UNIVERSITY OF WEST ATTICA
SCHOOL OF ENGINEERING
DEPARTMENT OF COMPUTER ENGINEERING AND INFORMATICS

University of West Attica · Department of Computer Engineering and Informatics

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Information Technology Security

Cryptography

Vasileios Evangelos Athanasiou
Student ID: 19390005

GitHub · LinkedIn

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Supervision

Supervisor: Ioanna Kantzavelou, Associate Professor

UNIWA Profile · LinkedIn

Co-supervisor: Angelos Georgoulas, Assistant Professor

Scholar · LinkedIn

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Athens, May 2023

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README

Cryptography

This project explores fundamental cryptographic operations using the OpenSSL BIGNUM (BN) library. It focuses on the practical implementation of RSA cryptography, including key generation, encryption, decryption, digital signatures, and certificate verification.

All implementations are written in C and utilize the OpenSSL BN library to handle large integer arithmetic beyond standard machine limits.

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Table of Contents

Section	Path / File	Description
1	assign/	Official laboratory exercise specifications
1.1	assign/Exercise 2 (Cryptography)_2023.pdf	Assignment description (English)
1.2	assign/Ασκηση 2 (Cryptography)_2023.pdf	Assignment description (Greek)
2	docs/	Project reports and theoretical analysis
2.1	docs/Cryptography.pdf	Technical report (English)
2.2	docs/Κρυπτογραφία.pdf	Technical report (Greek)
3	src/	Cryptographic implementations and verification tools
3.1	src/private_key.c	RSA private key generation
3.2	src/public_key	RSA public key extraction
3.3	src/crypto_msg.c	Message encryption using public key
3.4	src/decrypto_msg.c	Message decryption using private key
3.5	src/sign_msg.c	Digital signature generation
3.6	src/verify_sign.c	Digital signature verification
3.7	src/verify_sign_cert.c	Signature verification using X.509 certificates
3.8	src/bn_sample.c	Big number (BN) operations example
3.9	src/c0.pem, src/c1.pem	RSA certificates
3.10	src/c0_body.bin	Binary certificate body
3.11	src/cert_info.txt	Certificate metadata and inspection output
4	screens/	Experimental evidence and execution results
4.1	screens/Activity1–6/	Step-by-step screenshots for each cryptographic activity
5	README.md	Project documentation
6	INSTALL.md	Usage instructions

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1. Project Structure

The laboratory work is divided into independent activities, each targeting a specific cryptographic concept:

• Private Key Generation (private_key.c)
  Calculates the RSA private key d using prime numbers p, q, and the public exponent e.

• Message Encryption (crypto_msg.c)
  Encrypts a plaintext message (e.g., a student's name) using the RSA encryption formula:

  $$ C = M^e \pmod{N} $$

• Message Decryption (decrypto_msg.c)
  Decrypts an encrypted hexadecimal ciphertext back into readable text using:

  $$ D = C^d \pmod{N} $$

• Digital Signature Creation (sign_msg.c)
  Generates a digital signature for a given message using the RSA private key.

• Signature Verification (verify_sign_msg.c)
  Verifies message authenticity by comparing the decrypted signature with the original message.

• X.509 Certificate Verification (verify_sign_cert.c)
  Manually extracts and verifies the digital signature of a real-world web server certificate
  (e.g., apachefriends.org).

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2. Key Mathematical Formulas Used

• Modulo (RSA modulus):

$$ N = p \times q $$

• Euler’s Totient Function:

$$ \phi(N) = (p-1)(q-1) $$

• Private Key Calculation:

$$ e \cdot d \equiv 1 \pmod{\phi(N)} $$

• Encryption:

$$ C = M^e \pmod{N} $$

• Decryption:

$$ D = C^d \pmod{N} $$

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3. Key Observations

3.1 Sensitivity

Even a single-bit change in a message or signature produces a completely different result, ensuring data integrity.

3.2 Efficiency

The OpenSSL BN library efficiently manages large integers required for secure RSA operations.

3.3 Real-world Application

The same RSA principles implemented in this lab are used in X.509 certificate verification for secure web communications.

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4. Conclusion

This laboratory project demonstrates how theoretical cryptographic principles are applied in practice using professional-grade libraries. It bridges the gap between academic RSA concepts and their real-world security applications, such as encrypted communication and digital certificate validation.