Time Complexity Research Articles

A new efficient decoder of linear block codes based on ensemble learning models: case of boosting

<p>Error-correcting codes are used to partially or completely correct errors as much as possible, while ensuring high transmission speeds. Several Machine Learning (ML) models such as Logistic Regression and Decision tree have been applied to correct transmission errors. Among the most powerful ML techniques are aggregation methods which have yielded to excellent results in many areas of research. It is this excellence that has prompted us to consider their application for the hard decoding problem. In this sense, we have successfully designed, tested and validated our proposed EL-BoostDec decoder (hard decision decoder based on Ensemble Learning - Boosting technique) which is based on computing of the syndrome of the received word and on using Ensemble Learning techniques to find the corresponding corrigible error. The obtained results with EL-BoostDec are very encouraging in terms of the binary error rate (BER) that it offers. Practically EL-BoostDec has succeed to correct 100% of errors that have weights less than or equal to the correction capacity of studied codes. The comparison of EL-BoostDec with many competitors proves its power. A study of parameters which impact on EL-BoostDec performances has been established to obtain a good BER with minimum run time complexity.</p>

Security analysis and prediction of multi-relay networks over Fisher–Snedecor [formula omitted] fading channels

This paper investigates the physical layer security (PLS) of multi-relay networks over Fisher-Snedecor F fading channels. Precise expressions for outage probability (OP), intercept probability (IP), secure outage probability (SOP), and probability of strictly positive secrecy capacity (SPSC) are derived based on this considered model, which the SOP and SPSC are provided in a unified manner using Meijer’s G-function. Moreover, simulation consequences of Monte Carlo experiments validate derived mathematical expressions. Through theoretical analysis and simulation results, the interesting results are that larger msRD, smaller mRD, μRE and msRE the better secrecy performance of this system. Because deep learning has characteristics of low latency, strong learning ability, and adaptability, in order to pursue lower latency and universal applicability, we combine deep learning and wireless communication. On the basis of constructing a data set with exact closed-form expressions, the secrecy performance is predicted by utilizing a multi-layer perceptron (MLP) deep learning model. Moreover, by comparing the three algorithms of convolutional neural network (CNN), deep neural network (DNN), and two-layer long short-term memory network (LSTM), the MLP has the advantages of higher performance and lower complexity. Experimentations exhibit that the presented algorithm enhances the precision by 75.69% with LSTM for comparison and reduces the time complexity by 80.05% compared with DNN.

Evaluation of sequential feature selection in improving the K-nearest neighbor classifier for diabetes prediction

The K-nearest neighbor (KNN) classifier employs distance metrics to measure the distance between the test instance and the samples used in training. With smaller samples, the KNN classifier achieves higher accuracy with low computational time. However, computing the distance between the test instance and all training samples to determine the class of the test instance requires higher computational time for a high-dimensional dataset. This research employs sequential feature selection (SFS) to select the optimal feature for diabetes prediction while reducing the computational time complexity of the KNN classifier. The KNN classifier showed effectiveness with an accuracy rate of 84.41% with nine features. The performance of the KNN improves by 2.6% when trained on the optimal features selected with the SFS. The result revealed glucose level, blood pressure (BP), skin thickness (ST), diabetes pedigree function (DPF), age, and body mass index (BMI) as the most representative features in diabetes prediction. The KNN classifier gives higher accuracy with these features. However, insulin and the number of times a woman is pregnant do not show a significant effect on the KNN classifier.

ResLMFFNet: a real-time semantic segmentation network for precision agriculture

Lightweight multiscale-feature-fusion network (LMFFNet), a proficient real-time CNN architecture, adeptly achieves a balance between inference time and accuracy. Capturing the intricate details of precision agriculture target objects in remote sensing images requires deep SEM-B blocks in the LMFFNet model design. However, employing numerous SEM-B units leads to instability during backward gradient flow. This work proposes the novel residual-LMFFNet (ResLMFFNet) model for ensuring smooth gradient flow within SEM-B blocks. By incorporating residual connections, ResLMFFNet achieves improved accuracy without affecting the inference speed and the number of trainable parameters. The results of the experiments demonstrate that this architecture has achieved superior performance compared to other real-time architectures across diverse precision agriculture applications involving UAV and satellite images. Compared to LMFFNet, the ResLMFFNet architecture enhances the Jaccard Index values by 2.1% for tree detection, 1.4% for crop detection, and 11.2% for wheat-yellow rust detection. Achieving these remarkable accuracy levels involves maintaining almost identical inference time and computational complexity as the LMFFNet model. The source code is available on GitHub: https://github.com/iremulku/Semantic-Segmentation-in-Precision-Agriculture.

