import numpy as np

from Crypto.Random import get$\_$random$\_$bytes

from Crypto.Util.Padding import pad, unpad

from Crypto.Cipher import AES

import base$64$

# LWE Parameters

n $=512$ # Dimension

q $=2**15$ # Modulus

sigma $=3\mathrm{.}2$ # Standard deviation for the error distribution

def lwe$\_$sample$($n$,$ q$,$ sigma$)$:

A $=$ np$.$random.randint$(0,$ q$,$ size$=($n$,$ n$))$

s $=$ np$.$random.randint$(0,$ q$,$ size$=$n$)$

e $=$ np$.$random.normal$(0,$ sigma, size$=$n$).$astype$($int$)\%$ q

b $=($np$.$dot$($A$,$ s$)+$ e$)\%$ q

return A$,$ b$,$ s

def pad$\_$key$($key$,$ n$)$:

key$\_$as$\_$ints $=$ np$.$frombuffer$($key$,$ dtype$=$np$.$uint$8)$

padded$\_$key $=$ np$.$zeros$($n$,$ dtype$=$np$.$uint$8)$

padded$\_$key$[$:key$\_$as$\_$ints.size$]=$ key$\_$as$\_$ints

return padded$\_$key

def lwe$\_$encrypt$($A$,$ b$,$ message, q$)$:

try:

# Ensure message is bytes

if isinstance$($message$,$ str$)$:

message $=$ message.encode$()$

# Symmetric encryption with AES

key $=$ get$\_$random$\_$bytes$(16)$

cipher $=$ AES.new$($key$,$ AES.MODE$\_$CBC$)$

ct$\_$bytes $=$ cipher.encrypt$($pad$($message$,$ AES.block$\_$size$))$

# Combine ciphertext and IV

ct $=$ base$64.$b$64$encode$($cipher$.$iv $+$ ct$\_$bytes$).$decode$(\text{'}$utf$-8\text{'})$

# Encryption using LWE

padded$\_$key $=$ pad$\_$key$($key$,$ n$)$

encrypted$\_$key $=($np$.$dot$($A$,$ padded$\_$key$)+$ b$)\%$ q

return ct$,$ encrypted$\_$key

except Exception as e:

print$($f$"$Encryption failed: $\{$e$\}")$

return None, None

def lwe$\_$decrypt$($A$,$ s$,$ ct$,$ encrypted$\_$key, q$)$:

try:

# Decryption using LWE

decrypted$\_$key$\_$int $=($np$.$dot$($A$,$ s$)+$ encrypted$\_$key$)\%$ q

decrypted$\_$key$\_$bytes $=$ decrypted$\_$key$\_$int$[$:$16].$astype$($np$.$uint$8).$tobytes$()$

# Symmetric decryption with AES

ct $=$ base$64.$b$64$decode$($ct$)$

iv $=$ ct$[$:AES.block$\_$size$]$

ct $=$ ct$[$AES$.$block$\_$size:$]$

cipher $=$ AES.new$($decrypted$\_$key$\_$bytes, AES.MODE$\_$CBC$,$ iv$)$

pt $=$ unpad$($cipher$.$decrypt$($ct$),$ AES.block$\_$size$)$

return pt$.$decode$(\text{'}$utf$-8\text{'})$

except Exception as e:

print$($f$"$Decryption failed: $\{$e$\}")$

return None

def main$()$:

try:

message $=$ input$("$Enter a message to encrypt: $")$

# Generate LWE sample

A$,$ b$,$ s $=$ lwe$\_$sample$($n$,$ q$,$ sigma$)$

# Encrypt the message

ct$,$ encrypted$\_$key $=$ lwe$\_$encrypt$($A$,$ b$,$ message, q$)$

if ct and encrypted$\_$key is not None:

print$($f$"$Encrypted message: $\{$ct$\}")$

print$($f$"$Encrypted key: $\{$encrypted$\_$key$\}")$

# Decrypt the message

decrypted$\_$message $=$ lwe$\_$decrypt$($A$,$ s$,$ ct$,$ encrypted$\_$key, q$)$

if decrypted$\_$message is not None:

print$($f$"$Decrypted message: $\{$decrypted$\_$message$\}")$

else:

print$("$Decryption failed."$)$

else:

print$("$Encryption failed."$)$

except Exception as e:

print$($f$"$Error in main: $\{$e$\}")$

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

main$()$

I tried to run this code with input message as hello world but the output came out like this. Decryption failed. Help solve this problem.