InfoSec Notes

Digital Signatures

Complete guide to digital signatures covering RSA and ECDSA signing, verification process, certificate chains, applications in code signing and documents, with Python implementations.

What are Digital Signatures?

A digital signature is a cryptographic mechanism that provides authentication, integrity, and non-repudiation for digital messages or documents. It is the digital equivalent of a handwritten signature but far more secure — it mathematically binds a message to the signer's identity.

Digital Signature vs Handwritten Signature

=============================================

Handwritten

- Can be forged (copied)

- Same for all documents

- Cannot detect document changes

- Disputed authenticity requires expert analysis

Digital

- Cannot be forged without private key

- Different for every document signed

- Any document change invalidates signature

- Verification is mathematical (objective)

How Digital Signatures Work

SIGNING PROCESS

==================

Document Private Key

| |

v |

[Hash Function] |

(SHA-256) |

| |

v v

Message Digest ---------> [Signing Algorithm]

(256-bit hash) (RSA-PSS/ECDSA)

Digital Signature

(attached to document)

VERIFICATION PROCESS

======================

Received Document Received Signature Public Key

| | |

v | |

[Hash Function] | |

(SHA-256) v v

| [Verification Algorithm] |

v | |

Computed Digest v |

| Extracted Digest <---------+

| |

+----------> [Compare] <-------+

VALID or INVALID

Implementation in Python

Example

from cryptography.hazmat.primitives.asymmetric import rsa, ec, padding, utils from cryptography.hazmat.primitives import hashes, serialization from cryptography.x509 import load_pem_x509_certificate import hashlib class DigitalSignatureService: """Complete digital signature implementation.""" def __init__(self, algorithm="rsa"): if algorithm == "rsa": self.private_key = rsa.generate_private_key( public_exponent=65537, key_size=2048 ) elif algorithm == "ecdsa": self.private_key = ec.generate_private_key(ec.SECP256R1()) self.public_key = self.private_key.public_key() self.algorithm = algorithm def sign_message(self, message: bytes) -> bytes: """Create digital signature for a message.""" if self.algorithm == "rsa": signature = self.private_key.sign( message, padding.PSS( mgf=padding.MGF1(hashes.SHA256()), salt_length=padding.PSS.MAX_LENGTH ), hashes.SHA256() ) else: # ECDSA signature = self.private_key.sign( message, ec.ECDSA(hashes.SHA256()) ) return signature def verify_signature(self, message: bytes, signature: bytes) -> bool: """Verify a digital signature.""" try: if self.algorithm == "rsa": self.public_key.verify( signature, message, padding.PSS( mgf=padding.MGF1(hashes.SHA256()), salt_length=padding.PSS.MAX_LENGTH ), hashes.SHA256() ) else: # ECDSA self.public_key.verify(signature, message, ec.ECDSA(hashes.SHA256())) return True except Exception: return False def sign_document(self, document_path: str) -> dict: """Sign a document file.""" with open(document_path, 'rb') as f: content = f.read() # Hash the document doc_hash = hashlib.sha256(content).hexdigest() # Sign the hash signature = self.sign_message(content) return { "document_hash": doc_hash, "signature": signature.hex(), "algorithm": f"{self.algorithm.upper()}-SHA256", "key_size": "2048" if self.algorithm == "rsa" else "256 (P-256)" } # Demonstration print("=== RSA Digital Signature ===") rsa_signer = DigitalSignatureService("rsa") message = b"I hereby authorize the transfer of $50,000 to Account #12345" signature = rsa_signer.sign_message(message) print(f"Message: {message.decode()}") print(f"Signature: {signature.hex()[:64]}...") print(f"Signature size: {len(signature)} bytes") # Verify valid signature valid = rsa_signer.verify_signature(message, signature) print(f"Verification (original): {valid}") # Verify tampered message tampered = b"I hereby authorize the transfer of $500,000 to Account #12345" valid_tampered = rsa_signer.verify_signature(tampered, signature) print(f"Verification (tampered): {valid_tampered}") print("\n=== ECDSA Digital Signature ===") ecdsa_signer = DigitalSignatureService("ecdsa") signature_ec = ecdsa_signer.sign_message(message) print(f"ECDSA Signature: {signature_ec.hex()[:64]}...") print(f"ECDSA Signature size: {len(signature_ec)} bytes (much smaller than RSA!)") print(f"Verification: {ecdsa_signer.verify_signature(message, signature_ec)}")

RSA vs ECDSA Signatures

Feature	RSA-2048	ECDSA (P-256)
Signature size	256 bytes	64 bytes
Public key size	256 bytes	64 bytes
Sign speed	Slower	Faster
Verify speed	Faster	Slower
Security level	112 bits	128 bits
Standard	PKCS#1, PSS	FIPS 186-4
Use cases	Certificates, email	TLS, Bitcoin, mobile

Applications of Digital Signatures

Code Signing

Code Signing Process

========================

Developer

Source Code → [Compile] → Binary

Binary → [Hash SHA-256] → Digest

Digest → [Sign with Dev Certificate] → Signature

Package: Binary + Signature + Certificate

User/OS Verification

Binary → [Hash SHA-256] → Computed Digest

Signature → [Verify with Dev's Public Key] → Original Digest

Compare: Computed == Original?