Considering liberation beyond statehood (deferred)

AbstractComplicating linear narratives of liberation, the Gaza Strip under Hamas rule, Somdeep Sen argues in Decolonizing Palestine, constitutes a microcosm of the Palestinian ‘long moment of liberation’ with Hamas assuming the dual role of an anticolonial force and postcolonial government. It is in this mix of the colonial and putatively postcolonial that this book treads. In so doing, Sen offers an important accounting of the messy temporalities of liberation that work against the grain of linear time. In this review, I think alongside Sen’s important provocation that we unbracket liberation from a unitary or single event to consider instead the punctuated, overlapping, and decisively non-linear temporalities that constitute decolonization. Equally, this review asks what dangers might inhere in tethering liberation to a governing authority? Bringing Sen’s work into conversation with contemporary Palestinian politics, movements, and revolutionary moments that cannot be contained within Hamas, this review asks how we might think with Sen about decolonisation as temporally unbounded but also as constituting heterogenous visions, forces, actors and practices that extend beyond formal structures and institutions. What might we gain, it asks, if we expand Sen’s invaluable ‘long moment of liberation’ to include this panoply of forces, visions, and instantiations of decoloniality in practice? It is here, in bridging the messy temporalities of liberation with the heterogenous forces and myriad of ways that Palestine’s decolonial futures are actively being made beyond formal parties and structures, that Sen’s thesis, it suggests, finds its liberatory potential.

Implementation of an effective transform technique for convergence analysis of the fractional enzyme kinetic and blood alcohol level models

In the current study, we solve the nonlinear time fractional‐order enzyme kinematic system and the linear time fractional blood alcohol level using an effective method called the Adomian natural decomposition method (ANDM), which is a combination of the Adomian decomposition method (ADM) and the natural transform method (NTM). On the basis of the Banach fixed point theorem, we offer proofs for the existence and uniqueness theorems as they apply to nonlinear ordinary differential equations. Using the current method, approximate analytical solutions of nonlinear time fractional‐order enzyme kinematic system and exact solutions to the linear time fractional‐order blood alcohol level problem have been obtained. The outcomes indicate that the ANDM is highly efficient and useful. The method outlined in this paper is intended to be applied in subsequent work to handle comparable nonlinear problems connected to fractional calculus.

An efficient exact algorithm for planted motif search on large DNA sequence datasets.

DNA motif is the pattern shared by similar fragments in DNA sequences, which plays a key role in regulating gene expression, and DNA motif discovery has become a key research topic. Exact planted (l,d)-motif search (PMS) is one of the motif discovery approaches, which aims to find from t sequences all the (l,d)-motifs that are motifs of l length appearing in at least qt sequences with at most d mismatches. The existing exact PMS algorithms are only suitable for small datasets of DNA sequences. The development of high-throughput sequencing technology generates vast amount of DNA sequence data, which brings challenges to solving exact PMS problems efficiently. Therefore, we propose an efficient exact PMS algorithm called PMmotif for large datasetsof DNA sequences, after analyzing the time complexity of the existing exact PMS algorithms. PMmotif finds (l,d) -motifs with strategy by searching the branches on the pattern tree that may contain (l,d) -motifs. It is verified by experiments that the running time ratio of the existing excellentPMS algorithmstoPMmotif isbetween14.83and 58.94. In addition, for the first time, PMmotif can solve the (15,5) and(17,6) challenge problem instances on large DNA sequence datasets within 24 hours.

