5. Hash Functions and Digital Signatures

Hash Functions and Digital Signatures

Cryptographic Hash Functions

• SHA-2: A family of cryptographic hash functions including SHA-256, SHA-384, and SHA-512.
• SHA-3: The latest member of the Secure Hash Algorithm family, designed to provide better security and performance than SHA-2.

Digital Signatures

• RSA: A widely-used public-key cryptosystem for secure communication and digital signatures.
• DSA (Digital Signature Algorithm): A Federal Information Processing Standard for digital signatures, designed for faster signing and verification compared to RSA.
• ECDSA (Elliptic Curve Digital Signature Algorithm): A variant of DSA using elliptic curve cryptography, offering shorter key lengths and faster performance.

Applications of Digital Signatures

• Authentication: Verifying the identity of the sender in electronic transactions.
• Integrity: Ensuring the integrity of transmitted data by detecting any unauthorized modifications.
• Non-repudiation: Preventing the sender from denying the authenticity or integrity of the message.

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Laboratory Activities

Lab 1: Digital Signature Generation and Verification using RSA in Python

from Crypto.PublicKey import RSA
from Crypto.Signature import pkcs1_15
from Crypto.Hash import SHA256

def generate_rsa_signature(message, private_key):
    hash_obj = SHA256.new(message)
    signature = pkcs1_15.new(private_key).sign(hash_obj)
    return signature

def verify_rsa_signature(message, signature, public_key):
    hash_obj = SHA256.new(message)
    try:
        pkcs1_15.new(public_key).verify(hash_obj, signature)
        return True
    except (ValueError, TypeError):
        return False

key = RSA.generate(2048)
public_key = key.publickey()
private_key = key

message = b"Hello World"
signature = generate_rsa_signature(message, private_key)
verification_result = verify_rsa_signature(message, signature, public_key)

print("Message:", message)
print("Signature:", signature)
print("Verification Result:", verification_result)

This lab demonstrates the generation and verification of digital signatures using RSA in Python.

Lab 2: Digital Signature Generation and Verification using ECDSA in Python

from Crypto.PublicKey import ECC
from Crypto.Signature import DSS
from Crypto.Hash import SHA256

def generate_ecdsa_signature(message, private_key):
    hash_obj = SHA256.new(message)
    signer = DSS.new(private_key, 'fips-186-3')
    signature = signer.sign(hash_obj)
    return signature

def verify_ecdsa_signature(message, signature, public_key):
    hash_obj = SHA256.new(message)
    verifier = DSS.new(public_key, 'fips-186-3')
    try:
        verifier.verify(hash_obj, signature)
        return True
    except (ValueError, TypeError):
        return False

key = ECC.generate(curve='P-256')
public_key = key.public_key()
private_key = key

message = b"Hello World"
signature = generate_ecdsa_signature(message, private_key)
verification_result = verify_ecdsa_signature(message, signature, public_key)

print("Message:", message)
print("Signature:", signature)
print("Verification Result:", verification_result)

This lab demonstrates the generation and verification of digital signatures using ECDSA in Python.