Certificate → [Verify against Trusted Root CAs]

All pass? → Software is authentic and untampered

Any fail? → "Unknown publisher" warning or block

Document Signing (PDF, DOCX)

Code example

PDF Digital Signature:
========================

Signer:                           Verifier:
1. Open PDF                       1. Open signed PDF
2. Add signature field            2. Software extracts signature
3. Hash document content          3. Verify certificate chain
4. Sign hash with private key     4. Verify hash matches content
5. Embed signature + cert in PDF  5. Check timestamp (if present)
                                  6. Display: ✓ Valid / ✗ Invalid

Certificate Chains and Trust

Certificate Chain of Trust

==============================

Root CA Certificate (self-signed, stored in OS/browser)

│ Signs ↓

├── Intermediate CA Certificate

│ │ Signs ↓

│ ├── End-Entity Certificate (your server/person)

│ │ Contains: Public Key, Identity, Validity Period

│ │ Signed by: Intermediate CA

│ │

│ └── Another End-Entity Certificate

│

└── Another Intermediate CA

└── End-Entity Certificates

Verification walks UP the chain

End-Entity → Signed by Intermediate? ✓

Intermediate → Signed by Root? ✓

Root → Trusted by OS/Browser? ✓

All valid? → Signature is trusted

Interview Questions

How do digital signatures provide non-repudiation?

Only the private key holder can create a valid signature. Since the private key is assumed to be under sole control of the owner, they cannot deny signing. The certificate authority vouches for key ownership, and timestamps prove when the signature was created.

What is the difference between encryption and signing with RSA?

Encryption: Encrypt with public key, decrypt with private key (confidentiality). Signing: Sign with private key, verify with public key (authentication/integrity). They are mathematically inverse operations but serve different purposes.

Why do we hash the message before signing rather than signing the entire message?

RSA can only operate on data smaller than the modulus (e.g., 256 bytes for RSA-2048). Hashing reduces any document to a fixed size. It's also much faster to sign a 32-byte hash than a multi-gigabyte file.

What happens when a code signing certificate expires?

Without timestamping, signatures become invalid after certificate expiry. With RFC 3161 timestamping, the signature includes a trusted timestamp proving it was created while the certificate was valid, so the signature remains valid even after expiration.

Explain the difference between RSA-PSS and PKCS#1 v1.5 signatures.

PKCS#1 v1.5 is the older scheme — deterministic (same message → same signature) and has known theoretical weaknesses (Bleichenbacher-style attacks). PSS (Probabilistic Signature Scheme) includes random salt, making signatures non-deterministic and provably secure under the RSA assumption.

Summary

Digital signatures are essential for establishing trust in the digital world. They provide mathematically verifiable proof of document authenticity and integrity. When implementing digital signatures, use RSA-PSS or ECDSA with SHA-256, include timestamps for long-term validity, validate certificate chains, and protect private keys with HSMs in production environments.

Exam Focus

Revise definitions, diagrams, examples, and short-answer points for Digital Signatures.

Interview Use

Prepare one clear explanation, one practical example, and one common mistake for this Information Security topic.

Search Terms

information-security, information security, information, security, cryptography, digital, signatures, digital signatures

Continue learning this concept

CryptographyAES - Advanced Encryption StandardComplete guide to the AES algorithm covering its structure, rounds, key expansion, modes of operation, implementation in Python, and why AES replaced DES as the global encryption standard.CryptographyAsymmetric Key CryptographyDeep dive into public key cryptography covering RSA, ECC, Diffie-Hellman key exchange, digital signatures, and how asymmetric algorithms solve the key distribution problem.CryptographyDES - Data Encryption StandardUnderstanding the Data Encryption Standard (DES), its Feistel structure, historical significance, vulnerabilities, evolution to 3DES, and why it was replaced by AES.CryptographyEncryption vs DecryptionUnderstanding the fundamental processes of encryption and decryption, their differences, step-by-step operations, and practical applications in modern information security.CryptographyCryptographic Hash FunctionsComprehensive guide to hash functions including MD5, SHA family, properties, applications in password storage, integrity verification, and digital signatures with Python implementations.CryptographyIntroduction to CryptographyFoundational guide to cryptography covering core concepts, terminology, classical ciphers, modern algorithms, and the role of cryptography in securing information systems.

PreviousDES - Data Encryption Standard NextEncryption vs Decryption

InfoSec Notes

Digital Signatures

Complete guide to digital signatures covering RSA and ECDSA signing, verification process, certificate chains, applications in code signing and documents, with Python implementations.