Enhancing donor engagement: Assessing the impact of online donation convenience on the willingness to donate to non-profit organizations

The competition for financial support among non-profit organizations (NPOs) has been intense for quite some time. It is crucial for these organizations to boost their competitive edge by gaining a deep understanding of donor behavior and fostering ongoing interactions with them. In today’s world, where convenience and efficiency are highly valued, factors such as the timing and location of donations can deter potential donors from contributing. Rigid and inconvenient donation methods can also hinder the donation process. As a result, this study aims to explore the role of convenience within the donation process, specifically investigating whether the convenience of online donation platforms provided by non-profit organizations significantly influences donors’ propensity to make contributions. This research differentiates the range of services offered by non-profit organizations and employs a questionnaire survey to examine the websites of the NPOs. A total of 466 valid responses were gathered. The empirical findings indicate that donors prioritize simplicity and speed in the online donation process. Additionally, donors prefer websites where they can easily locate necessary information and various details about the donation process, with relevant links that minimize time waste and complexity in navigating the website. The study also reveals that the convenience factor significantly influences donation behavior. Based on these insights, the study offers recommendations for non-profit organizations on how to provide donor-centric services by focusing on the aspects of convenience that donors value most in the donation process.

Constrained Device Performance Benchmarking with the Implementation of Post-Quantum Cryptography

Advances in quantum computers may pose a significant threat to existing public-key encryption methods, which are crucial to the current infrastructure of cyber security. Both RSA and ECDSA, the two most widely used security algorithms today, may be (in principle) solved by the Shor algorithm in polynomial time due to its ability to efficiently solve the discrete logarithm problem, potentially making present infrastructures insecure against a quantum attack. The National Institute of Standards and Technology (NIST) reacted with the post-quantum cryptography (PQC) standardization process to develop and optimize a series of post-quantum algorithms (PQAs) based on difficult mathematical problems that are not susceptible to being solved by Shor’s algorithm. Whilst high-powered computers can run these PQAs efficiently, further work is needed to investigate and benchmark the performance of these algorithms on lower-powered (constrained) devices and the ease with which they may be integrated into existing protocols such as TLS. This paper provides quantitative benchmark and handshake performance data for the most recently selected PQAs from NIST, tested on a Raspberry Pi 4 device to simulate today’s IoT (Internet of Things) devices, and provides quantitative comparisons with previous benchmarking data on a range of constrained systems. CRYSTALS-Kyber and CRYSTALS-Dilithium are shown to be the most efficient PQAs in the key encapsulation and signature algorithms, respectively, with Falcon providing the optimal TLS handshake size.

#2118 Monitoring hemodynamics in dialysis: on the feasibility of semi-continuous and multifrequency thoracic bioimpedance measurements by a wearable device

Abstract Background and Aims Hemodialysis patients face a high hemodynamic variability in blood pressure and fluid status, which contributes to their cardiovascular mortality. Currently, intradialytic hemodynamic monitoring has to rely on cuff-based blood pressure measurements. During the interdialytic interval, no monitoring system is applied. An interesting alternative to monitor hemodynamics continuously can be found in the bioimpedance technique, and more specifically in bioimpedance measurements of the thoracic segment. Repeated single-point measurements of thoracic bioimpedance at single (low)-frequency are strongly related to fluid changes during hemodialysis. Extension to semi-continuous measurements may provide longitudinal details in the time pattern of the bioimpedance signal, and multifrequency measurements may add in-depth information on the distribution between intra- and extracellular fluid. This study aims to investigate the feasibility of semi-continuous multifrequency thoracic bioimpedance measurements by a wearable device in hemodialysis patients. Method Thoracic bioimpedance was recorded semi-continuously (i.e. every ten minutes) at nine frequencies (8–160 kHz) in 68 patients during two consecutive hemodialysis sessions, complemented by an interdialytic single-point measurement at home. The wearable bioimpedance device was provided by imec, The Netherlands (Fig. 1). A linear mixed model was built to integrate all measurements at frequencies 8 and 160 kHz, incorporating the different dialysis sessions up until 240 minutes after the start of dialysis as well as the home measurement that was performed. Results On average, the thoracic resistance signals increased during the first hemodialysis session, decreased during the interdialytic interval, and increased again during the second hemodialysis session, at all frequencies. The average intradialytic increase was larger at 8 kHz (∆ 32.6 Ω during session 1 and ∆ 10 Ω during session 2) compared to 160 kHz (∆ 29.5 Ω during session 1 and ∆ 5.1 Ω during session 2). By measuring semi-continuously and at multiple frequencies, a different time pattern became clear within and between frequencies. The resistance at 8 kHz followed a linear time pattern, whereas the evolution of the resistance at 160 kHz showed a significant quadratic trend in the first dialysis session (p < 0.0001). During the first interdialytic interval (from the end of the first dialysis session towards the home measurement), the decrease in resistance was more distinct at 8 kHz (∆ −2.27 Ω) compared to a small increase of 0.84 Ω in 160 kHz. This finding reveals a certain inertia in the higher frequencies, mirroring the changes in intracellular volume. Finally, the statistical model could create individual predicting profiles over time, including as well the intradialytic as the interdialytic interval (Fig. 2). Conclusion In this study, we showed that it is feasible to perform semi-continuous and multifrequency bioimpedance measurements by a wearable device during hemodialysis. Semi-continuous and multifrequency measurements provided a broader, and respectively profounder knowledge on the trend of the bioimpedance signal during fluid changes compared to single-point and single-frequency measurements. Measuring thoracic bioimpedance semi-continuously and with a multifrequency current is a major step forward in the understanding of fluid dynamics in hemodialysis patients, by which the road is paved towards remote fluid monitoring and the prevention of hemodynamic instabilities.

