암호화된 상태에서의 기계학습과 동형 비교연산

학위논문 (박사) -- 서울대학교 대학원 : 자연과학대학 수리과학부, 2021. 2. 천정희.기계학습은 최근 분야불문 빅데이터 분석의 가장 보편적인 방법 중 하나로 인식되고 있지만, 기업이나 기관들이 실제 데이 터에 활용하기에는 데이터 프라이버시 문제가 큰 우려로 남아있다. 데이터 프라이버시 보호를 위해 여러 비암호학적 방법론들이 그 동안 활용되어 왔지만, 각 과정 속에서 불가피하게 일어나는 정보 손실은 결국 데이터 유용성을 현저하게 떨어뜨리는 단점을 가지고 있다. 동형암호는 복호화 과정없이 암호화된 상태로 연산을 지원하기 때문에 데이터 프리이버시와 유용성을 동시에 보존하고, 기계학습에 적용하기에 가장 적합한 암호학적 프리미티브 중 하나로 여겨지고 있다. 하지만 그 동안 타켓 연산함수의 깊이가 깊거나 다수의 비다항식 연산을 포함하는 경우 굉장히 연산이 오래걸리는 문제 때문에, 지금까지 개발된 동형기계학습 알고리즘의 범주는 굉장히 제한되어 있었다. 본 논문에서는 이러한 한계점을 극복하기 위한 두가지 방법론을 제시한다. 첫번째 방법론은 기존 기계학습 알고리즘의 비다항식 연산을 동형암호 친화적인 형태로 변형시키는 방법이다. 기계학습에서 가장 널리 사용되는 기본적인 방법인 로지스틱 회귀분석에 이 방법론을 기반으로 한 연구를 진행하였고, 전장유전체연관분석 등 실제 많이 활용되는 응용분야에 적용하여 실효성을 입증하였다. 두번째 방법론은 기존 기계학습 알고리즘 자체를 변형하기보다 그 내부의 비다항식 연산에 대한 효율적인 다항식 근사 방법을 찾는 것이다. 본 논문에서는 가장 널리 사용되는 비다항식 연산들 중 하나인 비교연산과 최대/최소연산을 타겟으로 연구를 진행하였고, 합성함수 근사법을 통해 이 연산들에 대한 최적 계산량을 가지는 동형암호 알고리즘 개발에 성공하였다.As machine learning (ML) has become a universal tool of big data analysis regardless of field, data privacy has emerged one of the most significant issues to be solved for applying ML to real-world applications. Some non-cryptographic methodologies have been applied so far for privacy preservation, but the loss of information is inevitable which leads to significant reduction in data usability. Homomorphic Encryption (HE) has been recognized one of the most appropriate cryptographic primitives for privacy-preserving ML preserving both data privacy and usability, from its beautiful functionality that allows computation over encrypted data without decryption. However, extremely high computational cost of HE computation originated from the large depth of target functions or a number of non-polynomial operations has remained a main bottleneck of applying HE in privacy-preserving ML. In this thesis, we introduce two main methodologies to overcome this limitation. The first one is to modify the existing ML algorithms into HE-friendly form. We instantiate this methodology to logistic regression, which is one of the most popular methods for classification, and show the practicality by applying our method to real-world applications including genome-wide association study (GWAS). The second one is to find efficient polynomial approximation of non-polynomial functions, instead of substituting them with some other HE-friendly operations. Based on composite function approximation methods, we develop complexity-optimal HE algorithms for comparison and min/max functions, which are the most frequently used non-polynomial operations in real-world computation. We also show the practicality of our algorithms by implementing them based on an approximate HE scheme HEaaN: The homomorphic comparison of two encrypted 16-bit integers takes only 1.22 milliseconds in amortized running time, which is 18 faster than the previous best result.1 Introduction 1 1.1 Our Contributions 3 1.2 List of Papers 6 2 Preliminaries 8 2.1 Notations 8 2.2 Mathematical