Multivariate Homomorphic Encryption for Approximate Matrix Arithmetics

김안드레이 서울대학교 대학원 2019 국내박사

혜안(Homomrphic Encryption for Arithmetics of Approximate Numbers, HEAAN) 은 근사 계산을 지원하는 동형 암호 스킴이다. 혜안의 벡터 패킹 기술은 데이터 분석 및 기계 학습 분야 등 근사적인 계산이 필요한 암호화 응용 프로그램에서 효율성을 입증하였다. 다변수 혜안(Multivariate HEAAN, MHEAAN)은 평문의 텐서 구조에 대한 HEAAN의 일반화이다. 본 설계는 연산 과정에서 줄어드는 유효 숫자의 길이가 연 산 서킷의 두께로 제한된다는 HEAAN의 장점을 그대로 가지고, 평문 상태에서의 근사 연산과 비교하였을 때에도 유효 숫자 낭비가 1비트를 넘지 않는다. 평문 벡터 의 회전 등 고차원 벡터의 다양한 구조들이 응용에 많이 쓰임에 따라, MHEAAN은 행렬 및 텐서와 관련된 응용 프로그램에서 기존 HEAAN에 비하여 보다 효율적인 결과를 낳는다. MHEAAN의 구체적인 2 차원 구조는 행렬 연산에 대한 MHEAAN 기법의 효 율성을 보여 주며, 로지스틱 회귀분석, 심 신경망 구조 및 회귀 신경망 구조와 같은 암호화 된 데이터 및 암호화 된 모델에 대한 여러 기계 학습 알고리즘에 적용될 수 있다. 또한 효율적인 재부팅 구현을 통하여, 이는 임의의 로지스틱 회귀 분석 등의 다양한 응용 분야에 쉽게 활용될 수 있다. Homomorphic Encryption for Arithmetics of Approximate Numbers (HEAAN) is a homomorphic encryption (HE) scheme for approximate arithmetics introduced by Cheon et.al. [CKKS17]. Its vector packing technique proved its potential in cryptographic applications requiring approximate computations, including data analysis and machine learning. Multivariate Homomorphic Encryption for Approximate Matrix Arithmetics (MHEAAN) is a generalization of HEAAN to the case of a tensor structure of plaintext slots. Our design takes advantage of the HEAAN scheme, that the precision losses during the evaluation are limited by the depth of the circuit, and it exceeds no more than one bit compared to unencrypted approximate arithmetics, such as floating-point operations. Due to the multi-dimensional structure of plaintext slots along with rotations in various dimensions, MHEAAN is a more natural choice for applications involving matrices and tensors. i The concrete two-dimensional construction shows the efficiency of the MHEAAN scheme on matrix operations and was applied to several Machine Learning algorithms on encrypted data and encrypted model such as Logistic Regression (LR) training algorithm, Deep Neural Network (DNN) and Recurrent Neural Network (RNN) classification algorithms. With the efficient bootstrapping, the implementation can be easily be scaled to the case of arbitrary LR, DNN or RNN structures.

Shearography를 이용한 6061-T6 마찰교반용접부의 strain 측정에 관한 연구

김안드레이 전북대학교 일반대학원 2013 국내석사

ABSTRACT Study on the strain measurement of 6061-T6 Friction Stir Weld joints using the Shearography Kim Andrey Dept. of Mechanical Design The Graduate School Chonbuk National University Friction Stir Welding(FSW) is an relatively new solid-state joining process which was developed at The Welding Institute UK in 1991. This joint method uses a new principle of stirring materials and the integration of non-consumable rotating tools. Because of the many advantages of this new method, things such as cracks or pores do not occur during melting or solidification and low welding deformation. By focusing on transportation equipment since the middle of 1990s many industries such as Rail Rolling Stock, Shipbuilding, Automotive, and Aerospace have made practical advances in welding technology and many have been recognized as revolutionary. Traditionally the welding of aluminum alloys in the MIG(Metal Inert Gas) or TIG(Tungsten Inert Gas) have been used by inert gas but because of the deformation of welded joints and cracks in welding of aluminum alloys many issues have emerged. Various development processes, characteristics and organization of joints have been used to perform considerable research, but still much remains unanswered to grasp a full understanding of joint principles and conditions. As FSW does not require any filler material, the metallurgical problems associated with it can also be eliminated and good quality weld can be obtained. FSW involves complex material movement and plastic deformation. Welding parameters, tool geometry, and joint design exert significant effect on the material flow pattern and temperature distribution, there by influencing the microstructural evolution of material. These tool geometry is the most influential aspect of process development. The design of the shoulder and the pin is very important for the quality of the weld. Clearly, different materials and different thicknesses will require different pin profiles. The variations in tool design are infinite and combinations of shoulder diameter, shoulder profile, pin length, diameter and profile, are all important parameters in determining the speed of welding and the quality of the finished weld. In this paper two different(threaded triangle and quadrangular pin profiles) tools were developed with excellent welding performance compared to the conventional threaded circular one to improve the weldability of the friction stir welded joints of aluminum plate according to the welding conditions. The rotation speed and traverse speed conditions were changed in this study, the other welding conditions are constant. Next purpose in this study was to measure the local strain of the FSW joints using Shearography and compare it with the tension test strain results. In the case of Shearography method has advantages that the inspection can be perfomed at a real time measurement and is more insensitive to environmental noise. Also, it uses simple optical configuration compared to other optical interferometers. Shearography is a laser-based technique for full-field, non-contacting measurement of surface deformation(strain or displacement), hence, it is a partical tool that can be used in a factory environment. An aluminum plate with a thickness of 6.0 mm was used in this investigation. The Shearographic technique was utilized to test FSW joint samples under tension loading condition. Shearography method results show the great possibility of measuring the strain of FSW joints by comparing it with the tension test strain results, and determine the effect of weld zone. Keywords: 마찰교반용접(Friction Stir Welding; FSW), 용접 툴(welding tool), 전단간섭계(Shearography), 변형율(strain), 비파괴 검사(Nondestructive measurement)

