❋❆❈❯▲❉❆❉❊ ❉❊ ❊◆●❊◆❍❆❘■❆ ▼❊❙❚❘❆❉❖ ❊▼ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆
P❘❖❈❊❙❙❆▼❊◆❚❖ ❉❊ ❙■◆❆■❙ ❊ ❊◆●❊◆❍❆❘■❆ ❇■❖▼➱❉■❈❆ ❈❆❘▲❖❙ ❍❊◆❘■◗❯❊ ❉❆ ❈❖❙❚❆ ❈❆◆❖
❚➱❈◆■❈❆ ❉❊ ❈❘■P❚❖●❘❆❋■❆ ❈❖▼ ❉❆❉❖❙ ●❊❖❉➱❙■❈❖❙
❈❆❘▲❖❙ ❍❊◆❘■◗❯❊ ❉❆ ❈❖❙❚❆ ❈❆◆❖
❚➱❈◆■❈❆ ❉❊ ❈❘■P❚❖●❘❆❋■❆ ❈❖▼ ❉❆❉❖❙ ●❊❖❉➱❙■❈❖❙
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡✱ ♣❡❧♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❞❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❞❛ P♦♥t✐❢í❝✐❛ ❯♥✐✈❡rs✐❞❛❞❡ ❈❛tó❧✐❝❛ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ❙✉❧✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❘✉❜❡♠ ❉✉tr❛ ❘✐❜❡✐r♦ ❋❛❣✉♥❞❡s
❆❣r❛❞❡❝✐♠❡♥t♦s
❆♦ ❖r✐❡♥t❛❞♦r Pr♦❢❡ss♦r ❉r✳ ❘✉❜❡♠ ❉✉tr❛ ❘✐❜❡✐r♦ ❋❛❣✉♥❞❡s ♣❡❧❛ ♦♣♦r✲ t✉♥✐❞❛❞❡ ❞❡ s❡r s❡✉ ♦r✐❡♥t❛♥❞♦ ❞✉r❛♥t❡ ♦ ♠❡str❛❞♦ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r s✉❛ ♠♦t✐✈❛çã♦✱ ❞❡❞✐❝❛çã♦ ❡ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ q✉❡ ♣♦ss✐❜✐❧✐t❛r❛♠ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦ ❝♦r♣♦ ❞❡ ♣r♦❢❡ss♦r❡s ❞♦ ▼❡str❛❞♦ ❞❛ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❞❛ P❯❈❘❙ ❛♦ q✉❛❧ ♠❡ ❞❡r❛♠ ❢❡rr❛♠❡♥t❛s ❡ ❝♦♥❤❡❝✐♠❡♥t♦s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦s ♠❡✉s ❝♦❧❡❣❛s ▲✉ís ❱✐tór✐♦ ❈❛r❣♥✐♥✐ ❡ ❉✐♦❣♦ ❙❝♦❧❛r✐ ♣♦r s✉❛s s✉❣❡stõ❡s ❞❛❞❛s ❛♦ ❛♣r✐♠♦r❛♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ♣r♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❞❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊♥❣❡♥✲ ❤❛r✐❛ ❊❧étr✐❝❛✱ ❡♠ ❡s♣❡❝✐❛❧ ♣❛r❛ ❛s ❝♦❧❡❣❛s ■♥❡❧✈❡ ❈♦❧♦❣♥❡s❡ ❡ ▼❛r✐❛ ❍❡❧❡♥❛ ▼❛❝✐❡❧ ❞❡ ❆❧♠❡✐❞❛ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ❞❡❞✐❝❛çã♦✳
❆ ♠✐♥❤❛ ❢❛♠í❧✐❛ ❡ ❛ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ q✉❡ ❝♦♠♣r❡❡♥❞❡r❛♠ ♠✐♥❤❛ ❛✉sê♥❝✐❛ ❡ ♠✐♥❤❛ ❞❡❞✐❝❛çã♦ ❛ ❡st❡ tr❛❜❛❧❤♦✳
❘❡s✉♠♦
❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❛ ❞✐ss❡rt❛çã♦ é ♠♦str❛r ❛ ❝r✐❛çã♦ ❡ ❛ ✐♠✲ ♣❧❡♠❡♥t❛çã♦ ❞❡ ✉♠❛ s♦❧✉çã♦ ❝♦♠♣♦st❛ ♣♦r ❝♦♠♣♦♥❡♥t❡s ❞❡ ♥❛✈❡❣❛çã♦ ❡ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❛t✉❛♥❞♦ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ♠ó❞✉❧♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❡ s♦❢t✇❛r❡s ❛❞✐❝✐♦♥❛✐s✳
❊st❛ ❡①t❡♥sã♦ s❡rá ❛tr❛✈és ❞❛ ✉t✐❧✐③❛çã♦ ❞♦ s✐st❡♠❛ ●❧♦❜❛❧ P♦s✐✲ t✐♦♥✐♥❣ ❙②st❡♠ ✭●P❙✮✱ q✉❡ é ✉♠ s✐st❡♠❛ ❞❡s❡♥✈♦❧✈✐❞♦ ✐♥✐❝✐❛❧♠❡♥t❡ ♣❛r❛ ✉s♦ ♠✐❧✐t❛r ❛♦ q✉❛❧ ♣r♦✈❡ ✐♥❢♦r♠❛çõ❡s ❝❛rt♦❣rá✜❝❛s ❢✉♥❞❛♠❡♥t❛✐s ❝♦♠♦✿ ❝♦♦r❞❡♥❛❞❛s ❣❡♦❣rá✜❝❛s✱ ✈❡❧♦❝✐❞❛❞❡✱ ❛❧t✉r❛✱ ❤♦r❛✳
❋♦r❛♠ ❡st✉❞❛❞♦s ❛❧❣♦rít✐♠♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ s✐♠étr✐❝♦s ❡ ❛ss✐♠étr✐✲ ❝♦s ❡ ❛❧é♠ ❞✐ss♦ ❢♦✐ r❡❛❧✐③❛❞❛ ✉♠❛ ❞❡s❝r✐çã♦ ❞❡t❛❧❤❛❞❛ ❞♦ s✐st❡♠❛ ●P❙ q✉❡ ❢✉♥❞❛♠❡♥t♦✉ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✳ ◆❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ❡s❝♦❧❤✐❞♦ ♦ ♣❛❞rã♦ ❆❊❙✱ ❛♦ q✉❛❧ é ❞❡ ❞♦♠í♥✐♦ ♣ú❜❧✐❝♦✱ s❡♠ r♦②❛❧t✐❡s ❡ ❢♦✐ ❡s❝♦❧✲ ❤✐❞♦ ♥✉♠ ♣r♦❝❡ss♦ ♣✉❜❧✐❝♦ ❡ r✐❣♦r♦s♦ ♣❡❧♦ ◆■❙❚ ❝♦♠♦ ♣❛❞rã♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛✳
P❛r❛ ✈❛❧✐❞❛çã♦ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ✉t✐❧✐③♦✉✲s❡ ✉♠ ❡q✉✐♣❛♠❡♥t♦ r❡❛❧ ❞❡ ●P❙✱ ❝♦♠ ♦ q✉❛❧ ❢♦r❛♠ r❡❛❧✐③❛❞♦s t❡st❡s ❞❡ ❝❛♠♣♦✳ ◆❡st❡s t❡st❡s ❢♦✐ ❞❡t❡r♠✐♥❛❞❛ ❛ ♣r❡❝✐sã♦ ❡❢❡t✐✈❛ ❞❡st❡s ❡q✉✐♣❛♠❡♥t♦s ❜❡♠ ❝♦♠♦ ❛ ✈❛❧✐❞❛çã♦ ❞❛ ♣r♦♣♦st❛ ❡♠ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ❝❛♠♣♦✳
❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❞❡♠♦♥str❛r❛♠ q✉❡ ❛ té❝♥✐❝❛ ❞❡ ✉t✐❧✐③❛çã♦ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❣❡♦❞és✐❝❛s ❣❧♦❜❛✐s ❞❡ ●P❙ ❜❡♠ ❝♦♠♦ ❛s ❝♦♦r❞❡♥❛❞❛s ❝❛r✲ t♦❣rá✜❝❛s ❝♦♠✉♥s sã♦ ❡✜❝✐❡♥t❡s ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ♣r♦♣♦st♦✳ ❈r✐❛♥❞♦ ❞❡st❛ ❢♦r♠❛ ✉♠ ♥♦✈♦ ♠♦❞❡❧♦ ❞❡ ❝r✐♣t♦❣r❛✜❛✳
❆❜str❛❝t
❚❤❡ ♠❛✐♥ ♦❜❥❡❝t✐✈❡ ♦♥ t❤✐s t❤❡s✐s ✐s t♦ s❤♦✇ t❤❡ ❝r❡❛t✐♦♥ ❛♥❞ ✐♠✲ ♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❛ s♦❧✉t✐♦♥ ❝♦♠♣♦s❡❞ ❜② ♥❛✈✐❣❛t✐♦♥❛❧✱ ♣♦s✐t✐♦♥❛❧ ❝♦♠✲ ♣♦♥❡♥ts ❛❝t✐♥❣ t♦❣❡t❤❡r ✇✐t❤ ❝r②♣t♦❣r❛♣❤② ♠♦❞✉❧❡s ❛♥❞ s♦❢t✇❛r❡✳
