, » ί ² (29-31.07.14) » Kurl Srh, Chukhn Yrslv FULLY HMMRPHIC NCRYPTIN. TSTING ND CMPRSIN T RS

Kurl Srh, Chukhn Yrslv FULLY HMMRPHIC NCRYPTIN. TSTING ND CMPRSIN T RS

: ί ² (29-31.07.14), 㳿

: 004.056.55

 

FULLY HMMRPHIC NCRYPTIN. TSTING ND CMPRSIN T RS

Kurl Srh, Chukhn Yrslv

Ntnl thnl unvrst f Ukrn “Kv lthn nsttut”, Ukrn, Kv

 

Sn th dsvr f full hmmrh rtgrh shm b Gntr, numbr f dffrnt shms hv bn rsd tht l th btstr thnqu f Gntr’s rgnl rh. Hwvr, t dt n mlmnttn f full hmmrh nrtn hs bn ubll rlsd. Ths r rsnts wrkng mlmnttn f shm b Gntr nd mr wth RS.

Kwrds: hmmrh nrtn, RS, nrtn, drtn.

 

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Intrdutn. full hmmrh ubl k nrtn shm hs bn “hl grl” f rtgrh fr vr lng tm. In th lst r ths rblm hs bn slvd b Gntr, b usng rrts f dl ltts. Vrus rtgrh shms mk us f ltts, smtms just t rgu but thr surt (suh s NTRU), n thr ss ltts r vtl t undrstnd th wrkngs f th shm lgrthms. Gntr’s full hmmrh shm flls nt th lttr tgr. In ths r w rsnt full hmmrh shm whh n b dsrbd usng th lmntr thr f lgbr numbr flds, nd hn w d nt rqur ltts t undrstnd ts nrtn nd drtn rtns. Hwvr, ur shm ds fll nt th tgr f shms whs bst knwn ttk s bsd n ltts. t hgh lvl ur shm s vr sml, nd s mnl rmtrzd b n ntgr N (thr r thr rmtrs whh r lss mrtnt). Th ubl k nssts f rm nd n ntgr α mdul . Th rvt k nssts f thr n ntgr z (f w r nrtng bts), r n ntgr lnml Z(x) f dgr N − 1 (f w r nrtng gnrl bnr lnmls f dgr N − 1). T nrt mssg n nds th mssg s bnr lnml, thn n rndmzs th mssg b ddng n tw tms smll rndm lnml. T btn th hrtxt, th rsultng lnml s vlutd t α mdul . s suh, th hrtxt s sml n ntgr mdul (rrstv f whthr w r nrtng bts r bnr lnmls f dgr N − 1). T drt n th s whr w knw th mssg s sngl bt, w multl th hrtxt b z nd dvd b . W thn rund ths rtnl numbr t th nrst ntgr vlu, nd subtrt th rsult frm th hrtxt. Th lntxt s thn rvrd b rdung ths ntrmdt rsult mdul 2. Whn w r drtng bnr lnml w fllw th sm rdur, but ths tm w multl b th lnml Z(x) nd dvd b , t btn rtnl lnml. Rundng th ffnts f ths lnml t th nrst ntgr, subtrtng frm th rgnl hrtxt, nd rdung mdul tw wll rsult gn n rvrng th lntxt.

ur Smwht Hmmrh Shm. In ths stn w rsnt ur smwht hmmrh shm nd nlz fr whh rmtr sts drtn wrks. T smlf th rsnttn w rsnt th shm t ths nt s n whh just nrts lmnts n P = {0, 1}.

 

 

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