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 decryption stage of encryption using RSA algorithm involves using the private key to decrypt the message back to its original form. The private key is calculated as the inverse of a value modulo the product of two large prime numbers.

Step-by-step explanation:

The subject of this question is Mathematics and it is suitable for High School level. The question is discussing the decryption stage of encryption using RSA algorithm. In RSA, while anyone can encrypt using the public key, only those with the private key can decrypt the message.

The private key d used in decryption is calculated as the inverse of e modulo (p-1)(q-1). This is based on the corollary which states that d can be used to decrypt m back to its original form (me) modulo n.

Example: If e is 3, p is 5, and q is 7, then (p-1)(q-1) is 24. Calculating the inverse of 3 modulo 24 gives us 19, which is the private key d. With n being the product of p and q, if we encrypt a message m using the public key, we can decrypt it back to m using the private key d.