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  1. ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ❍é❧è♥❡ ▲❡ ❇♦✉❞❡r ✱ ❚❤✐❡r♥♦ ❇❛rr②✱ ❉❛♠✐❡♥ ❈♦✉r♦✉ssé✱ ❏❡❛♥✲▲♦✉✐s ▲❛♥❡t ❛♥❞ ❘♦♥❛♥ ▲❛s❤❡r♠❡s ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✶✴✷✸

  2. ❙✐❞❡ ❈❤❛♥♥❡❧ ❆♥❛❧②s✐s ✭❙❈❆✮ ❙❈❆ ❝♦♥s✐sts ✐♥ ♦❜s❡r✈✐♥❣ s♦♠❡ ♣❤②s✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ✇❤✐❝❤ ❛r❡ ♠♦❞✐✜❡❞ ❞✉r✐♥❣ t❤❡ ❝♦♠♣✉t❛t✐♦♥ ♣❡r❢♦r♠❡❞ ♦♥ t❤❡ ❝✐r❝✉✐t✳ ▼♦st ❝❧❛ss✐❝ ❧❡❛❦❛❣❡s ❛r❡✿ t✐♠✐♥❣✱ ♣♦✇❡r ❝♦♥s✉♠♣t✐♦♥✱ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ❡♠✐ss✐♦♥s ✭❊▼✮ ✳✳✳ ❚❤❡ ♠❛✐♥ ❞✐✣❝✉❧t② ♦❢ t❤❡ ❛tt❛❝❦ ✐s t♦ s✉❝❝❡❡❞ ✇✐t❤ ✈❡r② ❢❡✇ tr❛❝❡s✳ ❚❡♠♣❧❛t❡ ❛tt❛❝❦ ✐s ❛ ❦✐♥❞ ♦❢ ❙❈❆✱ ❜❛s❡❞ ♦♥ ❝❤❛r❛❝t❡r✐③❛t✐♦♥✳ ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ P❡rs♦♥❛❧ ■❞❡♥t✐✜❝❛t✐♦♥ ◆✉♠❜❡r ✭P■◆✮ ❝♦❞❡s✳ ❯s❡❞ t♦ ❛✉t❤❡♥t✐❝❛t❡ t❤❡ ✉s❡r✱ ✐♥ ♣❛②♠❡♥t ❝❛r❞s ♦r ❙■▼ ❝❛r❞s✳✳✳ ❚❛r❣❡ts ♦❢ ❝❤♦✐❝❡ ❢♦r ♠❛❧✐❝✐♦✉s ❛❞✈❡rs❛r✐❡s✳ ❆ ❧✐♠✐t❡❞ ♥✉♠❜❡r ♦❢ tr✐❛❧s✳ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✷✴✷✸

  3. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ P❡rs♦♥❛❧ ■❞❡♥t✐✜❝❛t✐♦♥ ◆✉♠❜❡r ✭P■◆✮ ❝♦❞❡s✳ ❯s❡❞ t♦ ❛✉t❤❡♥t✐❝❛t❡ t❤❡ ✉s❡r✱ ✐♥ ♣❛②♠❡♥t ❝❛r❞s ♦r ❙■▼ ❝❛r❞s✳✳✳ ❚❛r❣❡ts ♦❢ ❝❤♦✐❝❡ ❢♦r ♠❛❧✐❝✐♦✉s ❛❞✈❡rs❛r✐❡s✳ ❆ ❧✐♠✐t❡❞ ♥✉♠❜❡r ♦❢ tr✐❛❧s✳ ❙✐❞❡ ❈❤❛♥♥❡❧ ❆♥❛❧②s✐s ✭❙❈❆✮ ❙❈❆ ❝♦♥s✐sts ✐♥ ♦❜s❡r✈✐♥❣ s♦♠❡ ♣❤②s✐❝❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ✇❤✐❝❤ ❛r❡ ♠♦❞✐✜❡❞ ❞✉r✐♥❣ t❤❡ ❝♦♠♣✉t❛t✐♦♥ ♣❡r❢♦r♠❡❞ ♦♥ t❤❡ ❝✐r❝✉✐t✳ ▼♦st ❝❧❛ss✐❝ ❧❡❛❦❛❣❡s ❛r❡✿ t✐♠✐♥❣✱ ♣♦✇❡r ❝♦♥s✉♠♣t✐♦♥✱ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ❡♠✐ss✐♦♥s ✭❊▼✮ ✳✳✳ ❚❤❡ ♠❛✐♥ ❞✐✣❝✉❧t② ♦❢ t❤❡ ❛tt❛❝❦ ✐s t♦ s✉❝❝❡❡❞ ✇✐t❤ ✈❡r② ❢❡✇ tr❛❝❡s✳ ❚❡♠♣❧❛t❡ ❛tt❛❝❦ ✐s ❛ ❦✐♥❞ ♦❢ ❙❈❆✱ ❜❛s❡❞ ♦♥ ❝❤❛r❛❝t❡r✐③❛t✐♦♥✳ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✷✴✷✸

  4. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ✷ ❆tt❛❝❦ ✸ Pr♦✜❧✐♥❣ ♣❤❛s❡ ❆tt❛❝❦ ♣❤❛s❡ ❘❡s✉❧ts ✹ ❚❡st ❜❡♥❝❤ ●❡♥❡r❛❧ r❡s✉❧ts ❋✐♥❛❧ ❛tt❛❝❦ ❈♦♥❝❧✉s✐♦♥ ✺ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✸✴✷✸

