ᱦᱚᱨᱰᱼᱠᱳᱨ ᱯᱨᱤᱰᱤᱠᱮᱴ ᱨᱮᱱᱟᱜ ᱯᱷᱮᱰᱟᱛ ᱧᱮᱞᱢᱮ

ᱠᱨᱤᱯᱴᱳᱯᱷᱨᱤ ᱨᱮ, ᱢᱤᱫ ᱥᱮᱫ ᱠᱷᱚᱱ ''ᱯᱷ''ᱟᱝᱠᱥᱚᱱ ᱯᱷ ᱨᱮᱭᱟᱜ '''ᱦᱟᱨᱰᱼᱠᱳᱨ''' ᱯᱮᱰᱤᱠᱮᱴ ᱫᱚ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ ᱯᱮᱰᱤᱠᱮᱴ ''ᱵᱤ'' (ᱟᱭᱮᱢᱟᱜᱟᱱ , ᱢᱤᱫᱴᱟᱝ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱡᱟᱦᱟᱸ ᱨᱮᱭᱟᱜ ᱚᱯᱴᱩᱯᱩᱴ ᱢᱤᱫᱴᱟᱝ ᱵᱤᱴ ᱠᱟᱱᱟ , ᱡᱟᱦᱟᱫᱚ ᱞᱮᱠᱷᱟ ᱞᱟᱹᱜᱤᱫ ᱟᱞᱜᱟ (x′ ᱨᱮᱭᱟᱜ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱞᱮᱠᱟᱛᱮ , ᱢᱮᱱᱠᱷᱟᱱ ᱯᱷ (x′) ᱮᱢ ᱠᱟᱛᱮ ᱞᱮᱠᱷᱟ ᱠᱚᱨᱟᱣ ᱫᱚ ᱟᱹᱰᱤ ᱟᱱᱟᱴ ᱾  ᱟᱹᱨᱤ ᱞᱮᱠᱟᱛᱮ ᱡᱟᱦᱟᱱ ᱯᱚᱨᱟᱢᱮᱥ ᱟᱱᱟᱜ ᱯᱳᱞᱤᱱᱳᱢᱤᱭᱟᱞᱼᱴᱟᱭᱚᱢ ᱵᱟᱝ ᱢᱮᱱᱟᱜᱼᱟ (PPT′ ᱮᱞᱟᱨᱜᱟᱢ ᱡᱟᱦᱟᱸ ᱫᱚ ᱵᱤ (x′ ᱠᱷᱚᱱ ''ᱯᱷ'' (''x''′) ᱨᱮ ᱟᱭᱩᱢᱟᱹᱱ ᱠᱟᱛᱮ , ᱟᱭᱩᱢᱟᱹᱱ ᱞᱮᱠᱟᱛᱮ ᱟᱭᱩᱢᱟᱹᱱ ᱢᱤᱫ ᱥᱮ ᱚᱱᱟ ᱠᱷᱚᱱ ᱰᱷᱮᱨ , ᱟᱨ ᱟᱭᱩᱢᱟᱹᱱ ᱟᱭᱩᱢᱟᱹᱱ x:34 ᱾ ᱮᱴᱟᱜ ᱠᱟᱛᱷᱟ ᱞᱮᱠᱟᱛᱮ , ᱡᱩᱫᱤ x ᱫᱚ ᱟᱭᱩᱢᱟᱹᱱ ᱟᱱᱟᱜ ᱞᱮᱠᱟᱛᱮ ᱟᱭᱩᱢᱟᱹᱞ ᱨᱮ ᱵᱮᱱᱟᱣ ᱦᱳᱭᱳᱜᱼᱟ , ᱮᱱᱠᱷᱟᱱ ᱮᱢ ᱦᱳᱭᱳᱜᱼᱟ f (x′ , ᱡᱟᱦᱟᱸ ᱮᱴᱟᱜ PPT ''ᱵᱤ''ᱨᱩᱫᱤᱭᱟᱹ ᱥᱩᱢᱩᱝ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱵᱤᱴ ᱵᱤ (xʼ) ᱟᱨ ᱢᱤᱫᱴᱟᱝ ᱟᱭᱩᱢᱟᱹᱱ ᱞᱮᱠᱟᱱ ᱵᱤᱴ ᱨᱮ ᱟᱭᱩᱢᱟᱹᱱᱟᱱ ᱮᱥᱮᱨ ᱥᱟᱶᱛᱮ ᱟᱭᱩᱢᱟᱹᱱ ᱫᱟᱲᱮ ᱥᱟᱶᱛᱮ , x ᱨᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ ᱪᱮᱛᱟᱱ ᱨᱮ ᱵᱷᱮᱜᱟᱨ ᱠᱚᱨᱟᱣ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ ᱾<ref>Definition 2.4 in {{Cite web |last=Lindell |first=Yehuda |title=Foundations of Cryptography 89-856 |url=http://u.cs.biu.ac.il/~lindell/89-856/complete-89-856.pdf |access-date=11 January 2016 |website=Computer Science, Bar Ilan University |publisher=Bar Ilan University |archive-date=19 January 2022 |archive-url=https://web.archive.org/web/20220119043828/https://u.cs.biu.ac.il/~lindell/89-856/complete-89-856.pdf |url-status=dead }}</ref>