Backgrounds 9 2.2.1 Minimax Polynomial Approximation on Sign Function 9 2.2.2 Gradient Descent with Errors 11 2.3 Homomorphic Encryption 13 2.3.1 Approximate HE Scheme HEaaN 15 2.3.2 Matrix Packing Method in HEaaN 19 2.4 Logistic Regression 20 2.5 Semi-parallel GWAS 21 3 Related Works 24 3.1 HE-based Logistic Regression and Ensemble Methods 24 3.2 Privacy-preserving Genome Analysis 25 3.3 Study on the Comparison Operation 27 3.3.1 Numerical Analysis on the Sign Function 27 3.3.2 Previous Homomorphic Comparison Methods 29 4 Approximate GWAS based on HE 31 4.1 Motivation 32 4.2 Summary of Results 33 4.3 Our Optimization Methodology 34 4.3.1 Our Modi ed semi-parallel GWAS Algorithm 37 4.4 Homomorphic Evaluation of the Modi ed Algorithm 38 4.5 Implementation 46 4.5.1 Dataset Description 46 4.5.2 Experimental Setting and Parameter Selection 46 4.5.3 Experimental Results and Evaluation 47 4.6 Discussion 50 5 Ensemble Logistic Regression based on HE 52 5.1 Motivation 53 5.2 Summary of Results 54 5.3 Our Ensemble Method 55 5.3.1 Ensemble Gradient Descent 56 5.3.2 Statistical Guarantee of Ensemble Gradient Descent 58 5.3.3 Ensemble GD with Errors and its Convergence 59 5.4 Implementation 63 5.4.1 Experimental Settings 63 5.4.2 Experimental Results 65 5.5 Discussion 68 6 Numerical Method for Homomorphic Comparison 70 6.1 Background and Overview 71 6.1.1 High-Level Idea 72 6.1.2 Summary of Results 74 6.2 Iterative Algorithms 76 6.2.1 Inverse 76 6.2.2 Square Root 78 6.3 Approximate min/max Algorithms 79 6.3.1 Min/Max Algorithm for two numbers 80 6.3.2 Min/Max Algorithm for several numbers 83 6.4 Approximate Comparison Algorithms 86 6.4.1 Comparison between two numbers 87 6.4.2 Max Index of several numbers 90 6.5 Asymptotic Optimality of our Methods 93 6.5.1 Min/Max from Minimax Approximation 95 6.5.2 Comparison from Minimax Approximation 96 6.6 Applications of Comparison Algorithms 100 6.6.1 Threshold Counting 100 6.6.2 Top-k Max 102 6.7 Experimental Results 104 6.7.1 Max of two integers 105 6.7.2 Comparison of two integers 106 6.7.3 Other Applications 108 7 Homomorphic Comparison with Optimal Complexity 110 7.1 Background and Overview 111 7.1.1 Our Idea and Technical Overview 113 7.1.2 Summary of Results 117 7.2 Our New Comparison Method 119 7.2.1 Composite Polynomial Approximation on the Sign Function 120 7.2.2 Analysis on the Convergence of f_n^(d) 124 7.2.3 New Comparison Algorithm NewComp 128 7.2.4 Computational Complexity of NewComp 129 7.2.5 Heuristic Methodology of Convergence Acceleration 132 7.3 Application to Min/Max 139 7.4 Additional Properties of f_n and g_n 142 7.4.1 Convergence of delta_0, S and g_{n,tau} 142 7.4.2 Heuristic Properties on g_n 143 7.4.3 Convergence of f_n^(d) in Erroneous Case 144 7.5 Experimental Results 149 7.5.1 Parameter Selection 149 7.5.2 Performance of NewComp and NewCompG 150 7.5.3 Performance of NewMax and NewMaxG 153 8 Conclusion 154 Abstract (in Korean) 174 Acknowledgement (in Korean) 175Docto