  5. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ✷ ❆tt❛❝❦ ✸ Pr♦✜❧✐♥❣ ♣❤❛s❡ ❆tt❛❝❦ ♣❤❛s❡ ❘❡s✉❧ts ✹ ❚❡st ❜❡♥❝❤ ●❡♥❡r❛❧ r❡s✉❧ts ❋✐♥❛❧ ❛tt❛❝❦ ❈♦♥❝❧✉s✐♦♥ ✺ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✹✴✷✸

  6. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ 1: procedure V ERIFY PIN(candidate PIN V ) counter = counter − 1 2: P■◆ ❝♦❞❡ ✐s ❛♥ ❛rr❛② ♦❢ ♠ if counter > 0 then 3: ❜②t❡s✳ status = C OMPARISON ( U , V ) 4: status 2 = C OMPARISON ( U , V ) 5: ❚r✉❡ P■◆ ✿ ❯ ✱ if status � = status 2 then 6: ERROR, device is blocked 7: ❈❛♥❞✐❞❛t❡ P■◆ ✿ ❱ ✱ else 8: if status = TRUE then ] ♠ ✳ 9: ❯ ∈ [ [ ✵ , ✾ ] counter initialized at original value. 10: ✶✵ ♠ ❞✐✛❡r❡♥t P■◆ ❝♦❞❡s✳ end if 11: end if 12: ❈♦✉♥t❡r♠❡❛s✉r❡ ❛❣❛✐♥st else 13: ❢❛✉❧t ❛tt❛❝❦✿ ❝♦♠♣❛r❡ ❯ device is blocked 14: end if 15: ❛♥❞ ❱ t✇✐❝❡✳ return status 16: 17: end procedure ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✺✴✷✸

  7. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ ❈♦♠♣❛r✐s♦♥ ♦❢ t✇♦ P■◆ ❝♦❞❡s 1: procedure C OMPARISON (candidate PIN V , true PIN U ) status = FALSE 2: diff = FALSE 3: fake = FALSE 4: for b = 0 to m do 5: if U b � = V b then 6: diff = TRUE 7: else 8: fake = TRUE 9: end if 10: if ( b = m ) and ( diff = FALSE ) then 11: status = TRUE 12: else 13: fake = TRUE 14: end if 15: end for 16: return status 17: 18: end procedure ❈♦✉♥t❡r♠❡❛s✉r❡ ❛❣❛✐♥st t✐♠✐♥❣ ❛tt❛❝❦✿ ❝♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ ❯ ❛♥❞ ❱ ❤❛s t♦ ❜❡ ✐♥ ❛ ❝♦♥st❛♥t t✐♠❡✳ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✻✴✷✸

  8. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ ■♥tr♦❞✉❝t✐♦♥ ✶ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ✷ ❆tt❛❝❦ ✸ Pr♦✜❧✐♥❣ ♣❤❛s❡ ❆tt❛❝❦ ♣❤❛s❡ ❘❡s✉❧ts ✹ ❚❡st ❜❡♥❝❤ ●❡♥❡r❛❧ r❡s✉❧ts ❋✐♥❛❧ ❛tt❛❝❦ ❈♦♥❝❧✉s✐♦♥ ✺ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✼✴✷✸

  9. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ✷ ♣❤❛s❡s ✶ ♣r♦✜❧✐♥❣ ♣❤❛s❡✱ ✷ ❛tt❛❝❦ ♣❤❛s❡✳ ❚❤❡ ❛tt❛❝❦❡r ❝❛♥ ✿ ♦❜t❛✐♥ ♦♥❡ tr❛❝❡ ♦♥ t❤❡ t❛r❣❡t❡❞ ❞❡✈✐❝❡❀ ❝❤❛♥❣❡ t❤❡ ❚r✉❡ P■◆ ✐♥ ❤❡r ♣r♦✜❧✐♥❣ ❞❡✈✐❝❡❀ ♦❜t❛✐♥ ♠❛♥② tr❛❝❡s ♦♥ ❤❡r ♣r♦✜❧✐♥❣ ❞❡✈✐❝❡✳ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✽✴✷✸

  10. ■♥tr♦❞✉❝t✐♦♥ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ❆tt❛❝❦ ❘❡s✉❧ts ❈♦♥❝❧✉s✐♦♥ Pr♦✜❧✐♥❣ ♣❤❛s❡ ■♥tr♦❞✉❝t✐♦♥ ✶ ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠ ✷ ❆tt❛❝❦ ✸ Pr♦✜❧✐♥❣ ♣❤❛s❡ ❆tt❛❝❦ ♣❤❛s❡ ❘❡s✉❧ts ✹ ❚❡st ❜❡♥❝❤ ●❡♥❡r❛❧ r❡s✉❧ts ❋✐♥❛❧ ❛tt❛❝❦ ❈♦♥❝❧✉s✐♦♥ ✺ ❆ t❡♠♣❧❛t❡ ❛tt❛❝❦ ❛❣❛✐♥st ❱❡r✐❢② P■◆ ❛❧❣♦r✐t❤♠s ▲❡ ❇♦✉❞❡r ❡t ❛❧✳ ✾✴✷✸

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