Cryptosystem

In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption). Typically, a cryptosystem consists of three algorithms: one for key generation, one for encryption, and one for decryption. The term cipher (sometimes cypher) is often used to refer to a pair of algorithms, one for encryption and one for decryption. Therefore, the term cryptosystem is most often used when the key generation algorithm is important. For this reason, the term cryptosystem is commonly used to refer to public key techniques; however both "cipher" and "cryptosystem" are used for symmetric key techniques. == Formal definition == Mathematically, a cryptosystem or encryption scheme can be defined as a tuple ( P , C , K , E , D ) {\displaystyle ({\mathcal {P}},{\mathcal {C}},{\mathcal {K}},{\mathcal {E}},{\mathcal {D}})} with the following properties. P {\displaystyle {\mathcal {P}}} is a set called the "plaintext space". Its elements are called plaintexts. C {\displaystyle {\mathcal {C}}} is a set called the "ciphertext space". Its elements are called ciphertexts. K {\displaystyle {\mathcal {K}}} is a set called the "key space". Its elements are called keys. E = { E k : k ∈ K } {\displaystyle {\mathcal {E}}=\{E_{k}:k\in {\mathcal {K}}\}} is a set of functions E k : P → C {\displaystyle E_{k}:{\mathcal {P}}\rightarrow {\mathcal {C}}} . Its elements are called "encryption functions". D = { D k : k ∈ K } {\displaystyle {\mathcal {D}}=\{D_{k}:k\in {\mathcal {K}}\}} is a set of functions D k : C → P {\displaystyle D_{k}:{\mathcal {C}}\rightarrow {\mathcal {P}}} . Its elements are called "decryption functions". For each e ∈ K {\displaystyle e\in {\mathcal {K}}} , there is d ∈ K {\displaystyle d\in {\mathcal {K}}} such that D d ( E e ( p ) ) = p {\displaystyle D_{d}(E_{e}(p))=p} for all p ∈ P {\displaystyle p\in {\mathcal {P}}} . Note; typically this definition is modified in order to distinguish an encryption scheme as being either a symmetric-key or public-key type of cryptosystem. == Examples == A classical example of a cryptosystem is the Caesar cipher. A more contemporary example is the RSA cryptosystem. Another example of a cryptosystem is the Advanced Encryption Standard (AES). AES is a widely used symmetric encryption algorithm that has become the standard for securing data in various applications. Paillier cryptosystem is another example used to preserve and maintain privacy and sensitive information. It is featured in electronic voting, electronic lotteries and electronic auctions.

ASR-complete

ASR-complete is, by analogy to "NP-completeness" in complexity theory, a term to indicate that the difficulty of a computational problem is equivalent to solving the central automatic speech recognition problem, i.e. recognize and understanding spoken language. Unlike "NP-completeness", this term is typically used informally. Such problems are hypothesised to include: Spoken natural language understanding Understanding speech from far-field microphones, i.e. handling the reverbation and background noise These problems are easy for humans to do (in fact, they are described directly in terms of imitating humans). Some systems can solve very simple restricted versions of these problems, but none can solve them in their full generality.