❚❤✐s ✐♠♣❧❡♠❡♥t❛t✐♦♥ ✇✐❧❧ ✉s❡ t❤❡ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠ ✭●P❙✮✱ t❤❛t ✐♥ ✐ts ❜❡❣✐♥♥✐♥❣ ✇❛s ✉s❡❞ ♠❛✐♥❧② ❢♦r ♠✐❧✐t❛r② ♦❜❥❡❝t✐✈❡s✱ t❤✐s s②s✲ t❡♠ ♣r♦✈✐❞❡ ❣❡♦❣r❛♣❤✐❝✱ ❝❛rt♦❣r❛♣❤✐❝ ❛♥❞ ❣❡♦❞❡s✐❝ ✐♥❢♦r♠❛t✐♦♥ ❛s✿ ❧❛t✲ ✐t✉❞❡✱ ❧♦♥❣✐t✉❞❡✱ ✈❡❧♦❝✐t②✱ t✐♠❡ ❛♥❞ ❤❡✐❣❤t✳
❙♦♠❡ ❡♥❝r②♣t✐♦♥ ❛❧❣♦r✐t❤♠s ♠♦❞❡ ❛s ❛s②♠♠❡tr✐❝ ❛♥❞ s②♠♠❡tr✐❝ ✇❡r❡ st✉❞✐❡❞✱ ❛❧s♦ t❤❡ ●P❙ s②st❡♠ ❛♥❞ ✐ts ✈❛r✐❛❜❧❡s t♦ ❜❡tt❡r ❞❡s❝r✐❜❡ t❤✐s ✇♦r❦✳ ■♥ t❤✐s ♣r♦♣♦s❛❧ ✇❛s ✉s❡❞ t❤❡ ❆❊❙ ✭❘✐❥♥❞❛❡❧✮ ❡♥❝r②♣t✐♦♥ ❢♦r ✐ts s❡❝✉r✐t② ❛♥❞ ❞❡s❡♠♣❡♥❤♦ ❝❡rt✐✜❡❞ ❜② t❤❡ ◆■❙❚ ❞❡♣❛rt♠❡♥t✳
❚♦ ✈❛❧✐❞❛t❡ t❤✐s ✇♦r❦ ❛ ●P❙ r❡❝❡✐✈❡r ✇❛s ✉s❡❞ t♦ ♠❛❦❡ ✜❡❧❞ t❡sts t♦ ❝❤❡❝❦ t❤❡ ♣r❡❝✐s✐♦♥ ❛♥❞ ❛❝❝✉r❛❝② ♦❢ t❤❡ r❡❝❡✐✈❡r ❛♥❞ t❤✐s ♣r♦♣♦s❛❧✳ ❚❤❡ ♦❜t❛✐♥❡❞ r❡s✉❧ts s❤♦✇ t❤❛t t❤✐s ♣r♦♣♦s❛❧ t❤❛t ✉s❡s ❣❡♦❞❡s✐❝ ❝♦♦r❞✐♥❛t❡s ❛♥❞ ❝r②♣t♦❣r❛♣❤② ❛♥❞ ❝❛rt♦❣r❛♣❤② ❝♦♦r❞✐♥❛t❡s t♦♦ ❛r❡ ❡✣❝✐❡♥t ✐♥ t❤✐s ❝r②♣t♦❣r❛♣❤✐❝ s②st❡♠ ♣r♦♣♦s❡❞✳ ❆s ✐♥ t❤✐s ♣r♦♣♦s❛❧ t❤❡ ❞❛t❛ tr❛♥s♠✐tt❡❞ ❤❛s ♠♦r❡ s❡❝✉r✐t② ❜❡❝❛✉s❡ t❤❡② ♦♥❧② ❝❛♥ ❜❡ ❞❡❝♦❞❡❞ ✐♥ t❤❡ r✐❣❤t ❝♦♦r❞✐♥❛t❡s ♦r ❣❡♦❞❡s✐❝ ✈❛r✐❛❜❧❡s✱ t❤❛t t❤❡ tr❛♥s♠✐tt❡r s❡t ✉♣✳
❈♦♥t❡ú❞♦
✶ ■♥tr♦❞✉çã♦ ✶✶
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✷ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✶✹
✷✳✶ ❈❛♠♣♦s ❋✐♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✶✳✶ ❆❞✐çã♦ ❞❡ ❈❛♠♣♦s ❋✐♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✶✳✷ ▼✉❧t✐♣❧✐❝❛çã♦ ❞❡ ❈❛♠♣♦s ❋✐♥✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✶✳✸ ▼✉❧t✐♣❧✐❝❛çã♦ ♣♦r x ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷✳✶✳✹ P♦❧✐♥ô♠✐♦s ❝♦♠ ❈♦❡✜❝✐❡♥t❡s ❡♠ GF(28) ✳ ✳ ✳ ✳ ✶✽
✷✳✷ ❈r✐♣t♦❣r❛✜❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✷✳✶ ❍✐stór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✷✳✷ ❙✐st❡♠❛s ❆ss✐♠étr✐❝♦s ❡ ❙✐♠étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✷✳✸ ❙✐st❡♠❛ ❞❡ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❈❤❛✈❡s Pú❜❧✐❝❛s ❡