ᱢᱤᱫᱴᱟᱝ '''ᱦᱟᱨᱰᱼᱠᱳᱨ ᱯᱷᱟᱝᱠᱥᱚᱱ''' ᱦᱚᱸ ᱚᱱᱟ ᱞᱮᱠᱟ ᱞᱮᱠᱟᱛᱮ ᱵᱚᱨᱱᱚᱱ ᱠᱚᱨᱟᱣ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ ᱾ ᱚᱱᱟ ᱫᱚ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ , ᱡᱩᱫᱤ ' x ' ᱫᱚ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱞᱮᱠᱟᱛᱮ ' ᱨᱮᱱᱰᱚᱢ ' ᱨᱮ ᱵᱟᱪᱷᱱᱟᱣ ᱦᱳᱭᱳᱜᱼᱟ , ᱮᱱᱠᱷᱟᱱ ' f ' ᱮᱢ ᱮᱢ ᱠᱟᱛᱮ ᱡᱟᱦᱟᱱ PPT ᱮᱞᱟᱨᱜᱟᱢ ᱥᱩᱢᱩᱝ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱯᱷᱚᱱᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱜᱚᱱᱚᱝ ' h ' (' ''x'' ') ᱟᱨ ' ''|h'' ' (' ′′ | ') ᱨᱮᱱᱟᱜ ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱨᱮᱱᱰᱚᱢ ᱵᱤᱴ ᱠᱚ ᱵᱷᱮᱜᱟᱨ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ , ᱡᱟᱦᱟᱸ ᱫᱚ ' ''x'' ' ᱨᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ ᱪᱮᱛᱟᱱ ᱨᱮ ᱟᱹᱰᱤ ᱠᱚᱢ ᱜᱮ ᱥᱤᱜᱤᱞᱮ ᱧᱟᱢ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ ᱾<ref>Goldreich's FoC, vol 1, def 2.5.5.</ref><ref>Definition 3 in {{Cite web |last=Holenstein |first=Thomas |display-authors=etal |title=Complete Classification of Bilinear Hard-Core Functions |url=https://www.iacr.org/archive/crypto2004/31520072/HMS_final_1.pdf |access-date=11 January 2016 |website=IACR eprint |publisher=IACR}}</ref>

ᱢᱤᱫᱴᱟᱝ ᱦᱚᱨᱰᱼᱠᱳᱨ ᱵᱨᱮᱰᱤᱠᱮᱴ " ᱚᱱᱛᱩᱛᱚᱱᱛᱚ ᱞᱮᱠᱟᱛᱮ " ᱤᱱᱵᱷᱟᱨᱴᱤᱝ ''ᱯᱷ'' " ᱨᱮᱭᱟᱜ ᱦᱚᱨᱰᱱᱮᱥ ᱠᱚ ᱦᱟᱛᱟᱣ ᱞᱮᱫᱟ ᱾

