Abstract: This paper briefly reviews the state of the art in artificial intelligence including inductive and deductive methods. Deep learning and ensemble machine learning lie in inductive methods while automated reasoning implemented in deductive computer languages (Prolog, Otter, and Z3) is based on deductive methods. In the inductive methods, intelligence is inferred by **pseudorandom** **number** for creating the sophisticated decision trees in Go (game), Shogi (game), and quiz bowl questions. This paper demonstrates how to wisely use the **pseudorandom** **number** for solving coin-weighing puzzles with the deductive method. Monte Carlo approach is a general purpose problem-solving method using random **number**. The proposed method using **pseudorandom** **number** lies in one of Monte Carlo methods. In the proposed method, **pseudorandom** **number** plays a key role in generating constrained solution candidates for coin-weighing puzzles. This may be the first attempt that every solution candidate is solely generated by **pseudorandom** **number** while deductive rules are used for verifying solution candidates. In this paper, the performance of the proposed method was measured by comparing with the existing open source codes by solving 12-coin and 24-coin puzzles respectively.

13 Read more

Cryptography is a fundamental technique for securing information. In this study, has shown how to design asymmetric encryption algorithm based on merging three **pseudorandom** **number** generators. The roles of **pseudorandom** **number** generators, in the proposed algorithm, serve different roles, one of them is helping to generate a dynamic representation for each character which gives the strength to the encryption algorithm; The proposed encryption algorithm solves the problem of exchange and distribution of private keys over the networks; The various examples and implementation of the algorithm prove that it exchanges the keys and encrypts successfully all the characters, and serves the goals of cryptography.

The PRNGs require a seed value to generate the sequence of random numbers. The seed need to have high entropy so as to be random and unpredictable. Since the seed determines the sequence to be generated, it is sufficient to store only the seed value. It has been proposed [5] to use sensor data as seed for PRNGs. The sensor seeds can’t be used directly as sensors are prone to be controlled by an attacker. Hong and Liu [6] proposed to process the sensor data to prevent adversarial control of an attacker. The sensors data are washed rinsed and then spin into random sequence. The wash process eliminates the predictable patterns, the rinse process further increases the randomness of seed, and the spin process generates the random numbers. The use of multiple sensor data leads to collinearity that affects the randomness. The rinse process takes more time to compute Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT). The spin process takes much more time to produce random numbers that are not suitable for secure applications. The proposed scheme is illustrated in Fig. 1. The collinear data from multiple sensors are washed and using Linear Congruential Generator (LCG) the random sequences are generated. The generated sequences are combined using twining technique to minimize collinearity. The combined sequence is taken as 128-bit random key to encrypt the counter value using AES. The resulting 128-bit cipher text is the cryptographically secure random **number**.

There are various methods through which random numbers can be generated, but the most commonly used method is multiplicative congruential generator also called as power residue generator. The function used to generate pseudo random **number** is

The randomness testing of random **number** and **pseudorandom** **number** gen- erators is used for many purposes including cryptographic, modeling and simulation applications; see, for example, Knuth, 1981; Maurer,1992; Rukhin and others, 2001. For such applications a required bit sequence should be true random, i.e., by definition, such a sequence could be interpreted as the result of the flips of a ”fair” coin with sides that are labeled ”0” and ”1” (for short, it is called a random sequence; see Rukhin and others, 2001). More formally, we will consider the main hypothesis H 0 that a bit sequence is

20 Read more

The Linux **pseudorandom** **number** generator (PRNG) is a PRNG with entropy inputs which is widely used in many security related applications and protocols. This PRNG is written as an open source code which is subject to regular changes. It was last analyzed in the work of Gutterman et al. in 2006 [GPR06] but since then no new analysis has been made available, while in the meantime several changes have been applied to the code, among others, to counter the attacks presented in [GPR06]. Our work describes the Linux PRNG of kernel versions 2.6.30.7 and upwards. We detail the PRNG architecture in the Linux system and provide its first accurate mathematical description and a precise analysis of the building blocks, including entropy estimation and extraction. Subsequently, we give a security analysis including the feasibility of cryptographic attacks and an empirical test of the entropy estimator. Finally, we underline some important changes to the previous versions and their consequences.

23 Read more

Through **pseudorandom** **number** generation secrecy can be easily provided to data. As it can be used for generating encryption keys through which original data can be encrypted and converted into ciphertext ‘C’. These can be generated by using any random **number** generation technique or by making own technique to generate such numbers which can’t be easily recognized by anyone other than sender and receiver. These **pseudorandom** numbers are used in various techniques in different ways for secure communication.