Pr✐✈❛❞❛s ✭❘❙❆✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✷✳✹ ❆t❛q✉❡s ♥❛ ❈r✐♣t♦❣r❛✜❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷✳✺ ❆✈❛❧✐❛çã♦ ❞❛ ❙❡❣✉r❛♥ç❛ ❞❡ ❙✐st❡♠❛s ❈r✐♣t♦❣rá✜❝♦s ✷✻ ✷✳✷✳✻ Pr♦❝❡ss♦ ❞❡ ❡s❝♦❧❤❛ P❛❞rã♦ ❆❊❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✷✳✼ ❆❧❣♦r✐t♠♦ ❆❊❙✭❘✐❥♥❞❛❡❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✸ ❉❛❞♦s ●❡♦❞és✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✸✳✶ ❙✐st❡♠❛s ❞❡ ❈♦♦r❞❡♥❛❞❛s ●❡♦❞és✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✸✳✷ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ●❡♦❣rá✜❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✸✳✸ ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷✳✸✳✹ ❚✐♣♦s ❞❡ ❙✐st❡♠❛s ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✳✸✳✺ ❈♦♠♣♦s✐çã♦ ❞♦ s✐st❡♠❛ ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✳✸✳✻ ❉❡s❝r✐çã♦ ❞♦s ❙✐♥❛✐s ❞♦ ❙✐st❡♠❛ ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✸✳✼ ▼❡❞✐çã♦ ❡ ❊q✉❛çõ❡s ❞❡ ❈♦♦r❞❡♥❛❞❛s ❛tr❛✈és ❞❡
●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✸✳✽ ●❡ó✐❞❡ ❲●❙✲✽✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✷✳✸✳✾ ❊rr♦s ❞♦ s✐st❡♠❛ ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✸ Pr♦♣♦st❛ ✺✸
✹ ▼❡t♦❞♦❧♦❣✐❛ ✺✽ ✹✳✶ P❧❛t❛❢♦r♠❛ ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✶✳✶ ❙✐st❡♠❛ ❘❡❝❡♣t♦r ❞❡ ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✷ ❋❛s❡s ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷✳✶ ❋❛s❡ ❞❡ ▼♦❞❡❧❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✷✳✷ ❋❛s❡ ❞❡ Pr♦t♦t✐♣❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✷✳✸ ❋❛s❡ ❞❡ ❚❡st❡ ❞❡ ❈❛♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸ ❉❡s❝r✐çã♦ ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸✳✶ ❈♦♠♣♦♥❡♥t❡s ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✸✳✷ ❚r❛♥s♠✐ssã♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✸✳✸ ❘❡❝❡♣t♦r ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✸✳✹ Pr♦t♦❝♦❧♦ ❞❡ ❈♦♠✉♥✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸✳✺ ■♥✐❝✐❛❧✐③❛çã♦ ❞♦ Pr♦t♦❝♦❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸✳✻ ❙❡ssã♦ ❞❡ ❈♦♥✜❣✉r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✸✳✼ ❚r❛♥s♠✐ssã♦ ❞♦s ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✸✳✽ ❘❡❝❡♣çã♦ ❞♦s ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✸✳✾ ▼❛♥✉t❡♥çã♦ ❡ ❋✐♥❛❧✐③❛çã♦ ❞❡ ❙❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽
✺ ❘❡s✉❧t❛❞♦s ✻✾
✺✳✶ Pr❡❝✐sã♦ ❞♦ ❘❡❝❡♣t♦r ●P❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✶✳✶ Pr❡❝✐sã♦ ❞♦ r❡❝❡♣t♦r ●P❙ ❢r❡♥t❡ ❛ ❝♦♦r❞❡♥❛❞❛s
❝❛rt♦❣rá✜❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✺✳✷ ❚❡st❡s ❞❡ tr❛♥s♠✐ssã♦ ❞❡ ❞❛❞♦s ❝r✐♣t♦❣r❛❢❛❞♦s ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✸ ❘❡s✉❧t❛❞♦ ❞❡ ❚r❛♥s♠✐ssã♦ ❡ ❉❡❝♦❞✐✜❝❛çã♦ ❈♦♠ ▲♦❝❛❧✲
✐③❛çã♦ ❋✐①❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✹ ❘❡s✉❧t❛❞♦ ❉❡ ❚r❛♥s♠✐ssã♦ ❊ ❉❡❝♦❞✐✜❝❛çã♦ ❈♦♠ ▲♦❝❛❧✲
✐③❛çã♦ ❊♠ ❯♠❛ ➪r❡❛ ❉❡❧✐♠✐t❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✺ ❘❡s✉❧t❛❞♦ ❞❡ ❚r❛♥s♠✐ssã♦ ❡ ❉❡❝♦❞✐✜❝❛çã♦ ◆✉♠❛ ❆❧t✉r❛
❉❡t❡r♠✐♥❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✻ ❈♦♥❝❧✉sã♦ ✼✻
✻✳✶ Pr♦♣♦s✐çõ❡s ❞❡ ❊st✉❞♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
▲✐st❛ ❞❡ ❋✐❣✉r❛s
❆❝rô♥✐♠♦s
❆❊❙ ❆❞✈❛♥❝❡❞ ❊♥❝r✐♣t✐♦♥ ❙t❛♥❞❛r❞
❆P■ ❆♣♣❧✐❝❛t✐♦♥ ♣r♦❣r❛♠♠✐♥❣ ✐♥t❡r❢❛❝❡
❆❙ ❆♥t✐✲❙♣♦♦✜♥❣
❉❊❙ ❉❛t❛ ❊♥❝r②♣t✐♦♥ ❙t❛♥❞❛r❞
❉❱❉ ❞✐❣✐t❛❧ ✈❡rs❛t✐❧❡ ❞✐s❝
❊❈❈ ❊❧❧✐♣t✐❝ ❈✉r✈❡ ❈r②♣t♦❣r❛♣❤②
●❋ ●❛❧♦✐s ❋✐❡❧❞
●❍❩ ●✐❣❛ ❍❡rt③
●P❙ ●❧♦❜❛❧ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠
❍❚▼▲ ❍②♣❡r❚❡①t ▼❛r❦✉♣ ▲❛♥❣✉❛❣❡
■❇●❊ ■♥st✐t✉t♦ ❇r❛s✐❧❡✐r♦ ❞❡ ●❡♦❣r❛✜❛ ❡ ❊st❛tíst✐❝❛
◆❉ ◆ã♦ ❉✐s♣♦♥í✈❡❧
◆■❙❚ ◆❛t✐♦♥❛❧ ■♥st✐t✉t❡ ♦❢ ❙t❛♥❞❛r❞s ❛♥❞ ❚❡❝❤♥♦❧♦❣②
◆▼❊❆ ◆❛t✐♦♥❛❧ ▼❛r✐♥❡ ❊❧❡❝tr♦♥✐❝s ❆ss♦❝✐❛t✐♦♥
P❑■ P✉❜❧✐❝ ❑❡② ■♥❢r❛str✉❝t✉r❡
PP❙ Pr❡❝✐s❡ P♦s✐t✐♦♥✐♥❣ ❙❡r✈✐❝❡
❘❆▼ ❘❛♥❞♦♠ ❆❝❝❡ss ▼❡♠♦r②
❙P❙ ❙t❛♥❞❛r❞ P♦s✐t✐♦♥✐♥❣ ❙②st❡♠
✶ ■♥tr♦❞✉çã♦