Faster classical boson sampling

Since its introduction boson sampling has been the subject of intense study in the world of quantum computing. In the context of Fock-state boson sampling, the task is to sample independently from the set of all n × n submatrices built from possibly repeated rows of a larger m × n complex matrix according to a probability distribution related to the permanents of the submatrices. Experimental systems exploiting quantum photonic effects can in principle perform the task at great speed. For classical computing, Aaronson and Arkhipov (2011) showed that exact boson sampling problem cannot be solved in polynomial time unless the polynomial hierarchy collapses to the third level. Indeed for a number of years the fastest known exact classical algorithm ran in O(m+n−1nn2n) time per sample, emphasising the potential speed advantage of quantum computation. The advantage was reduced by Clifford and Clifford (2018), who gave a significantly faster classical solution taking O(n2n+poly(m,n)) time and linear space, matching the complexity of computing the permanent of a single matrix when m is polynomial in n. We continue by presenting an algorithm for Fock boson sampling whose average-case time complexity is much faster when m is proportional to n. In particular, when m = n our algorithm runs in approximately O(n · 1.69 n ) time on average. This result further increases the problem size needed to establish quantum computational advantage via the Fock scheme of boson sampling.

Enhancing blockchain security: a novel approach to integrated malware defence mechanisms

This paper introduces a novel integrated hybrid malware attack detection algorithm, focusing on enhancing cybersecurity within blockchain systems by addressing the prevalent challenges of Byzantine fault tolerance, Reentrancy, and DDOS attacks. The significance of this research lies in its contribution to safeguarding blockchain technology, a cornerstone for secure, decentralized digital transactions, against sophisticated malware threats. Current cybersecurity solutions frequently fall short of offering a complete defense mechanism, making it difficult to effectively combat a variety of dynamic malware attacks at the same time. Thus, the main objective of this research is to provide a hybrid framework that combines DDOS attack prevention, reentrancy attack detection, and Byzantine fault tolerance detection into a single, cohesive architecture. The proposed hybrid framework encompasses a detailed algorithmic approach integrating SHA-256 and DSA to analyze the aforementioned three malware attacks. A hybrid model combining these algorithms, implemented in one block, has been developed to mitigate malicious activity. These measures aim to improve computational complexity and expedite execution within the network of nodes. To test the efficacy of the proposed framework, the approach is tested on the NSL-KDD dataset to analyze the malicious activities. The performance analysis of the proposed frameworks presents a recall and F1 score of 73 and .68 respectively. Furthermore, for efficient mitigation, the time and space complexity analysis is performed on proposed algorithms for attack analysis, which resulted in a combination of constant and linear time complexity operations. The findings reveal that the proposed algorithm successfully identifies and mitigates the targeted malware attacks and maintains optimal performance in terms of time and space complexity. Specifically, the algorithm showcases linear and constant time complexities across different attack vectors, ensuring swift and scalable defense capabilities. This research’s contribution to the cybersecurity field is significant, offering a robust, scalable solution that enhances the resilience of blockchain networks against a broad spectrum of malware attacks.