In this paper, we have presented hardware implementations of Warbler in CMOS 65nm and CMOS 130nm ASICs. We proposed an architecture that takes advantage of standard registers without chip- enable signals. In addition, we investigated two methods for designing the FSM: binary counter-based and LFSR counter-based. We used three different compilation techniques to optimize our designs. We can achieve the areas of 498 GEs and 534 GEs after the place and route phase in CMOS 65nm and CMOS 130nm respectively. The corresponding maximum frequencies are 1430 MHz and 250 MHz respectively, for CMOS 65nm and CMOS 130nm. The power consumption of Warbler is very small at 100 KHz: only 1.239 µW and 0.296 µW respectively, for CMOS 65nm and CMOS 130nm. From the ASIC results, we have determined that the LFSR counter-based design is better than the binary counter- based design in terms of smaller area and lower total power consumption. In addition, the sequential logic ratios for all our designs are larger than 65% for both CMOS 65nm and CMOS 130nm. Our analysis has verified that the areas of NLFSRs and combinational logic are dependent upon the type of registers and the adopted technologies. The area of the WG-5 transformation table depends upon the selected decimation value, giving us some suggestions for future ciphers and **pseudorandom** **number** generator designs using WG-5 transformations. When compared with other lightweight primitives, the area of our Warbler implementation is smaller than the estimated areas of LAMED, Melia-Segui et al.’s PRNG, and J3Gen, and also smaller than the areas of AKARI1B, Grain, Trivium, S IMON , S PECK , PHOTON- 80/20/16, and SPONGENT-88. In conclusion, Warbler can fit into passive RFID systems.

13 Read more

In this paper we have proposed a **pseudorandom** **number** generator (PRNG) based on the combination of chaotic logistic map and Middle Square Method, the chaotic system iterated independently starting from initial condi- tions could help to generate appropriate values; we have also tested the generated sequences using the NIST tests to detect the unique characteristics expected from truly random bit sequences. The results of statistical testing are reliable so has been used as a part of encryption sys- tem to generate secret key and have an efficient algo- rithm. Finally the result of their statistical tests presented in the Table 1.

When a member wants to join the group, the member sends a message to the server asking for its permission to join the group. The Server authenticates the member and gives it an individual key through a secure channel. The member is added to the rightmost shallowest node. If the tree is balanced then a new node is created and added. Then the server updates the entire key on the path from the leaf to the root of the added member. For key generation and updation the server uses derivation keys and key derivation function. The key derivation function used is the Rabin‟s Squaring trap-door function which can be used as the **pseudorandom** **number** generator. At each level (i) the server selects a key among the keys which is not to be changed, which act as the derivation key for the node at the previous level (i-1). This message is broadcast to all the users. All the users who have these keys calculate the new keys by themselves and the server has to send the messages only to the remaining members thus reducing the **number** of rekey messages.

Random and **pseudorandom** **number** generators (RNG and PRNG) are used for many purposes including cryptographic, modeling and simulation applications. For such applications a generated bit sequence should mimic true random, i.e., by definition, such a sequence could be interpreted as the result of the flips of a fair coin with sides that are labeled 0 and 1. It is known that the Shannon entropy of this process is 1 per letter, whereas for any other stationary process with binary alphabet the Shannon entopy is stricly less than 1. On the other hand, the entropy of the PRNG output should be much less than 1 bit (per letter), but the output sequence should look like truly random. We describe random processes for which those, in a first glance contradictory properties, are valid.

14 Read more

Theorem 8.1. If the iO is indistinguishably secure, PRG is a secure **pseudorandom** generator, and PPRF is selective **pseudorandom**, then the PEPRFs are adaptive weak **pseudorandom**. Proof. The proof follows immediately from [SW14]. Here we only describe the proof in sketch. To base adaptive weak pseudorandomness of PEPRFs on the security of PRG, iO, and PPRF, we proceed via a sequence of games where the first game corresponds to the original adaptive weak **pseudorandom** game for PEPRFs. We prove that A’s advantage must be negligible close between each successive game and that A has zero advantage in the final game.

38 Read more

Recent methods in [10], [33], [43], [46], and [63] aim at reducing the switching activity during scan shift cycles, whose test generator allows automatic selection of their parameters for LP **pseudorandom** test generation. However, many of the previous LP BIST approaches cause fault coverage loss to some extent. Therefore, achieving high fault coverage in an LP BIST scheme is also very important. Weighted pseudo- random testing schemes [21], [24], [37], [44] and methods in [20], [50], [56], and [57] can effectively improve fault cov- erage. However, these approaches usually result in much more power consumption due to more frequent transitions at the scan flip flops in many cases. Therefore, we intend to propose an LP scan-based **pseudorandom** pattern generator (PRPG). This is one of the major motivations of this paper.

