ÄÂÀ ÍÀÏÐÀÂËÅÍÈß ÈÑÑËÅÄÎÂÀÍÈÉ Îáôóñêàöèÿ äëÿ îáåñïå÷åíèÿ êîìïüþòåðíîé áåçîïàñíîñòè C. Wang, ¾A Security Architecture for survivability Mechanisms¿, PhD thesis, Dep. of Computer Science, University of Virginia, 2000. G. Wroblewski, ¾General Method of Program Code Obfuscation¿, PhD thesis, Wroclaw University, 2002. À.Â. ×åðíîâ, ¾Èññëåäîâàíèå è ðàçðàáîòêà ìåòîäîëîãèè ìàñêèðîâêè ïðîãðàìì¿, Äèññ. íà ñîèñêàíèå ó÷. ñò. ê.ô.-ì.í, ÂÌÊ ÌÃÓ, 2003. Y. T. Kalai, ¾Attacks on the Fiat-Shamir Paradigm and Program Obfuscation¿, PhD thesis, MIT, 2006
ÎÁÔÓÑÊÀÖÈß ×ÀÑÒÈ×ÍÎ ÇÀÙÈÙÅÍÍÛÕ ÏÐÎÃÐÀÌÌ R. Ostrovsky, Ecient computation on oblivious RAM, Proc. of 22nd ACM Symposium on Theory of Computing (STOC-90) Çàùèùåííûé ïðîöåññîð P èìååò îòêðûòóþ ïàìÿòü M : M ⇐⇒ P
ÎÁÔÓÑÊÀÖÈß ÏÐÅÄÈÊÀÒΠÄîêàçàòåëüñòâî Íóæíî ñäåëàòü íåîòëè÷èìûìè äðóã îò äðóãà äâå ïðîãðàììû prog π0 ; prog πa ; var x : string y : bit; var x : string y : bit; input (x) ; const a : string; y = 0; output (y); input (x) ; end of prog if x==a then y=1 else y=0; output (y); end of prog
ÎÁÔÓÑÊÀÖÈß ÏÐÅÄÈÊÀÒΠÄëÿ ïðîãðàììû π0 : 1) âûáðàòü äâå ñëó÷àéíûå ñòðîêè w, u , 2) âû÷èñëèòü v = ϕ(w) è σ = n i=1 wi ui mod 2 . Äëÿ ïðîãðàììû πa : 1) âûáðàòü ñëó÷àéíóþ ñòðîêó u , 2) âû÷èñëèòü v = ϕ(a) è σ = 1 + n i=1 ai ui mod 2 .
ÎÁÔÓÑÊÀÖÈß ÏÐÅÄÈÊÀÒΠÄëÿ ïðîãðàììû π0 : 1) âûáðàòü äâå ñëó÷àéíûå ñòðîêè w, u , 2) âû÷èñëèòü v = ϕ(w) è σ = n i=1 wi ui mod 2 . Äëÿ ïðîãðàììû πa : 1) âûáðàòü ñëó÷àéíóþ ñòðîêó u , 2) âû÷èñëèòü v = ϕ(a) è σ = 1 + n i=1 ai ui mod 2 . Òîãäà êàæäàÿ èç ïðîãðàìì π0 , πa , ãäå a ∈ {0, 1}n ïðèìåò âèä: prog O(π) ; var x : string y : bit; const u,v : string, σ : bit; input (x) ; if ϕ (x)==v then if σ == n i=1 xi ∗ ui mod 2 then y=0 else y=1 else y=0; output (y); end of prog
ÄÎÑÒÈÆÅÍÈß ÏÎÑËÅÄÍÈÕ ËÅÒ Â èþëå 2013 ã. áûëà îïóáëèêîâàíà ñòàòüÿ Candidate Indistinguishability Obfuscation and Functional Encryption for All Circuits S. Garg, C. Gentry, S. Halevi, M. Raykova, A. Sahai, B. Waters â êîòîðîé àâòîðû ïîêàçàëè, ÷òî âåðíà Òåîðåìà [S. Carg, C. Gentry, et al, 2013] Íåîòëè÷èìàÿ îáôóñêàöèÿ âîçìîæíà äëÿ ïðîèçâîëüíûõ ïðîãðàìì (ïðè íåêîòîðûõ ïðåäïîëîæåíèÿõ î òðóäíîñòè ðåøåíèÿ çàäà÷ òåîðèè ãðóïï)
ÄÎÑÒÈÆÅÍÈß ÏÎÑËÅÄÍÈÕ ËÅÒ 30 ñåíòÿáðÿ 2013 ã. áûëà îïóáëèêîâàíà ñòàòüÿ Virtual Black-Box Obfuscation for All Circuits via Generic Graded Encoding. Zvika Brakerski, Guy N. Rothblum We present a new general-purpose obfuscator for all polynomial-size circuits. The obfuscator uses graded encoding schemes, a generalization of multilinear maps. We prove that the obfuscator exposes no more information than the program's black-box functionality, and achieves virtual black-box security , in the generic graded encoded scheme model.