Basic Cryptography

Introduction to Cryptography

Cryptography, the science of secure communication, plays a pivotal role in our modern society. It involves the use of mathematical algorithms to transform data into a form that is unintelligible to unauthorized parties. In this article, we will explore the fundamental concepts of cryptography, its key components, and its significance in safeguarding sensitive information

Key Concepts

Cryptography revolves around two main operations: encryption and decryption. Encryption involves converting plaintext (readable data) into ciphertext, while decryption reverses this process to retrieve the original plaintext. Two primary types of cryptography are commonly used: symmetric key cryptography and asymmetric key cryptography. Symmetric key cryptography employs a shared secret key for both encryption and decryption, while asymmetric key cryptography uses a pair of mathematically related keys, including a public key for encryption and a private key for decryption. Additionally, hash functions are employed to generate fixed-length outputs (hashes) from variable-length inputs.

Symmetric Key Cryptography

Symmetric key cryptography relies on a single shared key, known only to the sender and the recipient, to encrypt and decrypt data. Prominent symmetric key algorithms include the Advanced Encryption Standard (AES) and the Data Encryption Standard (Broken). Key generation and secure key distribution are vital aspects of symmetric key cryptography. While symmetric key cryptography is efficient, the challenge lies in securely sharing the secret key between communicating parties.

Operation Mode in AES

Electronic Codebook (ECB) Mode

The Electronic Codebook (ECB) mode is the simplest mode of operation in AES cryptography. In this mode, each block of plaintext is encrypted independently with the AES algorithm using the same key. While ECB mode is straightforward to implement, it has some drawbacks. Identical plaintext blocks will result in identical ciphertext blocks, which can leak information and lead to patterns in the encrypted data. As a result, ECB mode is not recommended for encrypting large amounts of data or when confidentiality and integrity are critical. Don’t use it

Cipher Block Chaining (CBC) Mode

Cipher Block Chaining (CBC) mode addresses the limitations of ECB mode by introducing a feedback mechanism. In CBC mode, each plaintext block is XORed with the previous ciphertext block before encryption. This chaining of blocks ensures that identical plaintext blocks do not produce identical ciphertext blocks. To ensure the security of the first block, an Initialization Vector (IV) is used as the XOR input for the first block. CBC mode provides confidentiality and integrity, making it suitable for applications such as secure file transfer and disk encryption. Don’t use it Read this article

Counter (CTR) Mode

Counter (CTR) mode transforms the AES block cipher into a stream cipher. In CTR mode, a unique counter value is encrypted with the key to generate a stream of pseudorandom bits. The plaintext is then XORed with the stream to produce the ciphertext. CTR mode offers parallel encryption and decryption, making it highly efficient and suitable for applications that require random access to encrypted data. It is important to use a unique counter value for each block to maintain the security of the encryption.

Galois/Counter Mode (GCM)

Galois/Counter Mode (GCM) combines the Counter (CTR) mode with an additional authentication component, providing both confidentiality and integrity. GCM mode uses a Galois field multiplication to generate an authentication tag that ensures the integrity of the ciphertext. It provides a high level of security and efficiency, making it popular in applications where both confidentiality and integrity are crucial, such as secure network communications. GCM mode also supports parallel encryption and decryption.

Another Mode

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Asymmetric Key Cryptography

Asymmetric key cryptography, also known as public-key cryptography, employs a pair of related keys: a public key and a private key. The public key is freely distributed, allowing anyone to encrypt messages intended for the owner of the corresponding private key. Only the private key holder can decrypt these messages. Common asymmetric key algorithms include RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography). Asymmetric key cryptography provides a solution to the key distribution problem faced by symmetric key cryptography.

RSA

RSA lies on mathematical properties of prime numbers and modular arithmetic. RSA employs a pair of keys - a public key used for encryption and a private key used for decryption. The security of RSA relies on the difficulty of factoring large composite numbers into their prime factors.

Key Generation

The RSA ecosystem begins with the generation of the public and private key pair. Key generation involves selecting two large prime numbers, calculating the modulus, and finding the public and private exponents. The public key is made available to others for encrypting messages, while the private key is kept secret and used for decryption.

Encryption and Decryption

With the RSA algorithm, data can be encrypted using the recipient’s public key, ensuring that only the corresponding private key holder can decrypt and read the message. Conversely, a message can be digitally signed using the sender’s private key, and the recipient can verify the authenticity of the message using the sender’s public key.

Digital Signatures

RSA enables the creation and verification of digital signatures, providing a means of verifying the authenticity and integrity of messages. Digital signatures are created by encrypting a hash value of the message with the sender’s private key. The recipient can then decrypt the signature using the sender’s public key and compare it with the computed hash of the received message.

Key Exchange

The RSA ecosystem also facilitates secure key exchange between two parties. By encrypting a randomly generated symmetric key with the recipient’s public key, the sender can securely transmit the key to the recipient. The recipient can then decrypt the encrypted key using their private key and use it for symmetric encryption of subsequent communications.

EC

Elliptic Curve Cryptography is a branch of public-key cryptography that leverages the mathematical properties of elliptic curves over finite fields. The core concept involves performing mathematical operations on points on the elliptic curve to achieve secure encryption and decryption. The security of EC cryptography is based on the elliptic curve discrete logarithm problem, which is computationally infeasible to solve

Elliptic Curve Parameters

The EC ecosystem begins with the selection of appropriate elliptic curve parameters. These parameters include the elliptic curve equation, the finite field over which the curve is defined, and a base point on the curve. The choice of parameters is critical to ensuring the security and efficiency of the cryptographic system.

