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cryptography and copy protection

# 41 rennes presentation a few spectacular examples

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Unformatted text preview: cy algorithm 100 and 600 iterations) 42 Rennes presentation More examples (Jupiter, HST) Telescope 43 Richardson-Lucy 600 iterations Rennes presentation More examples (Jupiter, HST) Telescope 44 Richardson-Lucy 300 iterations Rennes presentation More examples (Saturn, HST) Telescope Richardson-Lucy 275 iterations 45 Rennes presentation The general formulation s Assuming or knowing the impulse response h(t) (linear filter), s How to find back x(t) out of the “noisy” observation y(t) ? y(t) = ò x(τ)h(τ -t)dτ + n(t) Deconvolution is a special case of the inversion problem: s of the first-kind Fredholm integral equation : g(s) = s an “ill-posed” problem Simple discretization = sampling & truncation from integral to matrix formulation n-1 Yi= å hi-u xu u=0 46 1 ò f(t)K(s,t)dt 0 ... é h(0) 0ù ú ê h(1) h(0) ú ê ê : h(1) h(0) ú ú Y=Hx with Toeplitz Matrix H= ê h(n - 1) h(1) ú ê ú ê h(n - 1) ú ê ê0 h(n - 1) ú û ë Rennes presentation Naive (useless) approaches æDFT(y) ö ç ÷ ç ÷ èDFT(h) ø s Fourier transform x= s Linear system inversion x = (HtH)-1Hty DFT-1 s Linear unbiased estimate with minimum variance x = (HtRnn-1H)-1HtRnn-1y Rnn covariance matrix of the noise s The “deconv” MATLAB function (similar to polynomial division) 47 Rennes presentation naive FFT (no noise) 48 Rennes presentation naive FFT (with noise) 49 Rennes presentation REGULARIZATION OF THE ILL-POSED PROBLEM (Tikhonov, Phillips, Twomey) • Give up optimality : minx||Hx-y||2 • Use a smooth criterion instead (L differential matrix operator) minx(||Hx-y||22 + ||Lx||2) • Simplest approach L = λ Id (Tikhonov) minx(||Hx-y||22 + λ||x||2) • Maximum entropy, constrained LSQ... WELCOME TO THE WORLD OF NUMERICAL RECIPES ! • Which strategy to select? which L and/or λ ? • Which algorithm : direct or iterative (long vectors) ? 50 Rennes presentation How does it work A s s s basic tool : the singular value decomposition (SVD) provides conditioning indicators and metrics is the basis of the direct algorithms (for both H and L) is the generalization of Eigensystems to rectangular matrices n H=USVt= Σ uiσivit (H: m×n, m≥n) i=1 UtU=VtV=Idn U=(u1,…,un), S=diag(σ1,…,σn) V=(v1,…,vn) σ1≥…≥σn≥0 General form of a direct solution (simple regularization L = λIdn) n xreg=Σ i=1 uity fi vi σi with filter factors fi Tikhonov: fi=σi2/(σi2+λ2) Damped SVD: fi=σi/(σi+λ) Truncation: fi=0 for i>k 51 Rennes presentation The data, model and solution (with noise) DS probability density Convolved noisy comb Hidden (smeared) DPA comb 52 Rennes presentation The continuous case 53 Rennes presentation TIKHONOV solutions (for several λ) 54 Rennes presentation TIKHONOV solutions (with optimised λ !) 55 Rennes presentation Iterative LSQR (various iteration attempts) 56 Rennes presentation OTHER ATTACKS: FIB s FIB: focused ion beam x Uses gallium ions to mill and form images x Operates like a SEM x Imaging to 5nm resolution s Possible attacks x Deposit probe pads x Defeat blown fuse links x Connect tracks x Cut tracks 57 Rennes presentation CHIP MODIFICATION: CUT... 260 Stage current (pA) 240 220 200 180 160 140 120 -0.1 0.0 0.1 0.2 0.3 0.4 Depth (microns) 58 Rennes presentation 0.5 0.6 0.7 CHIP MODIFICATION: CONNECT... 59 Rennes presentation ADVANCED FIB ATTACKS 60 Rennes presentation JAVA ATTACKS Applets local code Verification local codel Applet type 2 Applet type 1 Applet type s Sandbox Domain 2 Domain 1 JVM system resources 61 Security policy Rennes presentation Conclusion s For any information/pointers on card security and card attacks: x [email protected] 62 Rennes presentation...
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