Among the most prevalent public-key algorithms are RSA and Diffie-Hellman. This discussion delves into these algorithms and introduces two additional ones.
RSA Public-Key Encryption Algorithm
The RSA algorithm, named after its inventors Ron Rivest, Adi Shamir, and Len Adleman at MIT in 1977, remains a cornerstone of public-key encryption. It operates as a block cipher with plaintext and ciphertext represented as integers between 0 and n - 1. Both sender and receiver must share knowledge of n and e for encryption: C = M^e mod n, while only the receiver knows d for decryption: M = C^d mod n. For effective encryption, e, d, and n must be chosen such that M^(ed) mod n = M for all M < n, enabling straightforward calculations of M^e and C^d, while making it infeasible to deduce d from e and n.
The RSA algorithm involves selecting two prime numbers p and q to compute their product n, followed by calculating Euler's totient f(n). An integer e, relatively prime to f(n), is chosen, and d is computed as the multiplicative inverse of e mod f(n). The strength of RSA lies in the difficulty of factoring large numbers, and its security improves with increased key sizes, currently recommending a 1024-bit key size for robustness.
Diffie-Hellman Key Exchange
Introduced by Diffie and Hellman, this algorithm facilitates the secure exchange of secret keys for encrypting subsequent messages. Its strength stems from the challenge of computing discrete logarithms. The process involves two users agreeing on a prime q and a primitive root α. Each user selects a private random integer and calculates a corresponding public value, which they exchange. Both users can then compute the shared secret key using the other's public value, ensuring secrecy. However, the protocol is susceptible to man-in-the-middle attacks in the absence of authentication measures like digital signatures.
Other Public-Key Cryptography Algorithms
Beyond RSA and Diffie-Hellman, Digital Signature Standard (DSS) and elliptic-curve cryptography (ECC) have gained commercial traction. DSS, utilizing SHA-1 and defined by NIST, provides digital signatures, contrasting RSA's broader functionality. ECC offers similar security with smaller key sizes, reducing processing demands in applications such as e-commerce. Despite its recent emergence and cryptanalytic scrutiny, ECC holds potential advantages over RSA in efficiency and security.
Each public-key algorithm has unique attributes and vulnerabilities, necessitating careful consideration of application needs and security requirements for effective implementation.
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