3.20 For a function g: {0, 1 }n --+ {0, 1}n, let g$(·) be an oracle that, on inp

Question

3.20 For a function g: {0, 1 }n --+ {0, 1}n, let g$(·) be an oracle that, on input 1n, chooses r +- {0, 1 }n uniformly at random and returns (r, g (r)). We say a keyed function F is a weak pseudorandom function if for all PPT algorithms D, there exists a negligible function negl such that:

| pr [ D^f^s (.) (1^n) =1] - pr [ D^f^s (.) (1^n) =1 ] | <= negl (n),

where k <-- {0, l }^n and f <-- Func n are chosen uniformly at random

(a) Prove that if F is pseudorandom then it is weakly pseudorandom.

(b) Let F' be a pseudorandom function, and define · .

Fk (x)=F`k(x)if x is even k . F`k(x+1) if x is odd

Prove that F is weakly pseudorandom, but not pseudorandom.

(c) Is counter-mode encryption instantiated using a weak pseudorandom function F necessarily CPA-secure? Does. it necessarily have indistinguishable encryptions in the presence of an eavesdropper? Prove your answers.

(d) Construct a CPA-secure encryption scheme based on a weak pseudorandom function. Hint: One of the constructions in this chapter will work.

This question from introduction to modern cryptography book chapter 3 question 3.20

Explanation / Answer

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Random;

public class KeyGenerator {

   Random rr=new Random();

public int getKeys(){

  
   String str="";
   str=String.valueOf(rr.nextInt(10))+String.valueOf(rr.nextInt(10))+String.valueOf(rr.nextInt(10))+String.valueOf(rr.nextInt(10))+String.valueOf(rr.nextInt(10))+String.valueOf(rr.nextInt(10));
   return Integer.parseInt(str);
  
  
}
  

public static void main(String args[]){

KeyGenerator Generator = new KeyGenerator();

System.out.println(Generator.getKeys());import java.io.File;

import java.io.FileInputStream;

import java.io.FileOutputStream;

import java.io.IOException;

import java.security.InvalidKeyException;

import java.security.Key;

import java.security.NoSuchAlgorithmException;

import javax.crypto.BadPaddingException;

import javax.crypto.Cipher;

import javax.crypto.IllegalBlockSizeException;

import javax.crypto.NoSuchPaddingException;

import javax.crypto.spec.SecretKeySpec;

public class CryptoUtils {

    private static final String ALGORITHM = "AES";

    private static final String TRANSFORMATION = "AES";

    public static void encrypt(String key, File inputFile, File outputFile)

            throws CryptoException {

        doCrypto(Cipher.ENCRYPT_MODE, key, inputFile, outputFile);

    }

    public static void decrypt(String key, File inputFile, File outputFile)

            throws CryptoException {

        doCrypto(Cipher.DECRYPT_MODE, key, inputFile, outputFile);

    }

    private static void doCrypto(int cipherMode, String key, File inputFile,

            File outputFile) throws CryptoException {

        try {

            Key secretKey = new SecretKeySpec(key.getBytes(), ALGORITHM);

            Cipher cipher = Cipher.getInstance(TRANSFORMATION);

            cipher.init(cipherMode, secretKey);

            FileInputStream inputStream = new FileInputStream(inputFile);

            byte[] inputBytes = new byte[(int) inputFile.length()];

            inputStream.read(inputBytes);

            byte[] outputBytes = cipher.doFinal(inputBytes);

            FileOutputStream outputStream = new FileOutputStream(outputFile);

            outputStream.write(outputBytes);

            inputStream.close();

            outputStream.close();

        } catch (NoSuchPaddingException | NoSuchAlgorithmException

                | InvalidKeyException | BadPaddingException

                | IllegalBlockSizeException | IOException ex) {

            throw new CryptoException("Error encrypting/decrypting file", ex);

        }

    }

}

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.