Computer Security

Q3: Public Key Cryptography 1) (8 pts) In RSA algorithm, if the modulus N=1723=391 and if the public key is e= 7 , please find the private key d. 2) (4 pts) Based on the above RSA key pairs, given a number 15 , what is the signature of this number? Please provide the equation. No need to do the calculation. 3) (4 pts) Assume that the square-and-multiply technique is used. How many modular multiplications are required to compute the signature above? 4) (8 pts) Given a prime elliptic curve E23(1,1), i.e., y2mod23=x3+x+1mod23, there are two points P=(5,4) and Q=(9,7) on the curve. Please find the point R on the curve, where R=P+Q. 5) (6 pts) Which difficult problem is the RSA algorithm based upon? How about the DiffieHellman algorithm and the ECC (elliptic curve cryptosystem)