The longest almost increasing subsequence problem with sliding windows

In this paper, we first define the longest almost increasing subsequence with sliding windows (LaISW), a generalization that combines the longest increasing subsequence with sliding windows (LISW) problem and the longest almost increasing subsequence (LaIS) problem. For a numeric sequence A, a window size w and a tolerance constant c, the goal of the LaISW problem is to identify the LaIS within all windows of size w in A. In an almost increasing subsequence, slight decreases smaller than c are permitted. We propose an efficient algorithm for solving the LaISW problem. Instead of constructing the entire row tower, our algorithm computes the change in drop out (occurrence) for each element in the row tower. The time complexity of our algorithm is O(nL), and the space complexity is O(L), where n and L represent the lengths of the input sequence and the LaISW answer, respectively.

Towards determinism in PDL: relations and proof theory

Abstract Guarded Kleene Algebra with Tests (GKAT) was presented as a fragment of KAT to abstract imperative programming languages, where only if-then-else and while-do statements are allowed in the language. The loss of expressiveness is, nevertheless, compensated by a clear advantage over KAT: it allows almost linear decidability of program equivalence. In this work, we give the first step to optimizing the complexity of dynamic logic equivalence, which is EXPTIME-complete in propositional dynamic logic (PDL). First, and based on strict deterministic PDL, we present guarded propositional dynamic logic (GPDL), a fragment of PDL where programs correspond to GKAT terms. It comes embedded, as expected, with a semantics over relational models and a sound axiomatisation. Then, we present a Natural Deduction system for GPDL, proving its soundness and completeness, concerning the axiomatisation. Based on Smolka et al. (2019, Proceedings of the ACM Programming Language 4), we obtain the main result of this work—the equivalence of GPDL programs can be established in almost linear time.

Enhancing aspect-based multi-labeling with ensemble learning for ethical logistics.

In the dynamic domain of logistics, effective communication is essential for streamlined operations. Our innovative solution, the Multi-Labeling Ensemble (MLEn), tackles the intricate task of extracting multi-labeled data, employing advanced techniques for accurate preprocessing of textual data through the NLTK toolkit. This approach is carefully tailored to the prevailing language used in logistics communication. MLEn utilizes innovative methods, including sentiment intensity analysis, Word2Vec, and Doc2Vec, ensuring comprehensive feature extraction. This proves particularly suitable for logistics in e-commerce, capturing nuanced communication essential for efficient operations. Ethical considerations are a cornerstone in logistics communication, and MLEn plays a pivotal role in detecting and categorizing inappropriate language, aligning inherently with ethical norms. Leveraging Tf-IDF and Vader for feature enhancement, MLEn adeptly discerns and labels ethically sensitive content in logistics communication. Across diverse datasets, including Emotions, MLEn consistently achieves impressive accuracy levels ranging from 92% to 97%, establishing its superiority in the logistics context. Particularly, our proposed method, DenseNet-EHO, outperforms BERT by 8% and surpasses other techniques by a 15-25% efficiency. A comprehensive analysis, considering metrics such as precision, recall, F1-score, Ranking Loss, Jaccard Similarity, AUC-ROC, sensitivity, and time complexity, underscores DenseNet-EHO's efficiency, aligning with the practical demands within the logistics track. Our research significantly contributes to enhancing precision, diversity, and computational efficiency in aspect-based sentiment analysis within logistics. By integrating cutting-edge preprocessing, sentiment intensity analysis, and vectorization, MLEn emerges as a robust framework for multi-label datasets, consistently outperforming conventional approaches and giving outstanding precision, accuracy, and efficiency in the logistics field.

On the circuit model of two quantum adiabatic search algorithms

The early work of Wei et al. has shown that it is possible to do the computation in constant time for quantum search in quantum local adiabatic evolution framework if the system Hamiltonian has an extra enlarged factor proportional to the square-root of the size of the problem. Also in our prior work, we have shown that it is possible to apply a linear interpolating path in the system Hamiltonian to achieve an O(1) time complexity for a quantum global adiabatic computation. In this paper, we discuss the issues when implementing these two quantum algorithms on the quantum circuit model, and find that to our surprise, the time slices produced does not equal to the time complexity of the algorithm in each case. This is in contrast to the previous related results, because there these two quantities always coincide. When taking into account of the whole energy-level increase of the system compared with that of the usual quantum adiabatic evolutions and the corresponding time complexity simultaneously, we find that the time slices needed always consist of the two quantities multiplying together. This result is new, and may be hopeful to find application in designing quantum adiabatic algorithm for problems beyond quantum search.

Krisp: A Python package to aid in the design of CRISPR and amplification-based diagnostic assays from whole genome sequencing data.