ᱮᱱᱦᱚᱸ ᱢᱤᱫ ᱥᱮᱫᱛᱮ ᱠᱟᱹᱢᱤ ᱫᱚ ᱵᱚᱫᱚᱞ ᱠᱚᱨᱟᱣ ᱟᱹᱰᱤ ᱟᱱᱟᱴ , ᱮᱱᱦᱚᱸ ᱪᱤᱛᱟᱹᱨ ᱯᱷ (x) ᱠᱷᱚᱱ ᱮᱛᱚᱦᱚᱵ ᱪᱤᱛᱟᱹᱨ ''ᱥᱤ'' ᱤᱫᱤ ᱠᱟᱛᱮ ᱦᱤᱸᱥ ᱛᱚᱛᱛ ᱞᱮᱠᱷᱟ ᱞᱮᱠᱷᱟ ᱨᱮᱭᱟᱜ ᱠᱟᱹᱢᱤ ᱫᱟᱲᱮᱱᱟᱜ ᱵᱟᱨᱮᱛᱮ ᱡᱟᱦᱟᱱ ᱵᱟᱛᱟᱣᱟᱜ ᱫᱚ ᱵᱟᱝ ᱠᱟᱱᱟ ᱾ ᱡᱮᱞᱮᱠᱟ, ᱡᱚᱠᱷᱚᱱ RSA ᱫᱚ ᱢᱤᱫᱴᱟᱹᱝ ᱦᱚᱨ ᱯᱷᱚᱱᱠᱥᱚᱱ ᱞᱮᱠᱟᱛᱮ ᱠᱚ ᱢᱟᱱᱟᱣ ᱵᱟᱛᱟᱣ ᱮᱫᱟ, ᱯᱨᱟᱭᱤᱢᱮᱡᱽ ᱨᱮᱱᱟᱜ ᱡᱮᱠᱳᱵᱤ ᱥᱤᱢᱵᱚᱞ ᱫᱚ ᱱᱚᱶᱟ ᱪᱤᱛᱟᱹᱨ ᱠᱷᱚᱱ ᱟᱞᱜᱟ ᱛᱮ ᱠᱚᱢᱯᱩᱴᱟᱨ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ: ᱑᱒᱑ 

ᱱᱚᱶᱟ ᱫᱚ ᱴᱷᱟᱹᱣᱠᱟᱹ ᱠᱟᱱᱟ ᱡᱮ ᱡᱩᱫᱤ ᱢᱤᱫᱼᱛᱮᱼ ᱢᱤᱫ ᱯᱷᱚᱱᱥᱚᱱ ᱨᱮ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱯᱮᱰᱤᱠᱮᱴ ᱢᱮᱱᱟᱜᱼᱟ ᱮᱱᱠᱷᱟᱱ ᱱᱚᱶᱟ ᱫᱚ ᱢᱤᱫ ᱞᱮᱠᱟᱛᱮ ᱦᱳᱭᱳᱜᱼᱟ ᱾  ᱳᱰᱰ ᱜᱳᱞᱰᱨᱟᱭᱤᱠ ᱟᱨ ᱞᱤᱭᱳᱱᱤᱰ ᱞᱮᱵᱷᱤᱱ (1989) ᱩᱫᱩᱜ ᱥᱚᱫᱚᱨ ᱞᱮᱫᱟᱭ ᱡᱮ , ᱪᱮᱫ ᱞᱮᱠᱟᱛᱮ ᱥᱟᱱᱟᱢ ᱢᱤᱫᱼᱥᱟᱠᱷᱟ ᱠᱟᱹᱢᱤ ᱫᱚ ᱢᱤᱫᱴᱟᱝ ᱢᱤᱫᱼᱥᱟᱥᱟᱠᱷᱟ ᱠᱟᱹᱢᱤ ᱧᱟᱢ ᱞᱟᱹᱜᱤᱫ ᱟᱹᱰᱤ ᱠᱚᱢ ᱞᱮᱠᱟᱛᱮ ᱵᱚᱱᱚᱫᱚᱞ ᱠᱚᱨᱟᱣ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ , ᱡᱟᱦᱟ ᱨᱮᱭᱟᱜ ᱢᱤᱫᱴᱟᱝ ᱜᱚᱴᱟᱵᱩᱴᱟᱹ ᱦᱚᱨᱰᱼᱠᱳᱨ ᱵᱨᱮᱰᱤᱠᱮᱴ ᱢᱮᱱᱟᱜᱼᱟ ᱾<ref name="GoldLevin">O. Goldreich and L.A. Levin, [http://citeseer.ist.psu.edu/viewdoc/download?doi=10.1.1.95.2079&rep=rep1&type=pdf A Hard-Core Predicate for all One-Way Functions], STOC 1989, pp25&#x2013;32.</ref>  ᱟᱭᱩᱢᱟᱹᱱ ᱟᱭᱢᱟᱜᱟᱱ ᱯᱷᱚᱱᱥᱚᱱ ᱦᱩᱭᱩᱜ ᱢᱮ ᱾ g (''x''′r′ = (f (x′R′) ᱡᱟᱦᱟᱸ ᱨᱮ r ᱨᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ x ᱨᱮᱭᱟᱜ ᱡᱮᱞᱮᱧ ᱞᱮᱠᱟ ᱾ ᱟᱭᱩᱢᱟᱹᱱ ''x''j , x ᱨᱮᱭᱟᱜ j ᱟᱱᱟᱜ ᱵᱤᱴ ''ᱟᱨ'' rj , r ᱨᱮᱭᱟᱜ j ᱟᱱᱟᱜ ᱵᱮᱴ ᱮ ᱩᱫᱩᱜᱟ ᱾ ᱚᱱᱟ ᱛᱟᱭᱚᱢ ᱾