Key Generation

EC cryptography employs a public-private key pair, similar to other asymmetric encryption algorithms. Key generation involves selecting a random private key and deriving the corresponding public key based on elliptic curve operations. The public key is made available to others for encryption, while the private key remains secret and is used for decryption.

Encryption and Decryption

With EC cryptography, data can be encrypted using the recipient’s public key and decrypted using the corresponding private key. The encryption process involves performing a series of elliptic curve operations on the plaintext, while decryption utilizes the private key to reverse the encryption process and recover the original message.

Digital Signatures:

EC cryptography enables the creation and verification of digital signatures, ensuring the authenticity and integrity of messages. Digital signatures are created by performing elliptic curve operations on a hash of the message using the sender’s private key. The recipient can then verify the signature using the sender’s public key and compare it with the computed hash of the received message.

Advantages of EC

1. Strong Security with Shorter Key Lengths: EC cryptography provides equivalent or higher security compared to traditional cryptographic algorithms, such as RSA or DSA, with significantly shorter key lengths. This makes it computationally more efficient and well-suited for resource-constrained devices, such as mobile devices and Internet of Things (IoT) devices.

2. Efficient Performance: The mathematical operations involved in EC cryptography are computationally efficient, leading to faster encryption and decryption operations. This efficiency is especially beneficial in scenarios that require real-time communication or large-scale data processing.

3. Scalability: The EC ecosystem supports a wide range of key sizes, allowing for scalability to meet different security requirements. This flexibility makes it adaptable to diverse applications and environments.

ED-DSA

The ED-DSA algorithm is a variant of the Digital Signature Algorithm (DSA) that utilizes Edwards curves. Edwards curves are a type of elliptic curve that provides a unified representation and efficient operations, making them well-suited for cryptographic purposes. The algorithm combines the security properties of elliptic curves with the efficiency and simplicity of Edwards curves to provide robust digital signatures.

Key Generation

The ED-DSA algorithm begins with the generation of a public-private key pair. Key generation involves selecting a random private key and deriving the corresponding public key based on Edwards curve operations. The public key is made available to others for verification, while the private key remains secret and is used for generating digital signatures.

Signature Generation

To generate a digital signature using the ED-DSA algorithm, the signer performs a series of computations involving the private key, the message to be signed, and additional parameters. These computations include scalar multiplication, hashing, and modular arithmetic. The result is a digital signature that is unique to the signer and the specific message.

Signature Verification

The recipient of the digital signature can verify its authenticity and integrity using the signer’s public key. The verification process involves performing computations on the received signature, the corresponding message, and the public key. If the computations match, the signature is deemed valid, indicating that the message has not been tampered with and was indeed signed by the claimed signer.

Hash Functions

Hash functions are algorithms that convert arbitrary data into fixed-length hash values. They are commonly used to verify data integrity and provide a unique identifier for data. Examples of hash functions include Secure Hash Algorithm (SHA-256) and Message Digest Algorithm 5 (MD5). Hash-based message authentication codes (HMAC) combine a secret key with a hash function to provide message authentication and integrity.

MD5

Don’t use it. Read this article

SHA1

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SHA2

Design Components of SHA-2

1. Message Padding: SHA-2 processes input messages in fixed-size blocks. If the message length is not an exact multiple of the block size, padding is applied to ensure a uniform size. Padding includes adding a bit sequence to indicate the end of the message and appending additional bits to achieve the desired block size.

2. Message Digest Calculation: SHA-2 employs a series of logical and arithmetic operations, including bitwise operations, modular addition, and logical functions such as XOR and AND. The input message is divided into blocks, and each block is processed to update the internal state of the hash function. The final internal state is then transformed into the hash value.

SHA3

Design Principles of SHA-3

1.Sponge Construction: SHA-3 employs a sponge construction, which is a flexible design paradigm for hash functions. The sponge construction absorbs the input message, applies transformations to it, and then squeezes out the resulting hash value. This design allows for customizable hash functions with varying security levels and hash sizes.

2.Keccak Algorithm: The core component of SHA-3 is the Keccak algorithm, which is based on a permutation called Keccak-f. The Keccak-f permutation operates on a state array, which undergoes a series of transformations to process the input message. The flexibility of the sponge construction allows for different versions of SHA-3 with varying security parameters.

Advantages of SHA-3

1. Enhanced Security: SHA-3 offers improved security compared to its predecessors, particularly in terms of resistance against known attacks. The design principles of SHA-3, including the sponge construction and the Keccak algorithm, make it resistant to various cryptographic attacks, such as collision attacks and pre-image attacks.

2. Customizable Hash Sizes: SHA-3 supports hash output sizes of 224, 256, 384, and 512 bits. This flexibility allows for adapting the hash function to specific applications or security requirements. It provides a range of options suitable for different contexts, from lightweight applications to high-security environments.

3. Performance and Efficiency: Despite its enhanced security, SHA-3 remains efficient in terms of performance and computational requirements. It benefits from optimized implementations and hardware acceleration, making it suitable for a wide range of computing platforms, including resource-constrained devices.

4. NIST Standard: SHA-3 is a standardized hash algorithm by NIST, ensuring interoperability and compatibility across different systems and applications. Its adoption as a standard demonstrates its credibility and trustworthiness, making it a preferred choice for secure hash functions.