Blockchain RSA
The Rivest-Shamir-Adleman (RSA) public-key cryptosystem is widely used for secure data transport. Asymmetric encryption uses public and private keys for encryption and decryption. Giving sensitive data a safe way to be transmitted via unprotected networks, such as the internet, is the main goal of RSA.
History of RSA
The Massachusetts Institute of Technology’s Ron Rivest, Adi Shamir, and Leonard Adleman initially publicly presented the Blockchain RSA algorithm in 1977. The algorithm was named after their last initials. They created it in response to the demand for safe digital communication over computer networks, specifically to facilitate private discussions via electronic systems such as the internet.
Secure key distribution was a problem for conventional cryptographic systems before Blockchain RSA since both parties had to share a secret key beforehand. Public-key cryptography and RSA addressed this by removing the necessity for prior secret key sharing and enabling users to communicate their public key publicly while maintaining the confidentiality of their private key.
The British intelligence organization Government Communications Headquarters (GCHQ) employed Clifford Cocks, an English mathematician, to covertly create a comparable system in 1973. Nevertheless, until 1997, this system was still classified. Although MIT was given a U.S. patent for the Blockchain RSA algorithm in 1983, the patent expired in 2000, and Blockchain RSA Security made the algorithm publicly available prior to that date.
How RSA Works
The computational complexity of factoring the product of two very big prime numbers is the foundational idea of the Blockchain RSA method. Multiplying these big prime numbers is easy, but it’s computationally difficult to reverse the process and get the initial primes. RSA’s security is based on this “factoring problem”.
The creation, distribution, encryption, and decryption of keys are the four primary processes of the Blockchain RSA algorithm.
Key Generation
The Blockchain RSA algorithm’s keys are produced in this manner:
- Select two prime numbers, usually represented by the letters p and q. These primes should be large enough, randomly selected, and significantly different from one another to make factoring challenging. P and Q are not revealed.
- Modulus n = p * q, the product of these two primes, is calculated. The public key discloses the modulus for the public and private keys, n. The key is n bits long.
- Calculate Carmichael’s totient function, λ(n). Since n = pq, λ(n) = lcm(p – 1, q – 1). Euler totient function φ(n) = (p – 1)(q – 1), utilized in the original study, can also be used since it is always divisible by λ(n). A secret is kept for λ(n) (or φ?).
- The public exponent, e, must be coprime to λ(n) (gcd(e, λ(n)) = 1) and 1 < e < λ(n). A popular option for e is 65537 since it enables more effective encryption. As part of the public key, e is made available.
- Take e modulo λ(n) and compute its modular multiplicative inverse, d, the private exponent. De ≡ 1 (mod λ(n)) for this. d must be kept hidden because it can be efficiently calculated using the Extended Euclidean algorithm.
- The (n, e) pair makes up the public key, whereas the (n, d) pair makes up the private key. Because they can be used to determine d, the numbers p, q, and λ(n) (or φ(n)) must likewise be kept hidden.
Key Distribution
Alice’s public key helps Bob secure messages and connections. Alice securely sends Bob her public key (n, e). Alice keeps her private key private.
Encryption
To encrypt, the sender changes M (plaintext) to padded m, ensuring 0 ≤ m < n. The sender will calculate ciphertext c using the recipient’s public key (n, e): c ≡ m^e (mod n). Fast modular exponentiation for large numbers. Gives recipient c.
Decryption
Using their private key (n, d), the recipient calculates: m ≡ c^d (mod n) to recover the original message m from the ciphertext c. To get the original message M, the recipient reverses the padding technique after recovering m.
Example of RSA Operation
An illustration of the procedure is provided: When p=61 and q=53 are chosen, n=3233 and λ(n)=780 are obtained. Choosing e=17 yields 413 d. Public keys are (3233, 17) while private keys are (3233, 413). For m=65, c = 65^17 mod 3233 = 2790 is the encryption. Calculate m = 2790^413 mod 3233 = 65 to decode c=2790. Prime numbers are substantially larger in real-world situations to avoid factoring n.
Signing Messages
Digital signatures that offer non-repudiation, integrity, and authentication can also be created using Blockchain RSA.
- A cryptographic hash function is used by the sender to create the message’s hash value.
- In order to create the digital signature, the sender then “signs” this hash value by utilizing their private key (d) to apply the Blockchain RSA method.
- The message is sent to the receiver along with its digital signature. They use the public key of the sender (e) to apply the Blockchain RSA algorithm to the digital signature.
- The recipient creates their own hash value for the message they received as well.
- The message’s integrity and the author’s ownership of the private key are verified if the hash value produced by the signature’s decryption and the hash value created over the message match (authentication and non-repudiation).
Efficiency Considerations
The computational complexity of RSA renders it impractical for directly encrypting large amounts of data, notwithstanding its power. Blockchain RSA encrypts a symmetric key, which is subsequently used to encrypt the actual, larger data. This hybrid approach is far more common. Both symmetric (for bulk encryption) and asymmetric (for key exchange) cryptography’s advantages are utilized here.
Using optimizations based on the Chinese Remainder Theorem (CRT), Blockchain RSA decryption and signing processes can be improved. Efficiency is greatly increased by this strategy, which divides the massive modular exponentiation into two smaller ones.