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Peter Gerstoft

Peter Gerstoft is a Danish-American scientist and engineer specializing in ocean acoustics, seismology, and signal processing. He is currently a professor in the Department of Electrical and Photonics Engineering at the Technical University of Denmark. He was previously a Distinguished Data Scientist at the Scripps Institution of Oceanography at the University of California, San Diego and an adjunct professor in the Department of Electrical and Computer Engineering at UC San Diego. == Education == Gerstoft received his MSc in engineering from the Technical University of Denmark in 1983 and another MSc from the University of Western Ontario in 1984. He completed his PhD in engineering at the Technical University of Denmark in 1986. == Career == Gerstoft began his career in acoustics and vibrations at Odegaard & Danneskiold-Samsøe (1987–1992). He then served as a Senior Scientist at the NATO SACLANT Undersea Research Centre in La Spezia, Italy, from 1992 to 1997. Between 1999 and 2000, Gerstoft worked as a Senior Seismic Acoustic Officer with the Comprehensive Nuclear-Test-Ban Treaty Organization. He has been a Data Scientist at the Scripps Institution of Oceanography since 1997. From 2013, he held an adjunct faculty position in Electrical and Computer Engineering at UC San Diego, where he taught courses on seismology, data assimilation, and machine learning for physical systems. Gerstoft retired from UC San Diego in 2025 and accepted an appointment as Professor of Electrical and Photonics Engineering at the Technical University of Denmark in 2026 . == Research and contributions == Gerstoft's research focuses on environmental signal processing, with a particular emphasis on inversion methods, including their theoretical development, algorithmic implementation, and practical applications. In the 1990s, he investigated the use of nonlinear optimization and Bayesian approaches in acoustic inverse problems related to source localization and environmental parameter estimation. His work integrated physical propagation models with Bayesian sampling methods and a range of likelihood functions. These techniques have been applied to various data types, including vertical sensor arrays, single-sensor broadband data, and transmission loss measurements, and contributed to a general framework for inversion based on Gaussian assumptions. He has also conducted research in machine learning and sparse signal processing, particularly in the context of sensor array data. This includes applications such as direction of arrival estimation and source localization, including for seismic events such as the 2011 Tōhoku earthquake and for ship tracking in ocean environments. His work on sparse Bayesian sequential methods and techniques for estimating Lagrange multipliers in constrained optimization problems has contributed to the development of adaptive and high-resolution signal processing techniques. Gerstoft has applied supervised learning and deep neural networks to problems in physical acoustics, including source localization in ocean waveguides. He has also co-authored several review articles on the use of machine learning in acoustics and seismology. == Honors == Fulbright Scholar, Massachusetts Institute of Technology (1989–1990) Fellow, Acoustical Society of America (2003) Member, American Geophysical Union (since 2004) Senior Member, Institute of Electrical and Electronics Engineers (2018) Fellow, Institute of Electrical and Electronics Engineers (2023) == Selected publications == === Book === Diachok, O., Caiti, A., Gerstoft, P., & Schmidt, H. (Eds.). Full Field Inversion Methods in Ocean and Seismo-Acoustics. Kluwer Academic Publishers, 1995. === Selected articles === Gerstoft, P. (1994). "Inversion of seismo-acoustic data using genetic algorithms and a posteriori probability distributions". Journal of the Acoustical Society of America. 95 (2): 770–782. doi:10.1121/1.408467. Gerstoft, P., & Mecklenbrauker, C. F. (1998). "Ocean acoustic inversion with estimation of a posteriori probability distributions". Journal of the Acoustical Society of America. 104 (2): 808–819. doi:10.1121/1.423287. Sabra, K. G., Gerstoft, P., Roux, P., Kuperman, W. A., & Fehler, M. (2005). "Extracting time-domain Green's function estimates from ambient seismic noise". Geophysical Research Letters. 32, L03310. Xenaki, A., Gerstoft, P., & Mosegaard, K. (2014). "Compressive beamforming". Journal of the Acoustical Society of America. 136, 260–271. Niu, H., Reeves, D., & Gerstoft, P. (2017). "Source localization in an ocean waveguide using supervised machine learning". Journal of the Acoustical Society of America. 142, 1176–1188.