<math> b(x,r) := \langle x, r\rangle = \bigoplus_j x_j r_j </math>

ᱱᱚᱶᱟ ᱫᱚ ' ᱜ ' ᱨᱮᱭᱟᱜ ᱢᱤᱫᱴᱟᱝ ᱦᱚᱨᱰ ᱠᱳᱨ ᱯᱮᱰᱤᱠᱮᱴ ᱾ ᱧᱮᱞ ᱢᱮ ᱡᱮ b (x′ r′ = < x′ rʼ) ᱡᱟᱦᱟᱸᱨᱮ < ′ ′ ·′ ᱵᱷᱮᱠᱴᱟᱨ ᱥᱯᱮᱥ (Z2′ n) ᱨᱮ ᱥᱟᱵᱟᱫ ᱟᱱ ᱤᱱᱟᱨ ᱯᱮᱠᱴᱚᱠ ᱮ ᱩᱫᱩᱜᱟ ᱾  ᱱᱚᱶᱟ ᱵᱨᱮᱰᱤᱠᱮᱴ ᱫᱚ ᱠᱚᱢᱯᱤᱭᱩᱴᱮᱥᱚᱱᱮᱞ ᱟᱱᱟᱴ ᱚᱡᱮᱛᱮ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱡᱟᱦᱟᱸ ᱫᱚ ᱱᱚᱶᱟ ᱞᱮᱠᱷᱟ ᱵᱟᱝ ᱟᱱᱟᱴ ᱚᱡᱮ ᱫᱚ ᱜ (x) ᱛᱚᱛᱛᱟᱹᱨᱤ ᱞᱮᱠᱟᱛᱮ ᱛᱚᱛᱛᱩᱛᱚ ᱾  ᱢᱮᱱᱠᱷᱟᱱ ᱡᱩᱫᱤ ᱱᱚᱶᱟ ᱵᱨᱮᱰᱤᱠᱮᱴ ᱫᱚ ᱠᱟᱹᱢᱤ ᱞᱮᱠᱟᱛᱮ ᱞᱮᱠᱷᱟ ᱞᱟᱹᱜᱤᱫ ᱡᱟᱦᱟᱱ ᱮᱞᱟᱨᱜᱟᱢ ᱢᱮᱱᱟᱜ ᱟ , ᱮᱱᱠᱷᱟᱱ ᱟᱨ ᱢᱤᱫᱴᱟᱝ ᱮᱞᱟᱨᱜᱟᱢ ᱢᱮᱱᱟᱜᱼᱟ ᱡᱟᱦᱟᱸ ᱫᱚ ᱠᱟᱹᱢᱤ ᱞᱮᱠᱟᱛᱮ ''ᱯᱷ'' ᱫᱚ ᱵᱮᱶᱦᱟᱨ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ ᱾