RSA Security
The difficulty of factoring the product of two huge prime numbers is what gives Blockchain RSA its security. The RSA problem is the cracking of RSA encryption.
Key Size
- The size of the key directly affects encryption strength. The longer the key, the more complicated factoring becomes.
- Deprecated in 2013, 1024-bit Blockchain RSA keys are no longer regarded as secure due to their crackability.
- A key at least 2048 bits long is now best practice. NIST says 2048-bit keys are enough till 2030.
- 4096-bit keys increase computational effort but give higher data security and are only used in high-security situations.
Future Challenges: Quantum Computing
Although RSA is thought to be safe from conventional attacks using big keys at the moment, quantum computing could pose a problem in the future. RSA would become outdated if practical quantum computers were created because Shor’s algorithm, a potent quantum algorithm, could factor big numbers effectively. Lattice-based encryption and other post-quantum cryptography techniques are being investigated as ways to mitigate this risk.
RSA Vulnerabilities and Attacks
Although RSA is widely used, there are a number of documented flaws that might arise if it is not implemented or used properly.
- Side-channel attacks: Rather than going straight after the algorithm, these attacks take advantage of physical data that has been compromised during cryptographic operations.
- Timing attacks: How long does it take a device to encrypt and decode data using RSA?
- Power analysis attacks: Examine the fluctuating power usage while RSA is operating.
- Branch-prediction analysis (BPA): finds private keys statistically by taking advantage of processor characteristics.
- Countermeasure: A random number is introduced in cryptographic blinding to mask the relationship between computation time and the secret key.
- Inadequate Key Length / Weak Key Generation
- Weak Random Number Generator: If the initial prime numbers are chosen using a poor random number generator, attackers may find it easier to figure out the pattern and factor the keys.
- Closeness of Prime Numbers: An RSA key’s security may be jeopardized if the values of the two prime numbers (p and q) are too near or if one is too tiny.
- Short Private Exponent d: It can be calculated effectively from n and e if the private exponent d is too small.
- Lost or Stolen Keys: Attackers have direct access to and decryption capabilities for encrypted messages if private keys are compromised.
- Fault-based attacks: Attackers intentionally develop flaws in software or hardware to produce weaker keys or retrieve private data.
- Attacks against plain RSA: RSA is susceptible to several attacks in the absence of enough padding, such as:
- The eth root can be easily decrypted due to the short plaintext values and low encryption exponents.
- Deterministic nature of chosen-plaintext attacks.
- Multiplicative property: The encryption of the product of two ciphertexts is known as the product of their plaintexts, which makes chosen-ciphertext attacks possible.
- Padding Vulnerabilities: Practical adaptive chosen-ciphertext attacks (such as the Bleichenbacher attack in 1998) were found to be able to compromise early padding schemes, such as PKCS#1 v1.5.
- ROCA vulnerability: Discovered in 2017, this vulnerability allowed attackers to factor weak RSA keys by affecting the RSA key generation in particular hardware security modules.
- Tricky Implementation: RSA implementation is difficult and requires careful attention to numerous details, including the use of a robust pseudorandom number generator (PRNG) and appropriate public exponents.
Applications and Use Cases of RSA
There are numerous applications for RSA in cryptography and information security:
Digital Signatures: The legitimacy, integrity, and non-repudiation of messages are often verified via RSA digital signatures.
Digital Certificates (SSL/TLS): It is crucial for digital certificates like SSL/TLS, which verify websites and businesses. Certificate issuer digital signatures are encrypted using RSA.
Secure Communication Protocols: RSA and protocols like Transport Layer Security (TLS) enable secure web server-browser communications for online transactions and surfing. VPNs and encrypted email are also helped.
Secure Key Exchange: RSA makes it possible for two parties who have never shared a secret key to safely exchange symmetric keys.
Online Transactions: RSA protects private financial data, hence securing online banking and e-commerce transactions.
Software Licensing: By guaranteeing that only authorised users can access or utilise particular software products, it serves as software protection.
Avoiding RSA Vulnerabilities and Best Practices
RSA security can be improved and vulnerabilities can be reduced by following these best practices:
Use strong key sizes: Always use a key that is at least 2048 bits long.
Strong prime number generation: For prime numbers to be surprising, use a powerful prime number generator. Weak prime numbers, such as those that are too small or too near to one another, should be avoided.
Secure key management: Use multiple RSA keys for different applications and rotate them regularly to protect them.
Protect against fault-based attacks: Protect yourself with tamper-resistant hardware.
Utilize secure padding schemes: Prior to encryption, use suggested padding strategies such as Optimal Asymmetric Encryption Padding (OAEP), which gives the message structure and randomness to make it more difficult for attackers to identify trends.
Vulnerability monitoring and updates: Maintain an eye out for fresh vulnerabilities and update the cryptographic libraries and RSA algorithm on a regular basis.
Consider alternative algorithms: Elliptic Curve Cryptography (ECC), which provides comparable security levels with reduced key sizes and enhanced efficiency, is a more contemporary technique to take into consideration given the changing cryptographic scene.