What are Digital Signatures?

Digital Signature vs Handwritten Signature

=============================================

Handwritten

- Can be forged (copied)

- Same for all documents

- Cannot detect document changes

- Disputed authenticity requires expert analysis

Digital

- Cannot be forged without private key

- Different for every document signed

- Any document change invalidates signature

- Verification is mathematical (objective)

How Digital Signatures Work

SIGNING PROCESS

==================

Document Private Key

| |

v |

[Hash Function] |

(SHA-256) |

| |

v v

Message Digest ---------> [Signing Algorithm]

(256-bit hash) (RSA-PSS/ECDSA)

Digital Signature

(attached to document)

VERIFICATION PROCESS

======================

Received Document Received Signature Public Key

| | |

v | |

[Hash Function] | |

(SHA-256) v v

| [Verification Algorithm] |

v | |

Computed Digest v |

| Extracted Digest <---------+

| |

+----------> [Compare] <-------+

VALID or INVALID

Implementation in Python

Example

RSA vs ECDSA Signatures

Feature	RSA-2048	ECDSA (P-256)
Signature size	256 bytes	64 bytes
Public key size	256 bytes	64 bytes
Sign speed	Slower	Faster
Verify speed	Faster	Slower
Security level	112 bits	128 bits
Standard	PKCS#1, PSS	FIPS 186-4
Use cases	Certificates, email	TLS, Bitcoin, mobile

Applications of Digital Signatures

Code Signing

Code Signing Process

========================

Developer

Source Code → [Compile] → Binary

Binary → [Hash SHA-256] → Digest

Digest → [Sign with Dev Certificate] → Signature

Package: Binary + Signature + Certificate

User/OS Verification

Binary → [Hash SHA-256] → Computed Digest

Signature → [Verify with Dev's Public Key] → Original Digest

Compare: Computed == Original?

Certificate → [Verify against Trusted Root CAs]

All pass? → Software is authentic and untampered

Any fail? → "Unknown publisher" warning or block

Document Signing (PDF, DOCX)

Code example

PDF Digital Signature:
========================

Signer:                           Verifier:
1. Open PDF                       1. Open signed PDF
2. Add signature field            2. Software extracts signature
3. Hash document content          3. Verify certificate chain
4. Sign hash with private key     4. Verify hash matches content
5. Embed signature + cert in PDF  5. Check timestamp (if present)
                                  6. Display: ✓ Valid / ✗ Invalid

Certificate Chains and Trust

Certificate Chain of Trust

==============================

Root CA Certificate (self-signed, stored in OS/browser)

│ Signs ↓

├── Intermediate CA Certificate

│ │ Signs ↓

│ ├── End-Entity Certificate (your server/person)

│ │ Contains: Public Key, Identity, Validity Period

│ │ Signed by: Intermediate CA

│ │

│ └── Another End-Entity Certificate

│

└── Another Intermediate CA

└── End-Entity Certificates

Verification walks UP the chain

End-Entity → Signed by Intermediate? ✓

Intermediate → Signed by Root? ✓

Root → Trusted by OS/Browser? ✓

All valid? → Signature is trusted

Interview Questions

How do digital signatures provide non-repudiation?

Only the private key holder can create a valid signature. Since the private key is assumed to be under sole control of the owner, they cannot deny signing. The certificate authority vouches for key ownership, and timestamps prove when the signature was created.

What is the difference between encryption and signing with RSA?

Encryption: Encrypt with public key, decrypt with private key (confidentiality). Signing: Sign with private key, verify with public key (authentication/integrity). They are mathematically inverse operations but serve different purposes.

Why do we hash the message before signing rather than signing the entire message?

RSA can only operate on data smaller than the modulus (e.g., 256 bytes for RSA-2048). Hashing reduces any document to a fixed size. It's also much faster to sign a 32-byte hash than a multi-gigabyte file.

What happens when a code signing certificate expires?

Without timestamping, signatures become invalid after certificate expiry. With RFC 3161 timestamping, the signature includes a trusted timestamp proving it was created while the certificate was valid, so the signature remains valid even after expiration.

Explain the difference between RSA-PSS and PKCS#1 v1.5 signatures.

PKCS#1 v1.5 is the older scheme — deterministic (same message → same signature) and has known theoretical weaknesses (Bleichenbacher-style attacks). PSS (Probabilistic Signature Scheme) includes random salt, making signatures non-deterministic and provably secure under the RSA assumption.

Summary

Exam Focus

Revise definitions, diagrams, examples, and short-answer points for Digital Signatures.

Interview Use

Prepare one clear explanation, one practical example, and one common mistake for this Information Security topic.

Search Terms

information-security, information security, information, security, cryptography, digital, signatures, digital signatures

Continue learning this concept

PreviousDES - Data Encryption Standard NextEncryption vs Decryption