Recent pandemics like COVID-19 highlighted the importance of rapidly developing diagnostics to detect evolving pathogens. CRISPR-Cas technology has recently been used to develop diagnostic assays for sequence-specific recognition of DNA or RNA. These assays have similar sensitivity to the gold standard qPCR but can be deployed as easy to use and inexpensive test strips. However, the discovery of diagnostic regions of a genome flanked by conserved regions where primers can be designed requires extensive bioinformatic analyses of genome sequences. We developed the Python package krisp to aid in the discovery of primers and diagnostic sequences that differentiate groups of samples from each other, using either unaligned genome sequences or a variant call format (VCF) file as input. Krisp has been optimized to handle large datasets by using efficient algorithms that run in near linear time, use minimal RAM, and leverage parallel processing when available. The validity of krisp results has been demonstrated in the laboratory with the successful design of a CRISPR diagnostic assay to distinguish the sudden oak death pathogen Phytophthora ramorum from closely related Phytophthora species. Krisp is released open source under a permissive license with all the documentation needed to quickly design CRISPR-Cas diagnostic assays.

Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transitions.

The nonequilibrium dynamics of a periodically driven extended XY model, in the presence of
linear time dependent magnetic filed, is investigated using the notion of dynamical quantum phase
transitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purpose
of this work is to search the fundamental concepts such as scaling and universality at the ramped
quench DQPTs. We have shown that the critical points of the model, where the gap closing occurs,
can be moved by tuning the driven frequency and consequently the presence/absence of DQPTs
can be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a ramp
across the single quantum critical point, the critical mode at which DQPTs occur is classified into
three regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the square
root of the sweep velocity, pre-saturated (PS) region, and the saturated (S) region where the critical
mode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points,
the critical modes disclose just KZ and PS regions. On the basis of numerical simulations, we find
that the dynamical free energy scales linerly with time, as approaches to DQPT time, with the
exponent ν = 1 ± 0.01 for all sweep velocities and driven frequencies.

Robust Incremental Broad Learning System for Data Streams of Uncertain Scale.

Due to its marvelous performance and remarkable scalability, a broad learning system (BLS) has aroused a wide range of attention. However, its incremental learning suffers from low accuracy and long training time, especially when dealing with unstable data streams, making it difficult to apply in real-world scenarios. To overcome these issues and enrich its relevant research, a robust incremental BLS (RI-BLS) is proposed. In this method, the proposed weight update strategy introduces two memory matrices to store the learned information, thus the computational procedure of ridge regression is decomposed, resulting in precomputed ridge regression. During incremental learning, RI-BLS updates two memory matrices and renews weights via precomputed ridge regression efficiently. In addition, this update strategy is theoretically analyzed in error, time complexity, and space complexity compared with existing incremental BLSs. Different from Greville's method used in the original incremental BLS, its results are closer to the solution of one-shot calculation. Compared with the existing incremental BLSs, the proposed method exhibits more stable time complexity and superior space complexity. The experiments prove that RI-BLS outperforms other incremental BLSs when handling both stable and unstable data streams. Furthermore, experiments demonstrate that the proposed weight update strategy applies to other random neural networks as well.

Nimber-preserving reduction: Game secrets and homomorphic Sprague-Grundy theorem

The concept of nimbers—a.k.a. Grundy-values or nim-values—is fundamental to combinatorial game theory. Beyond the winnability, nimbers provide a complete characterization of strategic interactions among impartial games in disjunctive sums. In this paper, we consider nimber-preserving reductions among impartial games, which enhance the winnability-preserving reductions in traditional computational characterizations of combinatorial games. We prove that Generalized Geography is complete for the natural class, IP, of polynomially-short impartial rulesets, under polynomial-time nimber-preserving reductions. We refer to this notion of completeness as Sprague-Grundy-completeness. In contrast, we also show that not every PSPACE-complete ruleset in IP is Sprague-Grundy-complete for IP.By viewing every impartial game as an encoding of its nimber—a succinct game secret richer than its winnability alone—our technical result establishes the following striking cryptography-inspired homomorphic theorem: Despite the PSPACE-completeness of nimber computation for IP, there exists a polynomial-time algorithm to construct, for any pair of games G1,G2 in IP, a Generalized Geography game G satisfying:nimber(G)=nimber(G1)⊕nimber(G2).