Network Security and Cryptography RSA variant. Let us consider the following variant of the RSA public key encryption scheme, named RSA-M1 = (KG1, Enc1, Dec1). The corresponding key generation and encryption algorithms are detailed next: • Key generation KG¡(A) Generate two distinct odd primes p and q of same bit-size d - Compute N = p•q and o = (p – 1)(q – 1) - Select a random integer 1 < e <¢ such that gcd(e, ø) = 1 - Compute the unique integer d such that 1 < d < ¢ and e.d = 1 mod ¢ The public key is PK = (N, e). The private key is SK (N, e, d) %3D Encryption Enc1(PK, m) of a message m e ZN proceeds as fol- lows: Generate a random integer r in ZN - Compute îm =m•r mod N - Compute ci = mº mod N Compute c2 =r=e mod N %3D - Output C = (c1, c2) %3D (a) Give the corresponding decryption algorithm Dec1 (SK,C). Prove your decryption algorithm is correct, i.e. given a legitimate key pair (PK, SK) + KG|(A) it holds that Dec1 (SK, Enc1(PK,m)) m for any admissible plaintext m. (b) Is the public key encryption scheme RSA-M1 one-way? Justify your answer.

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Hash Table

A hash table also called a hash map, is a data structure that maps key-value pairs. The hash table can be used in complex systems to provide fast access and compact storage. A hash table is a structure that stores data in an abstract data type kind of associative array. It keeps data in an array format, with a distinct index value for every data value. If the index of the required data is known, then the data can be accessed very easily.