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

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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

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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

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