Show that the multiplicative property holds for rsa

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Reference no: EM133428725

Question:

(a) Show that the multiplicative property holds for RSA, i.e., show that the product of two ciphertexts y1,y2 is equal to the encryption of the product of the two respective plaintexts x1,x2: y1y2 mod n = RSAe(x1x2).

(b) Bob receives an encrypted message y1 from Alice using the RSA keys (d, e) and the exponent n. Eve obtains y1 by eavesdropping and is able to encrypt some other plaintext x into a ciphertext y using the public key e and the exponent n. She then sends Bob a new ciphertext y2 = yy1 mod n. Bob doesn't suspect anything and decrypts it to find that corresponding plaintext x2 doesn't make any sense and discards it. Eve is then able to obtain x2 too. Describe a chosen-ciphertext attack against RSA in this setting that allows Eve to obtain the original plaintext x1 from the information known to her. Which condition should x satisfy for this attack to work?

Reference no: EM133428725

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