Suppose Alice has a public key with modulus 815153 and encryption exponent 91. Eve intercepts a ciphertext 766247from Bob that was encrypted using this key. She calculates 766247⋅941^91(mod815153)=143804 and asks Alice to decrypt this message as an authentication test. Alice responds with the decrypted message 167698 Find the plaintext without factoring Alice’s modulus.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Suppose Alice has a public key with modulus 815153 and encryption exponent 91. Eve intercepts a ciphertext 766247from Bob that was encrypted using this key. She calculates

766247⋅941^91(mod815153)=143804

and asks Alice to decrypt this message as an authentication test. Alice responds with the decrypted message

167698

Find the plaintext without factoring Alice’s modulus.

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