Regularization perspectives on support vector machines

Within mathematical analysis, Regularization perspectives on support-vector machines provide a way of interpreting support-vector machines (SVMs) in the context of other regularization-based machine-learning algorithms. SVM algorithms categorize binary data, with the goal of fitting the training set data in a way that minimizes the average of the hinge-loss function and L2 norm of the learned weights. This strategy avoids overfitting via Tikhonov regularization and in the L2 norm sense and also corresponds to minimizing the bias and variance of our estimator of the weights. Estimators with lower Mean squared error predict better or generalize better when given unseen data. Specifically, Tikhonov regularization algorithms produce a decision boundary that minimizes the average training-set error and constrain the Decision boundary not to be excessively complicated or overfit the training data via a L2 norm of the weights term. The training and test-set errors can be measured without bias and in a fair way using accuracy, precision, Auc-Roc, precision-recall, and other metrics. Regularization perspectives on support-vector machines interpret SVM as a special case of Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a loss function. This provides a theoretical framework with which to analyze SVM algorithms and compare them to other algorithms with the same goals: to generalize without overfitting. SVM was first proposed in 1995 by Corinna Cortes and Vladimir Vapnik, and framed geometrically as a method for finding hyperplanes that can separate multidimensional data into two categories. This traditional geometric interpretation of SVMs provides useful intuition about how SVMs work, but is difficult to relate to other machine-learning techniques for avoiding overfitting, like regularization, early stopping, sparsity and Bayesian inference. However, once it was discovered that SVM is also a special case of Tikhonov regularization, regularization perspectives on SVM provided the theory necessary to fit SVM within a broader class of algorithms. This has enabled detailed comparisons between SVM and other forms of Tikhonov regularization, and theoretical grounding for why it is beneficial to use SVM's loss function, the hinge loss. == Theoretical background == In the statistical learning theory framework, an algorithm is a strategy for choosing a function f : X → Y {\displaystyle f\colon \mathbf {X} \to \mathbf {Y} } given a training set S = { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle S=\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\}} of inputs x i {\displaystyle x_{i}} and their labels y i {\displaystyle y_{i}} (the labels are usually ± 1 {\displaystyle \pm 1} ). Regularization strategies avoid overfitting by choosing a function that fits the data, but is not too complex. Specifically: f = argmin f ∈ H { 1 n ∑ i = 1 n V ( y i , f ( x i ) ) + λ ‖ f ‖ H 2 } , {\displaystyle f={\underset {f\in {\mathcal {H}}}{\operatorname {argmin} }}\left\{{\frac {1}{n}}\sum _{i=1}^{n}V(y_{i},f(x_{i}))+\lambda \|f\|_{\mathcal {H}}^{2}\right\},} where H {\displaystyle {\mathcal {H}}} is a hypothesis space of functions, V : Y × Y → R {\displaystyle V\colon \mathbf {Y} \times \mathbf {Y} \to \mathbb {R} } is the loss function, ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{\mathcal {H}}} is a norm on the hypothesis space of functions, and λ ∈ R {\displaystyle \lambda \in \mathbb {R} } is the regularization parameter. When H {\displaystyle {\mathcal {H}}} is a reproducing kernel Hilbert space, there exists a kernel function K : X × X → R {\displaystyle K\colon \mathbf {X} \times \mathbf {X} \to \mathbb {R} } that can be written as an n × n {\displaystyle n\times n} symmetric positive-definite matrix K {\displaystyle \mathbf {K} } . By the representer theorem, f ( x i ) = ∑ j = 1 n c j K i j , and ‖ f ‖ H 2 = ⟨ f , f ⟩ H = ∑ i = 1 n ∑ j = 1 n c i c j K ( x i , x j ) = c T K c . {\displaystyle f(x_{i})=\sum _{j=1}^{n}c_{j}\mathbf {K} _{ij},{\text{ and }}\|f\|_{\mathcal {H}}^{2}=\langle f,f\rangle _{\mathcal {H}}=\sum _{i=1}^{n}\sum _{j=1}^{n}c_{i}c_{j}K(x_{i},x_{j})=c^{T}\mathbf {K} c.} == Special properties of the hinge loss == The simplest and most intuitive loss function for categorization is the misclassification loss, or 0–1 loss, which is 0 if f ( x i ) = y i {\displaystyle f(x_{i})=y_{i}} and 1 if f ( x i ) ≠ y i {\displaystyle f(x_{i})\neq y_{i}} , i.e. the Heaviside step function on − y i f ( x i ) {\displaystyle -y_{i}f(x_{i})} . However, this loss function is not convex, which makes the regularization problem very difficult to minimize computationally. Therefore, we look for convex substitutes for the 0–1 loss. The hinge loss, V ( y i , f ( x i ) ) = ( 1 − y f ( x ) ) + {\displaystyle V{\big (}y_{i},f(x_{i}){\big )}={\big (}1-yf(x){\big )}_{+}} , where ( s ) + = max ( s , 0 ) {\displaystyle (s)_{+}=\max(s,0)} , provides such a convex relaxation. In fact, the hinge loss is the tightest convex upper bound to the 0–1 misclassification loss function, and with infinite data returns the Bayes-optimal solution: f b ( x ) = { 1 , p ( 1 ∣ x ) > p ( − 1 ∣ x ) , − 1 , p ( 1 ∣ x ) < p ( − 1 ∣ x ) . {\displaystyle f_{b}(x)={\begin{cases}1,&p(1\mid x)>p(-1\mid x),\\-1,&p(1\mid x)

Live Transcribe

Live Transcribe is a mobile app for real-time captioning, developed by Google for the Android operating system. Development on the application began in partnership with Gallaudet University. It was publicly released as a free beta for Android 5.0+ on the Google Play Store on February 4, 2019. As of early 2023 it had been downloaded over 500 million times. == Development == Researchers Dimitri Kanevsky, Sagar Savla and Chet Gnegy at Google developed the app in collaboration with researchers at Gallaudet University, an American university for the education of the deaf and hard of hearing. The app uses machine learning to generate captions, similar to YouTube's auto-generated captions. In August 2019, Google made Live Transcribe an open-source project. == Features == The app uses speech recognition to generate live captions in over 80 languages with varying accuracy. The app, which requires connection to the Internet to function, is available to download on the Google Play Store. A later update to the app displayed information on sounds such as clapping, laughter, music, applause, and whistling. In May 2020, the app started supporting transcription in Albanian, Burmese, Estonian, Macedonian, Mongolian, Punjabi, and Uzbek, supporting 70 languages. In March 2022, the app was updated with support to transcribe offline, without Internet connection, so long as the appropriate language pack has been installed. The offline mode is only available for devices with 6GB of RAM and certain Google Pixel devices.

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