Single and Double Spin Asymmetries for Deeply Virtual Exclusive π^0 Production on Longitudinally Polarized Proton Target with CLAS : CLAS를 이용한 세로방향의 편극양성자 과녁에 대한 심층가상 배타적 π^0 생성에서의 단일 및 이중 스핀 비대칭성

김안드레이 경북대학교 대학원 2014 국내박사

심층가상 배타적 과정들은 카이럴 짝수의 일반화된 쪽입자 분포(Generalized Parton Distributions, GPDs)와 카이럴 홀수의 가로방향 GPDs에 민감한 구조함수와 그 비율들을 측정함으로써 핵자의 내부구조를 조사한다. GPDs는 세로방향의 운동량 공간 및 가로방향의 충격 파라미터 공간에서 쪽입자 분포들의 상관관계를 표시하며 중간자 생성의 와 에 대한 의존도를 측정함으로써 획득되어질 수 있다. CLAS 검출기의 넓은 운동학적 범위는 전체 방위각 범위에서 배타적 전자생성의 측정을 가능하게 한다. 심층가상 배타적 전자생성은 심층 비탄성 산란 영역에서 과녁과 이중스핀 비대칭성이 처음으로 측정되었다. 이 실험은 제퍼슨 가속기 연구소의 Hall B에서 최대 에너지 6 GeV의 세로방향 편극 전자빔과 빔 축 방향으로 정렬된 자유 양성자 스핀의 동역학적 편극 NH3 과녁을 이용하여 실행되었다. 배타적 채널에서 나타난 4개의 최종상태 입자들, 즉, 전자, 양성자, 붕괴에서 나온 2개의 광자들이 모두 확인되었다. 비대칭성들은 강입자 질량중심계에서 각도 조정에 따라 fitting 되고 모멘트들이 추출되었다. 카이럴 짝수와 카이럴 홀수 GPDs의 기여가 포함된 두 종류의 핸드백 기반의 계산과 실험 데이터와의 비교는 넓은 운동학적 영역에서 실행되었다. 수정된 섭동 접근 체제 내에서 일반화된 쪽입자 분포에 기반을 둔 수식체계의 적용 가능성이 논의되었다. Deeply virtual exclusive processes probe the internal structure of nucleons through measurements of structure functions and their ratios, which are sensitive to the chiral-even generalized parton distributions (GPDs) and the chiral-odd transversity GPDs. The GPDs encode correlations of parton distributions in longitudinal momentum space and transverse impact parameter space and are accessible through the measurements of the $x_B$ and $t$ dependence of meson production. The wide kinematic coverage of CLAS detector allowed measurements of exclusive $π^0$ electroproduction in full azimuthal range. The target and double spin asymmetries for the deeply virtual exclusive $π^0$ electroproduction were measured for the first time in the DIS region. The experiment was carried out at Hall B, Jefferson Lab using the longitudinally polarized electron beam with energy of up to 6 GeV and a dynamically polarized NH$_3$ target with spins of free protons aligned along the beam axis. All four final-state particles from exclusive channel, electron, proton and two photons from $π^0$ decay, were identified. The asymmetries were fitted according to their angular modulations in the hadronic center-of-mass system, and their moments were extracted. The data comparison with two handbag-based calculations involving the contribution from both chiral-even and chiral-odd GPDs was performed in wide kinematic range. The applicability of a formalism based on generalized parton distributions within the framework of modified perturbative approach is discussed.