❆ s♦❝✐❡❞❛❞❡ ❤✉♠❛♥❛ t❡♠ ❞❡♠♦♥str❛❞♦ ♥♦s ú❧t✐♠♦s t❡♠♣♦s ✉♠❛ ❝r❡s❝❡♥t❡ ❛❝❡❧❡r❛çã♦ ❡ ❛✈❛♥ç♦s ♥♦s s❡✉s ♠❛✐s ❞✐✈❡rs♦s ❝❛♠♣♦s ❞❡ ❝✐ê♥❝✐❛✳ ❉❡s❞❡ ♦ ❛❞✈❡♥t♦ ❞❛ ❡❧❡tr✐❝✐❞❛❞❡✱ ❞♦ t❡❧é❣r❛❢♦ ❡ ❞♦s ❝♦♠♣✉t❛❞♦r❡s✳ ◆ã♦ s❡ ♣❛ss♦✉ ♠❛✐s ❞❡ ✉♠ sé❝✉❧♦ ♣❛r❛ ✐ss♦✳ ❖ ♣r♦❣r❡ss♦ s❡ ❛♣r❡s❡♥t❛ ❞❡ ❢♦r♠❛ ❝❛❞❛ ✈❡③ ♠❛✐s rá♣✐❞❛ ❡ ❝♦♠♣❧❡①❛ ❡♠ ❝♦♥s❡qüê♥❝✐❛ ❞❡st❡s ❛✈❛♥ç♦s✳
❉❛s ♥❡❝❡ss✐❞❛❞❡s ♠✐❧✐t❛r❡s ♣❛r❛ ❝á❧❝✉❧♦s ❞❡ ❛rt✐❧❤❛r✐❛ ❡ ❞❡ ♦✉tr❛s ❢♦r✲ ♠❛s ❞❡ s✐♠✉❧❛çã♦✱ ♦s ❝♦♠♣✉t❛❞♦r❡s ♣r♦❣r❡❞✐r❛♠ ❡♥♦r♠❡♠❡♥t❡✱ ♥♦✈❛s ♥❡❝❡s✲ s✐❞❛❞❡s ❡ ✉s♦s ❢♦r❛♠ ❝r✐❛❞♦s ♥✉♠❛ ❡s❝❛❧❛❞❛ ❝❛❞❛ ✈❡③ ♠❛✐♦r ❡ ❝♦♠♣❧❡①❛✳
❉❡♥tr♦ ❞❡st❡s ❛✈❛♥ç♦s✱ ♦ ❝❛♠♣♦ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❢♦✐ ✉♠ ❞♦s q✉❡ ❛✈❛♥ç❛r❛♠ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡✳ ❉♦ t❡❧é❣r❛❢♦ ❛té ♦ t❡❧❡❢♦♥❡ ❡ ❛s ♣♦st❡r✐♦r❡s ❢♦r♠❛s ❞✐❣✐t❛✐s ❢♦✐ ✉♠ ♣❛ss♦✳ ❖s ❝✉st♦s ❞❡st❛ ❝♦♠✉♥✐❝❛çã♦ ❡ ♦s ❡q✉✐♣❛♠❡♥t♦s ✉t✐❧✐③❛❞♦s ✱ sã♦ ❝❛❞❛ ✈❡③ sã♦ ♠❛✐s ❜❛✐①♦s✱ ♦♥❞❡ ❛♥t❡s s❡ ♣r❡❝✐s❛✈❛ ❞❡ ✉♠❛ s❛❧❛ ❝❤❡✐❛ ❞❡ ♦♣❡r❛❞♦r❡s ❡ t❡❧❡❢♦♥✐st❛s✱ ❤♦❥❡ ❢❛③✲s❡ ❝♦♠ ✉♠ ❡q✉✐♣❛♠❡♥t♦ ♣♦rtát✐❧✳
❈♦♠ ♦s s✐st❡♠❛s r❡❝❡♣t♦r❡s ❞❡ ●P❙ ❝❛❞❛ ✈❡③ ♠❛✐s ❜❛r❛t♦s ❡ ❛♦ ♠❡s♠♦ t❡♠♣♦ ♠❛✐s ♣r❡s❡♥t❡s ♥❛s ♥♦ss❛s ✈✐❞❛s✱ ❝♦♠♦ ✈❡í❝✉❧♦s✱ ❝❡❧✉❧❛r❡s✱ ♠✐❝r♦❝♦♠✲ ♣✉t❛❞♦r❡s✳ ❙✉❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❡ ♥♦✈♦s ✉s♦s ❞❡✈❡♠ s❡r ✉s❛❞♦s ❛❧é♠ ❞❡ s✐♠♣❧❡s ♣♦s✐❝✐♦♥❛♠❡♥t♦ ♦✉ r❡❢❡r❡♥❝✐❛♠❡♥t♦ ❣❡♦❞és✐❝♦✳
❆s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ s❡ ✉s❛r ❛s ✐♥❢♦r♠❛çõ❡s ❞♦ s✐st❡♠❛ ●P❙ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ✉♠ s✐st❡♠❛ ❞❡ ❝r✐♣t♦❣r❛✜❛ sã♦ ✐♠❡♥s❛s✱ ♣♦❞❡♥❞♦ ❝r✐❛r✲s❡ s✐st❡♠❛s q✉❡ ♣♦❞❡r✐❛♠ s❡r ❤❛❜✐❧✐t❛❞♦s ♣❛r❛ ❢✉♥❝✐♦♥❛r❡♠ s♦♠❡♥t❡ q✉❛♥❞♦ ❡st✐✈❡ss❡ ♥❛ ❧♦✲ ❝❛❧✐❞❛❞❡ ❣❡♦❣rá✜❝❛ ❝♦rr❡t❛✱ ♥♦ ❤♦rár✐♦✱ ♦✉ ❡♥tã♦ ❛té ♠❡s♠♦ ♥❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡s✐❣♥❛❞❛✳
P♦❞❡r✐❛✲s❡ ♦❜r✐❣❛r ✉♠ ❝❛♠✐♥❤ã♦ ♦✉ ♦✉tr♦ t✐♣♦ ❞❡ tr❛♥s♣♦rt❡ ❛ ♣❡r❝♦rr❡r ✉♠ ❝❛♠✐♥❤♦ ♣ré✲❞❡t❡r♠✐♥❛❞♦ ♣❛r❛ q✉❡ ❡❧❡ r❡❝❡❜❡ss❡ ❛s ✐♥str✉çõ❡s ❛❞✐❝✐♦♥❛✐s✱ ♦✉ ❡♥tã♦✱ ♦ ❡♥❞❡r❡ç♦ ✜♥❛❧✳ ❆♦ ♠❡s♠♦ t❡♠♣♦ ❞✐ss♦✱ ❤á ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ r❡str✐♥❣✐r ♦ ♠❡s♠♦ ♠❡✐♦ ❞❡ tr❛♥s♣♦rt❡ s❡ ❡❧❡ s❡ ❞❡s✈✐❛ss❡ ❞♦s ❧✐♠✐t❡s ✐♠♣♦st♦s ❞❡ ✈❡❧♦❝✐❞❛❞❡✳