ᱢᱤᱫ ᱞᱮᱠᱟᱱ ᱵᱮᱱᱟᱣ ''ᱳ'' (log |x|′) ᱚᱯᱴᱩᱯᱩᱴ ᱵᱤᱴ ᱥᱟᱶᱛᱮ ᱢᱤᱫᱴᱟᱝ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱮ ᱵᱮᱱᱟᱣᱼᱟ ᱾ ᱢᱚᱱᱮ ᱦᱩᱭᱩᱜ ᱢᱮ , ''ᱯᱷ'' ᱢᱤᱫᱴᱟᱝ ᱫᱟᱲᱮ ᱟᱱ ᱢᱤᱫᱼᱥᱟᱠᱷᱟᱱᱟᱜ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱾ g (x′ r′ = (f (x′ ′ r′) ᱡᱟᱦᱟᱸ ᱨᱮ | r| = 2|x| ᱞᱟᱹᱭ ᱢᱮ ᱾ ᱢᱤᱫᱴᱟᱝ ᱡᱮᱞᱮᱧ ᱯᱷᱚᱱᱥᱚᱱ l (n′ = O (log n′ s. t. l (n′′ ≤ n) ᱵᱟᱪᱷᱱᱟᱣ ᱢᱮ ᱾ ᱢᱮ ᱾

<math> b_i(x, r) = \bigoplus_j x_j r_{i+j}. </math>

ᱚᱱᱟ ᱛᱟᱭᱚᱢ h (x′ r′:= b1 (x′r′ b2 (x′ R′... bl (|x|′ (x′R′)) ᱢᱤᱫᱴᱟᱝ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱡᱟᱦᱟᱸ ᱨᱮᱭᱟᱜ ᱚᱯᱴᱩᱯᱚᱴ ᱞᱟᱹᱞᱤᱥ l (|x1|′)᱾<ref>Goldreich's FoC, vol 1, Theorem 2.5.6.</ref>

ᱡᱟᱦᱟᱸ ᱚᱠᱛᱮ ᱨᱮ ᱤᱱᱯᱩᱛ ''x'' ᱨᱮᱭᱟᱜ ᱢᱤᱫᱴᱟᱝ ᱟᱥᱚᱞ ᱵᱤᱴ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱦᱳᱭᱳᱜᱼᱟ ᱾ ᱫᱟᱹᱭᱠᱟᱹ ᱞᱮᱠᱟᱛᱮ , ᱟᱨ ᱮᱥ ᱮ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱨᱮ ᱡᱚᱛᱚ ᱵᱤᱴ ᱤᱱᱯᱩᱴ ᱫᱚ ᱟᱨ ᱮᱥ ᱮ ᱨᱮᱭᱟᱜ ᱢᱤᱫᱴᱟᱝ ᱦᱟᱨᱰᱼᱠ''ᱳ''ᱨ ᱯᱮᱰᱤᱠᱮᱴ ᱟᱨ ᱳ (log |''x''. x) ᱼ ᱨᱮᱭᱟᱜ ᱵᱞᱳᱠᱠᱚ ᱯᱳᱞᱤᱱᱳᱢᱤᱭᱟᱞ ᱚᱠᱛᱚ ᱨᱮ ᱨᱮᱱᱰᱚᱢ ᱵᱤᱴ ᱥᱴᱨᱤᱝ ᱠᱷᱚᱱ ᱵᱷᱮᱜᱟᱨ ᱵᱟᱝ ᱦᱳᱭᱳᱜᱼᱟ ᱾<ref name="JohanNaslund">[[Johan Håstad|J. Håstad]], M. Naslund, [http://www.csc.kth.se/tcs/tfrutv99/rsabit.pdf The Security of all RSA and Discrete Log Bits (2004)]: Journal of the ACM, 2004.</ref>

ᱦᱚᱨᱰᱼᱠᱳᱨ ᱵᱨᱮᱰᱤᱠᱮᱴ ᱠᱚᱫᱚ ᱡᱟᱦᱟᱱ ᱢᱤᱫᱼᱥᱟᱠᱷᱟᱱᱟᱜ ᱯᱚᱨᱢᱩᱡᱚᱱ ᱠᱷᱚᱱ ᱢᱤᱫᱴᱟᱝ ᱥᱩᱰᱳᱨᱟᱱᱰᱚᱢ ᱡᱮᱱᱟᱴᱟᱨ ᱵᱮᱱᱟᱣ ᱨᱮᱭᱟᱜ ᱰᱟᱦᱟᱨ ᱠᱚ ᱮᱢᱼᱟ ᱾ ᱡᱚᱫᱤ ''ᱵᱤ'' ᱢᱤᱫᱼᱥᱟᱛᱚᱠ ᱯᱚᱨᱢᱩᱴᱤᱥᱚᱱ ᱯᱷᱼ ᱟᱨ ᱮᱥ ᱢᱤᱫᱴᱟᱝ ᱨᱮᱱᱰᱚᱢ ᱥᱤᱰᱼ ᱨᱮᱭᱟᱜ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱯᱮᱰᱤᱠᱮᱴ ᱦᱩᱭᱩᱜ ᱠᱷᱟᱱ ᱾

