Which public-key cryptographic system uses the properties of large prime numbers for secure data transmission?

Which public-key cryptographic system uses the properties of large prime numbers for secure data transmission?

• A. RSA Cryptosystem
• B. AES
• C. DES
• D. ECDSA

Answer: (A)

Public-key cryptography often relies on hard mathematical problems; RSA specifically rests on factoring large numbers. In RSA, you generate two large prime numbers, multiply them to form a modulus n, and publish n with a public exponent. The private key uses the original primes to enable decryption. The security comes from the fact that, given n, factorizing it into its prime factors p and q is extremely hard when n is large, so the private key remains protected. The other options don’t hinge on this prime-factorization challenge: AES and DES are symmetric-key ciphers using the same secret key for encryption and decryption, and ECDSA relies on the difficulty of the elliptic-curve discrete log problem rather than factoring large primes. Therefore, the RSA cryptosystem is the one that uses properties of large prime numbers for secure data transmission.

Public-key cryptography often relies on hard mathematical problems; RSA specifically rests on factoring large numbers. In RSA, you generate two large prime numbers, multiply them to form a modulus n, and publish n with a public exponent. The private key uses the original primes to enable decryption. The security comes from the fact that, given n, factorizing it into its prime factors p and q is extremely hard when n is large, so the private key remains protected. The other options don’t hinge on this prime-factorization challenge: AES and DES are symmetric-key ciphers using the same secret key for encryption and decryption, and ECDSA relies on the difficulty of the elliptic-curve discrete log problem rather than factoring large primes. Therefore, the RSA cryptosystem is the one that uses properties of large prime numbers for secure data transmission.