Merge pull request #44 from wfus/decode

Decode

Author: raylin1000

CMakeLists.txt

@@ -50,3 +50,8 @@ target_link_libraries(decode_server seal ${OpenCV_LIBS})
 # Image testing, debugging only
 add_executable(image_test homo/image_test.cpp ${LIBRARY_SOURCES})
 target_link_libraries(image_test seal ${OpenCV_LIBS})
+
+
+# Image testing, debugging only
+add_executable(test_decode tests/test_decode.cpp ${LIBRARY_SOURCES})
+target_link_libraries(test_decode seal ${OpenCV_LIBS})

README.md

@@ -1,6 +1,22 @@
 # Fast Homomorphic Image Processing
 These days neural networks and fully homomorphic encryption are a meme. For example, Microsoft demonstrated with Cryptonets of a neural network generating predictions fully homomorphically on the MNIST dataset. However, it would be useful to have a way to preprocess images homomorphically. Consider the use case where an edge device sends a homomorphically encrypted image to a server that runs a prediction algorithm with two neural networks that take in different sized features, as is common. It would be prohibitive to make the edge device homomorphically encrypt two copies of the images, since that would be prohibitively expensive. Therefore, having proprocessing and feature extraction computed homomorphically will provide much more flexibility for homomorphic neural nets.  
 
+## Homomorphic Image Decompression
+
+We will show how to homomorphically compute something simpler than JPEG decompression, run length decoding. The idea is the same: we would like to expand out a [run length encoding](https://en.wikipedia.org/wiki/Run-length_encoding) (which is used after DCT step of the JPEG standard)
+This is difficult to do because converting the run length decoding into a boolean circuit is completely unfeasable due to the number of gates needed. Without resorting to evaluating a boolean circuit, the following operations are not possible with homomorphic encryption
+
+* Dividing by a ciphertext
+* Conditionals (if, else)
+* No looping on variables
+* Cannot prematurely exit program
+
+Since the boolean circuit approach is not feasable by __many multiple orders of magnitude__, we use an approximation approach. For each run length tuple, we approximate a "step" function defined by 1 if between b1 and b2 and 0 otherwise using a discrete Fourier series. We also taylor expand the cosine and sine function. Note that it is difficult to use a sigmoid type function for approximating, because we cannot use division. A sample approximation of the step-like function with a discrete fourier series is shown in the following graph.
+
+![approximategraph](docs/approxstep.png)
+
+
+
 ### Homomorphic Image Resizing
 There are two common types of interpolation used when images are scaled: [bilinear interpolation](https://en.wikipedia.org/wiki/Bilinear_interpolation) and [bicubic interpolation](https://en.wikipedia.org/wiki/Bicubic_interpolation). Bilinear interpolation requires a 2 by 2 square around the point to be interpolated, and involves linear interpolation in one direction and then in the other in a two dimensional space. Bicubic interpolation is similar except cubic rather than linear interpolation is used, and it requires a 4 by 4 square around a point to be interpolated.
 

benchmark/benchmark.py

@@ -1,22 +1,24 @@
 from subprocess import call
+import os
 
 CWD = "../"
 IMAGE_NAMES = [("image/boazbarak.jpg", 'boaz')]
 POLY_N = [2048, 4096, 8192, 16384]
 PLAIN_MOD = [11, 31, 101, 307, 1009, 3001, 10007, 30011, 100003]
+DBC = [16, 32, 60]
 WIDTH_HEIGHT_PAIRS = [(17, 17)]
 LOG_DIR = "../logs"
 
-def log_resize(imname, inter, width, height, poly_n, plain_mod):
-    return "{}/resize_{}_{}_{}_{}_{}_{}.txt".format(LOG_DIR, imname, inter, width, height, poly_n, plain_mod)
+def log_resize(imname, inter, width, height, poly_n, plain_mod, dbc):
+    return "{}/resize_{}_{}_{}_{}_{}_{}_{}.txt".format(LOG_DIR, imname, inter, width, height, poly_n, plain_mod, dbc)
 
 def log_jpeg(imname, poly_n, plain_mod):
     return "{}/jpg_{}_{}_{}.txt".format(LOG_DIR, imname, poly_n, plain_mod)
 
-def call_resize(image, logname, outname, inter, width, height, poly_n, plain_mod):
+def call_resize(image, logname, outname, inter, width, height, poly_n, plain_mod, dbc):
     f = open(logname, 'w')
     print("Resize Client (Sending)")
-    call(['./bin/client_resize', '--width', str(width), '--height', str(height), '--send', '-f', image, '--cmod', str(poly_n), '--pmod', str(plain_mod)], 
+    call(['./bin/client_resize', '--width', str(width), '--height', str(height), '--send', '-f', image, '--cmod', str(poly_n), '--pmod', str(plain_mod), '--dbc', str(dbc)], 
           cwd=CWD, stdout=f)
     print("Resize Server")
     call(['./bin/server_resize', '--width', str(width), '--height', str(height), inter, '--cmod', str(poly_n), '--pmod', str(plain_mod)], 
@@ -38,17 +40,19 @@ def call_jpeg(image, logname, outname, poly_n, plain_mod):
           cwd=CWD, stdout=f)
 
 if __name__ == '__main__':
+    os.system('mkdir -p ../logs')
     for image_name, short_name in IMAGE_NAMES:
         for poly_n in POLY_N:
             for plain_mod in PLAIN_MOD:
                 for width, height in WIDTH_HEIGHT_PAIRS:
-                    for inter in ['bilinear', 'bicubic']:
-                        logname = log_resize(short_name, inter, width, height, poly_n, plain_mod)
-                        outname = "logs/{}_{}_{}_{}_{}_{}.png".format(short_name, inter, width, height, poly_n, plain_mod)
-                        inter_param = '' if inter == 'bilinear' else '--bicubic'
-                        call_resize(image_name, logname, outname, inter_param, width, height, poly_n, plain_mod)
+                    for dbc in DBC:
+                        for inter in ['bicubic']:
+                            logname = log_resize(short_name, inter, width, height, poly_n, plain_mod, dbc)
+                            outname = "logs/{}_{}_{}_{}_{}_{}_{}.png".format(short_name, inter, width, height, poly_n, plain_mod, dbc)
+                            inter_param = '' if inter == 'bilinear' else '--bicubic'
+                            call_resize(image_name, logname, outname, inter_param, width, height, poly_n, plain_mod, dbc)
 
-                logname = log_jpeg(short_name, poly_n, plain_mod)
-                outname = "logs/new_{}_{}_{}.jpg".format(short_name, poly_n, plain_mod)
-                call_jpeg(image_name, logname, outname, poly_n, plain_mod)
+                # logname = log_jpeg(short_name, poly_n, plain_mod)
+                # outname = "logs/new_{}_{}_{}.jpg".format(short_name, poly_n, plain_mod)
+                # call_jpeg(image_name, logname, outname, poly_n, plain_mod)