<math> \{ b(f^n(s))\}_n</math>

ᱫᱚ ᱢᱤᱫ ᱥᱩᱰᱳᱨᱟᱱᱰᱚᱢ ᱵᱤᱴ ᱥᱤᱠᱣᱮᱸᱥ ᱠᱟᱱᱟ, ᱡᱟᱦᱟᱸᱨᱮ fn ᱫᱚ s ᱨᱮ f ᱮᱯᱞᱤᱠᱮᱥᱚᱱ ᱨᱮᱱᱟᱜ n-th ᱤᱴᱮᱨᱮᱥᱚᱱ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ, ᱟᱨ b ᱫᱚ ᱡᱚᱛᱚ ᱨᱟᱣᱩᱱᱰ n ᱛᱮ ᱛᱮᱭᱟᱨ ᱟᱠᱟᱱ ᱦᱟᱨᱰ-ᱠᱚᱨ ᱵᱤᱴ ᱠᱟᱱᱟ: 132 

ᱴᱨᱮᱯᱰᱳᱨ ᱢᱤᱫᱼᱥᱟᱠᱷᱟᱱᱟᱜ ᱯᱚᱨᱢᱩᱴᱟᱵᱷᱚᱱ ᱨᱮᱭᱟᱜ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱵᱨᱮᱰᱤᱠᱮᱴ (ᱴᱨᱮᱯᱰᱩᱨ ᱵᱨᱮᱰᱤᱠᱤᱴ ᱧᱩᱛᱩᱢ ᱛᱮ ᱩᱯᱨᱩᱢ) ᱥᱮᱢᱮᱱᱴᱤᱠ ᱞᱮᱠᱟᱛᱮ ᱨᱩᱠᱷᱤᱭᱟᱹᱣᱟᱱ ᱦᱚᱲᱼᱠᱤ ᱮᱱᱠᱨᱤᱯᱥᱚᱱ ᱥᱤᱠᱤᱢ ᱵᱮᱱᱟᱣ ᱞᱟᱹᱜᱤᱫ ᱵᱮᱣᱦᱟᱨ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ ᱾ 

== ᱱᱚᱶᱟ ᱦᱚᱸ ᱧᱮᱞ ᱢᱮ ==

* ᱛᱟᱹᱞᱤᱠᱟᱼᱰᱤᱠᱳᱰᱤᱝ (ᱵᱤᱪᱷᱚᱱᱟ ᱛᱟᱹᱞᱤᱠᱟ ᱰᱤᱠᱳᱰᱤᱝ) ᱜᱳᱞᱰᱨᱤᱪᱼᱞᱤᱵᱷᱤᱱ ᱨᱮᱭᱟᱜ ᱢᱩᱲᱩᱫ ᱦᱤᱸᱥ ᱢᱤᱫ ᱥᱮᱫ ᱠᱷᱚᱱ ᱯᱷᱟᱝᱠᱥᱚᱱ ᱠᱷᱚᱱ ᱦᱟᱨᱰᱼᱠᱳᱨ ᱵᱨᱮᱰᱤᱠᱮᱴ ᱵᱮᱱᱟᱣ ᱞᱟᱹᱜᱤᱫ ᱦᱟᱰᱟᱢᱟᱨᱰ ᱠᱳᱰ ᱨᱮᱭᱟᱜ ᱛᱟᱹᱞᱤᱠᱟ ᱼᱰᱤᱠᱳᱰᱤᱝ ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫᱴᱟᱝ ᱮᱞᱟᱨᱜᱟᱢ ᱞᱮᱠᱟᱛᱮ ᱧᱮᱞ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ ᱾

== ᱥᱟᱹᱠᱷᱭᱟᱹᱛ ==
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[[ᱛᱷᱚᱠ:ᱛᱷᱭᱳᱨᱤ ᱚᱯᱷ ᱠᱨᱭᱴᱚᱜᱽᱨᱟᱯᱷᱤ]]
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