(A)Study on robust and optimal integration of active 4 wheel steering and direct yaw moment control

학위논문(석사) --서울대학교 대학원 :기계항공공학부,2006.Maste

분사 표면처리된 교정용 미니스크류 임플란트의 조직형태학적 연구

Dept. of Dental Science/박사Diabetic peripheral neuropathy (DPN) is the most common complication of diabetic mellitus (DM) that can cause significant morbidity and mortality, and is found in >60% of patients over the course of their disease. DPN is characterized by diffuse or focal damages to peripheral somatic or autonomic nerve fibers which produce dysfunctions of skin, muscles, and visceral organs. The primary risk factor is hyperglycemia which activates multiple biochemical pathways including AGE, polyol, hexosamine, PKC, and PARP pathways to result in cell dysfunctions and death. Generally, DPN can be divided into sensory motor neuropathy and autonomic neuropathy. The latter is further classified as cardiaovascular, gastrointestinal, and genitourinary autonomic neuropathies. Among them, genitourinary autonomic neuropathy has been poorly understood in terms of its cellular and molecular mechanism. The major clinical symptoms of genitourinary autonomic neuropathy are bladder and sexual dysfunctions. Major pelvic ganglion (MPG), located on the lateral surfaces of the prostate gland in rat provides autonomic innervation to the distal colon and urogenital organs including the urinary bladder, the prostate, and the penis. Among autonomic ganglia, MPG is very unique since sympathetic and parasympathetic neurons are colocalized in the same ganglion capsule. Thus, MPG is critical for autonomic reflexes such as micturition and penile erection together with visceral sensory dorsal root ganglion (DRG). To date, it is little known whether DM affects functions of MPG and DRG neurons. Accordingly, I hypothesized that DM causes plastic changes of MPG and DRG neuronal functions by altering expression of certain types of ion channels, which may contribute to autonomic genitourinary dysfunctions. Thus, the purposes of the present study were to test whether excitability of MPG and DRG neurons is altered in an experimantal diabetic rat model, and to define the molecular and cellular mechanisms underlying DM-induced changes in excitability.Experimental DM was induced by injection of streptozocin (STZ, 60 mg/kg, i.p.) into S/D rats (8 week-old). After three days, the levels of blood glucose in control and STZ-injected rats were measured. STZ-injected rats with hyperglycemia (>300 mg/dl) were divided into two groups (STZ and STZ+insluin). Insulin (10 IU) was injected into diabetic rats once per day. After 8 weeks, development of diabetic neuropathy in the STZ group was assessed by measuring motor nerve conduction velocity (MNCV) in sciatic nerves, myelin area, bladder micturition pattern, and intracarvernous pressure (ICP). As results, motor and autonomic neuropathies were found to be developed in the STZ group. H & E staining revealed the enlarged bladder with hypetropied urothelium in the STZ group. DM significantly decreased testosterone level while increased corticosterone, a stress hormone. Interestingly, DM was found to increase serum and tissue oxidative stress as the malondialdehyde level was measured. Under the gramicidine-perforated configuration of the patch-clamp techniques, spike firing was recorded in MPG and capsaicin-sensitive C-fiber DRG neurons (L6-S1). Spike firing frequency was decreased in both sympathetic and parasympathetic MPG neurons, while increased in DRG neurons from the STZ group. However, insulin significantly attenuated the effects of DM on the excitability of MPG and DRG neurons. DM did not alter the passive properties (input impedence, and resting membrane potentials) in MPG and DRG neurons. However, DM significantly increased the duration of afterhyperpolarization (AHP) in MPG neurons, while decreased it in DRG neurons, which might alter the excitability of neurons. Real-time RT-PCR and western blot analyses revealed that expression of T-type 1H Ca2+ channels was down-regulated in MPG, but up-regulated in DRG from the STZ group. Consistent with these molecular data, T-type Ca2+ currents were decreased in sympathetic MPG neurons, but increased in DRG neurons from the STZ group. Furthermore, expression of SK channels determining AHP duration was up-regulated in MPG neurons, while down-regulated in DRG neurons from the STZ group. In in vitro studies, T-type current density was significantly decreased by high glucose and the pro-inflammatory cytokines in MPG neurons. In DRG neurons, however, T-type current density was increased only by high glucose. In addition, H2O2 significantly reduced T-type current density in MPG neurons, while slightly increased it with no statistical significance in DRG neurons. Taken together, experimental DM alters the excitability of autonomic MPG and DRG neurons by differential regulation of expression of T-type Ca2 and SK potassium channels, which might produce autonomic imbalance contributing to the genitourinary dysfunctions. The significances of the present study are as follow; I studied for the first time the effects of DM on functional plasticity of autonomic ganglion neurons innervating the urogenital system. More importantly, I suggest the molecular and cellular mechanisms underlying the DM-induced autonomic plasticity.restrictio