12 Read more

Beyond the foundational appeal, correlation intractability is desirable in real world applications. For example, consider the hash function used to build the block chain in the Bitcoin protocol [Nak08]. Its main security property, needed to obtain proofs of work, can be stated as correlation intractability with respect to a specific set of relations, which come from protocol-defined constraints on the input and the output. (Specifically, the input needs to contain appropriate transaction information and the output needs to begin with the correct **number** of zeros.) It should be noted that we do not claim that our result directly applies to the Bitcoin protocol: in this paper we consider only relations that are negligibly sparse, while for Bitcoin and other proof-of-work applications, it is necessary to consider relations that are moderately sparse and to define a more precise analog of correlation intractability (in which the difficulty of finding (x, f(x)) ∈ R is closely related to the density of R).

27 Read more

Our circuits will be a five tuple f = (n, q, A, B, GateType). We let n be the **number** of inputs and q be the **number** of gates. We define inputs = [n], Wires = [n + q] and Gates = [n + q]\[n]. The wire n + q is designated as the output wire, outputwire. A : Gates → Wires\{outputwire} is a function where A(w) identifies w’s first incoming wire and B : Gates → Wires\{outputwire} is a function where B(w) identifies w’s second incoming wire. Finally, GateType : Gates → {AND, OR} is a function that identifies a gate as either an AND gate or an OR gate. We require that w > B(w) > A(w). We also define a function depth(w) where if w ∈ inputs, depth(w) = 1 and in general depth(w) of a wire w is equal to the length of the shortest path to an input wire plus one. Since our circuit is layered, we require that for all w ∈ Gates, if depth(w) = j, then depth(A(w)) = depth(B(w)) = j − 1.

18 Read more

The security argument is organized as follows. We first introduce a hybrid game where the calls to the universal sampler scheme are answered by a samples oracle that generates a fresh sample every time it is called. The security definition of universal samplers schemes argues (in the random oracle model) that the attacker’s advantage in this game must be negligibly close to the original advantage. Furthermore, any polynomial time attacker will cause this samples oracle to be called at most some polynomial Q **number** of times. One of these calls must correspond to the eventual challenge input x ∗ .

15 Read more

– MPC-friendly primitives. Historically, the design of symmetric cryptographic primitives (such as block ciphers, **pseudorandom** generators, and **pseudorandom** functions) has been motivated by ef- ficiency considerations (memory consumption, hardware compatibility, ease of implementation,...). The field of multiparty computation (MPC), where parties want to jointly evaluate a function on se- cret inputs, has led to the emergence of new efficiency considerations: the efficiency of secure evalua- tion of symmetric primitives is strongly related to parameters such as the circuit depth of the prim- itive, and the **number** of its AND gates. This observation has motivated the design of MPC-friendly symmetric primitives in several recent works (e.g. [ARS + 15, CCF + 16, MJSC16, GRR + 16]). Local **pseudorandom** generators make very promising candidate MPC-friendly PRGs (and lead, through the GGM transform [GGM84], to promising candidates for MPC-friendly **pseudorandom** func- tions). Secure evaluation of such symmetric primitives enjoys a wide variety of applications. – Cryptographic capsules. In [BCG + 17], Boyle et al. studied the recently introduced primitive of

40 Read more

Many **number**-theoretic PRF constructions follow the GGM paradigm [13], such as [27,21,1]. Naor and Reingold introduced **pseudorandom** synthesizer (PRS) that can be used to construct parallel computable **pseudorandom** function [26,1]. A PRF construction that is not based on either the GGM or synthesizers paradigm is the PRF of Dodis-Yampolskiy, which is in fact a direct construction, but whose security is closely related to its underlying bilinear q-type assumption [10]. Recently, Chase and Meiklejohn showed that this q-type assumption can be reduced to the subgroup hiding assumption in composite order groups [9]. The PRF of Naor, Reingold, and Rosen is a clever variant of the Naor-Reingold PRF that is secure under the factoring assumption [29]. The work of Boneh, Montgomery, and Raghunathan combines a generalization of the GGM tree with the Dodis-Yampolskiy PRF to get a large-domain (simulateable) verifiable random function [7].

19 Read more

We show that it is possible to upgrade an obfuscator for a weak complexity class WEAK into an obfuscator for arbitrary polynomial size circuits, assuming that the class WEAK can compute **pseudorandom** functions. Specifically, under standard intractability assumptions (e.g., hardness of factoring, Decisional Diffie-Hellman, or Learning with Errors), the existence of obfuscators for NC 1 or even TC 0 implies the existence of general-purpose obfuscators for P. Previously, such a bootstrapping procedure was known to exist under the assumption that there exists a fully-homomorphic encryption whose decryption algorithm can be computed in WEAK. Our reduction works with respect to virtual black-box obfuscators and relativizes to ideal models.

However the proposed hash table is in a global or- der, made up of small patches that are ordered inter- nally and with respect to each other. This means probe positions can be interpolated from the keys at the up- per and lower limit starting from the beginning and end of the table reducing the **number** of probes required for lookups to 1 + log 2 (1 + log 2 ( 2−2α 2−α )). The exact term depends on implementation details like the way the po- sition is interpolated. For a numerical simulation see figure 3.