**3.9** A **decryption exponent** for an RSA public key \((N, e)\) is an integer \(d\) with the property that \(a^{de} \equiv a \ (\text{mod} \ N)\) 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 exponents \(e\). 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 encryption 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 encryption/decryption pairs for \(N\):\[(70583995, 4911157), \quad (173111957, 7346999), \quad (180311381, 29597249).\]Use this information to factor \(N\).**(d)** Let \(N = 1291233941\). Eve’s magic box tells her the following three encryption/decryption pairs for \(N\):\[(1103927639, 76923209), \quad (1022313977, 106791263), \quad (387632407, 7764043).\]Use this information to factor \(N\).---### Explanation of Diagrams/GraphsThis section contains mathematical exercises related to encryption, specifically involving RSA encryption. Each part provides a scenario where Eve has access to certain encryption and decryption pairs or exponents, allowing her to potentially factor a large modulus \(N\). These exercises are used to illustrate the relationship between public keys, encryption exponents, and decryption exponents in RSA encryption. The given examples and pairs are purely numerical and do not involve visual diagrams or graphs.

RSA (Rivest-Shamir-Adleman) is a widely used asymmetric cryptographic algorithm that provides secure…

3.9. 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. 178 Exercises (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.

3.9. 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. 178 Exercises (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.

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

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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