Anatomical characteristics of the midpalatal suture area for miniscrew implantation using CT image

치의학과/석사[한글] 고정원으로서 임플란트를 사용하기 위해서는 무엇보다 식립후에 안정적이어야 한다. 이를 위해서 식립부위의 골상태가 중요하다. 즉 피질골이 충분한 두께를 가지는 부위에 식립하여 충분한 초기 고정을 얻는 것이 임플란트의 안정성을 위해서 매우 중요하다. 이러한 관점에서 하악골에 비하여 전반적으로 골질이 좋지 않고 특히 협측에서 피질골의 두께가 얇은 상악골에서는 충분한 두께의 피질골을 가지고 있는 정중구개봉합부위가 임플란트의 식립 부위로 주목을 받고 있다. 하지만 교정용 임플란트 사용에 있어서 정중구개봉합부위의 골조직의 높이에 대한 구체적인 해부학적 자료가 없어서 임상에 적용시 이론적 근거가 부족한 것이 사실이었다. 이에 본 연구는 전산화단층촬영과 재구성 프로그램인 V works 4.0 (Cybermed Inc., Seoul, Korea)을 이용하여 보철용 임플란트 식립을 위해 촬영한 성인 남자 14명, 성인 여자 14명의 CT 자료를 통해 1) 정중 시상면에서 상악골의 길이를 계측하고 2) 정중 구개 봉합 부위에서 골조직 두께를 측정하며 3) 교정용 임플란트를 안전하게 식립할 수 있는 구체적 부위를 설정하고자 하여 다음과 같은 결과를 얻었다. 1. ANS에서 PNS까지의 상악골의 길이를 계측한 결과 남자에서는 평균 51.08mm, 여자에서는 평균 47.34mm였다. 남녀 사이에는 통계적으로 유의한 차이가 있었다.(p<0.05) 2. 정중구개봉합부위의 골조직 두께를 측정한 결과 남자의 ANS-PNS길이의 중점에서 구개평면을 따라 PNS쪽으로 15mm지점을 제외하고는 남녀모두에서 6mm이상의 골조직이 존재하였다. 3.정중구개봉합부위에 교정용 임플란트를 적용할 때 안정적인 식립부위는 구개평면을 따라서 ANS로부터 남자는 19.43mm 후방부위, 여자는 17.62mm 후방부위에 해당하였다. 이상의 결과로 정중구개봉합부위의 안정적인 식립부위에서는 교정용 임플란트 식립이 적합하다고 판단되며 이를 바탕으로 정중구개봉합부위의 교정용 임플란트를 활용하여 교정치료영역을 넓힐 수 있을 것이다. [영문]Since the miniscrew stability is mainly obtained from the cortical bone, it is important to take this into consideration to improve miniscrew stability. In this point, miniscrews implanted in the maxilla have less stability than that in the mandible due to the porous bony structure. However, the midpalatal suture area composed of dense cortical bone has been determined as the best anchorage site in the maxilla. But there is lack of data for the amount of vertical bone in the midpalatal region for miniscrew implantation. The purpose of this study was to measure the structure of the midpalatal suture area using CT image and V-works 4.0 program(Cybermed Inc., Seoul, Korea). CT images of 14 male and 14 female adults were reconstructed. In detail, it was 1) to measure the length of maxilla on the midsagittal plane 2)to measure vertical bone height in the midpalatal area 3) to establish the zone of safety for miniscrew implantation. The following results were obtained. 1. In the length of ANS-PNS, the mean length was 51.08mm in males and 47.34mm in females. There was a statistically significant difference between male and female. (p<0.05) 2. The vertical bone height of the midpalatal suture area was above 6mm except 15mm posterior from the central point of ANS-PNS in males. 3. The zone of safety was located 19.43mm posterior from the ANS in males while it was 17.62mm in females upon the palatal plane. These results support that the safety zone of the midpalatal area is suitable for screw implantation. Midpalatal miniscrew implantation is a powerful tool in modern orthodontics. Through many applications, it can expand the modern orthodontic field.ope