◆♦ ❝❛♠♣♦ ❞❡ ❡♥tr❡t❡♥✐♠❡♥t♦ é ♣♦ssí✈❡❧ r❡str✐♥❣✐r q✉❡ ✉♠ ♣r♦❣r❛♠❛ s♦✲ ♠❡♥t❡ r♦❞❡ ❛ ♣❛rt✐r ❞❡ ❝❡rt❛ ❧♦❝❛❧✐❞❛❞❡✱ ❝r✐❛♥❞♦ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ❛♦ ✉s♦ ❞❡ ❝ó❞✐❣♦s r❡❣✐♦♥❛✐s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦s ♥♦s ❞✐s❝♦s ❞❡ ❉❱❉ ♦✉ ❞❡ ❥♦❣♦s✳
➱ ✐♥❡❣á✈❡❧ ❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡ ❞❛s t❡❝♥♦❧♦❣✐❛s ❞❡ ✐♥❢♦r♠❛çã♦ ❡ ❝♦♠✉♥✐❝❛çõ❡s
❞❡♥tr♦ ❞♦ ♥♦ss♦ ❝♦t✐❞✐❛♥♦✱ ❝♦♠ ❛♣❛r❡❧❤♦s t❡❧❡❢ô♥✐❝♦s ♠ó✈❡✐s✱ t❡❧❡❢♦♥❡s ♣♦r s❛té❧✐t❡s✱ r❡❞❡s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ♠✉❧t✐✲♥❛❝✐♦♥❛✐s ❡ ❛té ♠❡s♠♦ ❡①tr❛✲t❡rr❡str❡s✳ ❆ ❝♦♥❝❡♣çã♦ ❞❛ ❛❧t❛ ✈✐❛ ❞❡ ✐♥❢♦r♠❛çã♦ ❛❣r❡❣❛♥❞♦ ✐♥❢♦r♠❛çõ❡s ❡ s❡r✈✐ç♦s ❞❡ ❢♦r♠❛ ✐♥st❛♥tâ♥❡❛ ❡ ✐♥t❡r❛t✐✈❛ t❛♠❜é♠ ❡stá ♣r❡s❡♥t❡✳
❆s ♣❡ss♦❛s ❡ ❝♦r♣♦r❛çõ❡s ✱ ❤♦❥❡ ❝❛❞❛ ✈❡③ ♠❛✐s✱ ✉t✐❧✐③❛♠ ❛ ■♥t❡r♥❡t✱ ❝♦rr❡✐♦ ❡❧❡trô♥✐❝♦s ❡ ♦✉tr❛s ❛♣❧✐❝❛çõ❡s ♣❛r❛ tr♦❝❛ ❞❡ ❞❛❞♦s ❡ ✐♥❢♦r♠❛çõ❡s✳
❉❡♥tr♦ ❞❡st❡s ❛✈❛♥ç♦s t❡❝♥♦❧ó❣✐❝♦s ❛s ♥❡❝❡ss✐❞❛❞❡s t❛♠❜é♠ ❢♦r❛♠ ♠✉✲ ❞❛♥❞♦✳ ❆ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✉♠❛ ❝♦♠✉♥✐❝❛çã♦ ❝♦♥✜á✈❡❧ ❡ s❡❣✉r❛✱ s❡ t♦r♥❛r❛♠ q✉❡stõ❡s ✐♥❝❧✉s✐✈❡ ❞❡ s❡❣✉r❛♥ç❛ ♥❛❝✐♦♥❛❧✱ ♦♥❞❡ q✉❡♠ t❡♠ ✐♥❢♦r♠❛çã♦ t❡♠ ♣♦❞❡r✳
❉❡♥tr♦ ❞❡st❡ ❡s❝♦♣♦ ❡st❛ ❝♦♠✉♥✐❝❛çã♦ ❞❡✈❡rá ♣r❡❡♥❝❤❡r ❛❧❣✉♥s r❡q✉✐s✐✲ t♦s ♣r❡✈✐❛♠❡♥t❡ ❛❝❡rt❛❞♦s ♥♦ s✐st❡♠❛✱ ❝♦♠♦ ♥í✈❡❧ ❞❡ s❡❣✉r❛♥ç❛✱ ❢♦r♠❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ ❡ ♦✉tr❛s ✈❛r✐á✈❡✐s ❞❡✜♥✐❞❛s✳❆ ❝r✐♣t♦❣r❛✜❛ ❡ ♦✉tr❛s té❝♥✐❝❛s ❞❡ s❡❣✉r❛♥ç❛ ❞❡ ❞❛❞♦s tê♠ ✉♠❛ ♣❛rt✐❝✐♣❛çã♦ ❢✉♥❞❛♠❡♥t❛❧ ♥♦ ❝❛♠♣♦ ❞❛s ❝♦✲ ♠✉♥✐❝❛çõ❡s✱ ♣♦✐s ♣r♦✈ê ✉♠❛ ❢♦r♠❛ ❞❡ ❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠✳ ❊ t❡♠ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❡q✉❡♥♦ ♣❛r❛ s❡✉s ❧❡❣ít✐♠♦s ♣❛rt✐❝✐♣❛♥t❡s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ✉♠ ✐♥✈❛s♦r ❛♦ ❞❛❞♦ ♦✉ ♠❡♥s❛❣❡♠ é ❛❧tíss✐♠♦✱ ❝r✐❛♥❞♦ ❛ss✐♠ ✉♠ ❛♠❜✐❡♥t❡ s❡❣✉r♦✳
