Question

Decryption Stage While everyone can do the encryption using public (n,e), not everyone can decrypt. To do this, you need to know the exact p and q, which is very large and kept secret in practice. Actually, the secret key d used in decryption is an inverse of emod(p−1)(q−1), i.e., ed≡1mod(p−1)(q−1). According to the corollary given below, d can decrypt (memodn) back to m by another exponential operation. Note that m

Answer 1

The question focuses on the decryption process in cryptography and the necessity of a private key for decrypting messages encrypted with a public key, highlighting the RSA algorithm's use of prime factorization and modular arithmetic.

Step-by-step explanation:

The subject of the question is centered on the process of decryption within the realm of cryptosystems, specifically discussing the use of a private key (d) in relation to the public components of a cryptosystem. It explains that while encryption can be performed by anyone with the public key (n, e), decryption requires the secret private key, which is computed using the large prime factors p and q.

The private key d is the multiplicative inverse of e modulo (p-1)(q-1), which means that ed is congruent to 1 modulo (p-1)(q-1). This formula is crucial for understanding the RSA encryption algorithm, which involves modular arithmetic and prime factorization.