(rmean))
    print("   ->\tmse(ctxt_x, ctxt_y)  = c_mse  --(decr)--> ", _r(rmse))




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    6. Decrypting results
     Original ciphertexts: 
       ->   ctxt_x --(decr)-->  [ 0.1  0.2 -0.3 ... -0.  -0.  -0. ]
       ->   ctxt_y --(decr)-->  [-1.5  2.3  4.7 ...  0.  -0.   0. ]
     Ciphertext-ciphertext Ops: 
       ->   ctxt_x + ctxt_y = ccSum --(decr)-->  [-1.4  2.5  4.4 ... -0.  -0.  -0. ]
       ->   ctxt_x - ctxt_y = ccSub --(decr)-->  [ 1.6 -2.1 -5.  ... -0.   0.  -0. ]
       ->   ctxt_x * ctxt_y = ccMul --(decr)-->  [-0.15  0.46 -1.41 ... -0.   -0.    0.  ]
     Single ciphertext: 
       ->   ctxt_x**2      = cSq   --(decr)-->  [ 0.01  0.04  0.09 ...  0.    0.   -0.  ]
       ->   - ctxt_x       = cNeg  --(decr)-->  [-0.1 -0.2  0.3 ...  0.   0.   0. ]
       ->   ctxt_x >> 4    = cRotR --(decr)-->  [ 0.002  0.001  0.1   ...  0.     0.    -0.   ]
       ->   ctxt_x << 4    = cRotL --(decr)-->  [-0.299  0.001 -0.    ...  0.     0.1    0.2  ]
     Ciphertext-plaintext ops: 
       ->   ctxt_x + ptxt_y = cpSum --(decr)-->  [-1.4  2.5  4.4 ... -0.  -0.  -0. ]
       ->   ctxt_x - ptxt_y = cpSub --(decr)-->  [ 1.6 -2.1 -5.  ... -0.  -0.  -0. ]
       ->   ctxt_x * ptxt_y = cpMul --(decr)-->  [-0.15  0.46 -1.41 ...  0.    0.    0.  ]
     Mean Squared error: 
       ->   mean(ctxt_x, ctxt_y) = c_mean --(decr)-->  [-0.7   1.25  2.2  ... -0.   -0.   -0.  ]
       ->   mse(ctxt_x, ctxt_y)  = c_mse  --(decr)-->  [5.33  4.903 4.168 ... 0.427 1.162 5.33 ]





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 4.500 seconds)

**Estimated memory usage:**  114 MB


.. _sphx_glr_download__autoexamples_Demo_3_Float_CKKS.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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      :download:`Download Python source code: Demo_3_Float_CKKS.py <Demo_3_Float_CKKS.py>`


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