3.10. A decryption exponent for an RSA public key (N, e) is an integer d with the property that ade - a (mod N) for all integers a that are relatively prime to N (a) Suppose that Eve has a magic box that creates decryption exponents for (N, e) for a fixed modulus N and for a large number of different encryption expo- nents e. Explain how Eve can use her magic box to try to factor N (b) Let N - 38749709. Eve's magic box tells her that the encryption exponent e-10988423 has decryption exponent d = 16784693 and that the encryp- tion exponent e - 25910155 has decryption exponent d- 11514115. Use this information to factor N (c) Let N-225022969. Eve's magic box tells her the following three encryp- tion/decryption pairs for N (70583995,4911157), (173111957,7346999), (180311381,29597249) Use this information to factor N (d) Let N = 1291233941 Eve's magic box tells her the following three encryp- tion/decryption pairs for N (1103927639, 76923209), (1022313977, 106791263), (387632407, 7764043) Use this information to factor N 3.10. A decryption exponent for an RSA public key (N, e) is an integer d with the property that ade - a (mod N) for all integers a that are relatively prime to N (a) Suppose that Eve has a magic box that creates decryption exponents for (N, e) for a fixed modulus N and for a large number of different encryption expo- nents e. Explain how Eve can use her magic box to try to factor N (b) Let N - 38749709. Eve's magic box tells her that the encryption exponent e-10988423 has decryption exponent d = 16784693 and that the encryp- tion exponent e - 25910155 has decryption exponent d- 11514115. Use this information to factor N (c) Let N-225022969. Eve's magic box tells her the following three encryp- tion/decryption pairs for N (70583995,4911157), (173111957,7346999), (180311381,29597249) Use this information to factor N (d) Let N = 1291233941 Eve's magic box tells her the following three encryp- tion/decryption pairs for N (1103927639, 76923209), (1022313977, 106791263), (387632407, 7764043) Use this information to factor N