Question: Bob considers a small RSA public-key crypto-system with modulus n=2021. He wants to choose a valid private key for the decryption, denoted by d, which

Bob considers a small RSA public-key crypto-system with modulus n=2021. He wants to choose a valid private key for the decryption, denoted by d, which is the smallest valid key of two digits.

i. Please help Bob to find d.

ii. On behalf of Bob, please decrypt the message 2019 with the private key d found in i. If you cannot solve i, please make use of d=13.

iii. Please help Bob to find the public exponent e for the encryption given the private key d and modulus n above. In case you cannot solve i, please make use of d=13

iv. (Bonus) Analyze possible risks if Bob, and so do the community and Oscar, receives one of "dangerous" cipher messages 43,47,86,94, which are not relatively prime to n ? Estimate the number of "dangerous (cipher) messages" in large RSA cryptosystems.

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