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**11 - 16**of**16**### Fourier transform (QFT). We give an upper bound of Fast

"... We give new bounds on the circuit complexity of the quantum ..."

### Chennai,Tamilnadu,

"... Confidentiality of data or resources is of primary importance in Privacy Preserving Data Mining (PPDM) Systems. The research work presented through this paper discusses the PPDM model in which the privacy of data transacted amongst the various Data Custodians involved is highlighted. The data availa ..."

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Confidentiality of data or resources is of primary importance in Privacy Preserving Data Mining (PPDM) Systems. The research work presented through this paper discusses the PPDM model in which the privacy of data transacted amongst the various Data Custodians involved is highlighted. The data available with each data custodian is assumed to be horizontally portioned. The proposed model considers the C5.0 algorithm for data mining and classification rule generation due to its advances and classification accuracy over its predecessors. Privacy of the data transacted or secure multiparty computation is achieved by using the commutative RSA cryptography scheme. The proposed model is compared with the existing secure group communication techniques like Secure Lock and Asynchronous Control Polynomial in terms of computational efficiency. Furthermore the privacy preserving feature of the proposed scheme is proved in terms of the computational indistinguishablity of the data transacted amongst the varied data custodians involved discussed in the paper.

### Some Connections Between Primitive Roots and Quadratic Non-Residues Modulo a Prime

"... Abstract—In this paper we present some interesting connections between primitive roots and quadratic non-residues modulo a prime. Using these correlations, we propose some polynomial deterministic algorithms for generating primitive roots for primes with special forms (for example, for safe primes). ..."

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Abstract—In this paper we present some interesting connections between primitive roots and quadratic non-residues modulo a prime. Using these correlations, we propose some polynomial deterministic algorithms for generating primitive roots for primes with special forms (for example, for safe primes). Index Terms—primitive roots, Legendre-Jacobi symbol, quadratic non-residues, square roots. I.

### CS 787: Advanced Algorithms Topic: Primality Testing

"... Primality test is a test to determine whether a given number is prime or not. These tests can be either deterministic or probabilistic. Deterministic tests determine absolutely whether a given number is prime or not. Probabilistic tests may, with some small probability, identify a ..."

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Primality test is a test to determine whether a given number is prime or not. These tests can be either deterministic or probabilistic. Deterministic tests determine absolutely whether a given number is prime or not. Probabilistic tests may, with some small probability, identify a

### Computing all MOD-functions simultaneously

"... The fundamental symmetric functions are EX n k (equal to 1 if the sum of n input bits is exactly k), TH n k (the sum is at least k), and MOD n m,r (the sum is congruent to r modulo m). It is well known that all these functions and in fact any symmetric Boolean function have linear circuit size. Si ..."

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The fundamental symmetric functions are EX n k (equal to 1 if the sum of n input bits is exactly k), TH n k (the sum is at least k), and MOD n m,r (the sum is congruent to r modulo m). It is well known that all these functions and in fact any symmetric Boolean function have linear circuit size. Simple counting shows that the circuit complexity of computing n symmetric functions is Ω(n 2−o(1) ) for almost all tuples of n symmetric functions. It is well-known that all EX and TH functions (i.e., for all 0 ≤ k ≤ n) of n input bits can be computed by linear size circuits. In this short note, we investigate the circuit complexity of computing all MOD functions (for all 1 ≤ m ≤ n). We prove an O(n) upper bound for computing the set of functions {MOD n 1,r, MOD n 2,r,..., MOD n n,r} and an O(n log log n) upper bound for {MOD n 1,r1, MODn 2,r2,..., MODn n,rn}, where r1, r2,..., rn are arbitrary integers.

### Modular Square Root Puzzles: Design of Non-Parallelizable and Non-Interactive Client Puzzles

, 2012

"... Denial of Service (DoS) attacks aiming to exhaust the resources of a server by overwhelming it with bogus requests have become a serious threat. Especially protocols that rely on public key cryptography and perform expensive authentication handshakes may be an easy target. A well-known countermeasur ..."

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Denial of Service (DoS) attacks aiming to exhaust the resources of a server by overwhelming it with bogus requests have become a serious threat. Especially protocols that rely on public key cryptography and perform expensive authentication handshakes may be an easy target. A well-known countermeasure against resource depletion attacks are client puzzles. The victimized server demands from the clients to commit computing resources before it processes their requests. To get service, a client must solve a cryptographic puzzle and submit the right solution. Existing client puzzle schemes have some drawbacks. They are either parallelizable, coarse-grained or can be used only interactively. In case of interactive client puzzles where the server poses the challenge an attacker might mount a counterattack on the clients by injecting faked packets with bogus puzzle parameters bearing the server’s sender address. In this paper we introduce a novel scheme for client puzzles which relies on the computation of square roots modulo a prime. Modular square root puzzles are non-parallelizable, i. e., the solution cannot be obtained faster than scheduled by distributing the puzzle to multiple machines or CPU cores, and they can be employed both interactively and non-interactively. Our puzzles provide polynomial granularity and compact solution and verification functions. Benchmark results demonstrate the feasibility of our approach to mitigate DoS attacks on hosts in 1 or even 10 Gbit networks. In addition, we show how to raise the efficiency of our puzzle scheme by introducing a bandwidth-based cost factor for the client. Furthermore, we also investigate the construction of client puzzles from modular cube roots.