❆ ❝♦♠✉♥✐❝❛çã♦ ❞❡✈❡ s❡ ❞❛r ❡♥tr❡ ♦s ♣❛rt✐❝✐♣❛♥t❡s ❞❡ ❢♦r♠❛ tr❛♥s♣❛r❡♥t❡✱ ❞❡ ❢♦r♠❛ q✉❡ ♥ã♦ ✐♥t❡rr♦♠♣❛ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ s✉❛s ♦✉tr❛s ❛t✐✈✐❞❛❞❡s ❡ ❢✉♥çõ❡s✳ Pr♦✈❡♥❞♦ ♣❛r❛ ❛q✉❡❧❡s q✉❡ ❛ ✉t✐❧✐③❛♠ ✉♠❛ ❢♦r♠❛ rá♣✐❞❛✱ ❜❛r❛t❛ ❡ tr❛♥s♣❛r❡♥t❡ ❞❡ s❡ ❝♦♠✉♥✐❝❛r✳
❆❧❣♦r✐t♠♦s ❝♦♠ ✉♠❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♠❛✐♦r✱ ♠❛✐s r♦❜✉st♦s ❡ ❝♦♠ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♠❛♥t❡r ❛ ❝♦♠✉♥✐❝❛çã♦ s❡❝r❡t❛ ♣♦r ✉♠ t❡♠♣♦ ❝♦♥✲ s✐❞❡rá✈❡❧ ❞❡ t❡♠♣♦✱ t❡♠ s❡ t♦r♥❛❞♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❝♦♠✉♠ ❡ ♠❛✐s ❞✐s♣♦♥í✈❡✐s✳ ❆✐♥❞❛ ❝♦♠ ♦ ❛✈❛♥ç♦ ❞❡ ♦✉tr❛s t❡❝♥♦❧♦❣✐❛s é ♣♦ssí✈❡❧ ❡①♣❛♥❞✐r ❛ ✉t✐❧✐③❛çã♦ ❡ ❢♦r♠❛s ❝♦♠♦ ❛ ❝r✐♣t♦❣r❛✜❛ é ✉s❛❞❛✳
✶✳✶ ❖❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ ❡st✉❞♦ ✈✐s❛ ❛♠♣❧✐❛r ❛ ❝♦♠✉♥✐❝❛çã♦ ❝r✐♣t♦❣rá✜❝❛ ❡ ❛❞✐❝✐♦♥❛r ✈❛r✐á✈❡✐s ❣❡♦❞és✐❝❛s✱ ♣❡r♠✐t✐♥❞♦ ❛ss✐♠✱ ♠❛✐♦r ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❡ ♥♦✈❛s ♣♦ss✐❜✐❧✲ ✐❞❛❞❡s ❞❡ ✉s♦ ♣❛r❛ ♦s s✐st❡♠❛s ❡♥✈♦❧✈✐❞♦s✳
❆tr❛✈és ❞❡ ✉♠ r❡❝❡♣t♦r ●P❙ ♦s ❞❛❞♦s ❣❡♦❞és✐❝♦s s❡rã♦ r❡❝❡❜✐❞♦s ❡ ✉s❛✲ ❞♦s ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ✉♠ ♠ó❞✉❧♦ ❝r✐♣t♦❣rá✜❝♦ ♣❛r❛ ❝r✐❛çã♦ ❞❡ ✉♠❛ ❝❤❛✈❡ ❡ ♣♦st❡r✐♦r ❞❡❝♦❞✐✜❝❛çã♦ ❞❡ ♠❡♥s❛❣❡♥s r❡❝❡❜✐❞❛s✳
❉❡st❛ ❢♦r♠❛ só ♦❝♦rr❡rá ❛ ❞❡❝♦❞✐✜❝❛çã♦ ❝♦rr❡t❛ ❞❛ ♠❡♥s❛❣❡♠ q✉❛♥❞♦ ♦ r❡❝❡♣t♦r ❡st✐✈❡r ♥❛s ❝♦♦r❞❡♥❛❞❛s ❣❡♦❞és✐❝❛s ❝♦rr❡t❛s✳ ❈r✐❛♥❞♦ ❞❡st❡ ♠♦❞♦ ✉♠❛ ♥♦✈❛ ❣❛♠❛ ❞❡ s♦❧✉çõ❡s ❛s q✉❛✐s ♣♦❞❡♠ s❡r ❛t✐✈❛❞❛s ♦✉ ❧✐♠✐t❛❞❛s ❝♦♥✲ ❢♦r♠❡s ❛s ❝♦♦r❞❡♥❛❞❛s ❞❡✜♥✐❞❛s✳
✷ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛
❖ ♦❜❥❡t✐✈♦ ❞❡st❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ é ♦ ❞❡ r❡✈✐s❛r ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐✲ ❝♦s✱ ❝r✐♣t♦❣rá✜❝♦s ❡ ❣❡♦❞és✐❝♦s ✉t✐❧✐③❛❞♦s✱ ♣❛r❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦ t❡①t♦✳
■♥✐❝✐❛❧♠❡♥t❡ s❡rá ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ♠❛t❡♠át✐❝❛ ❞❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❝♦♠♦ ❝❛♠♣♦s ✜♥✐t♦s✳ ❊st❡s ❝♦♥❝❡✐t♦s sã♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ✉s❛❞♦s ♥♦ ❝❛♠♣♦ ❞❡ ❝r✐♣✲ t♦❣r❛✜❛ ❡ ❞❡ ❝♦♠✉♥✐❝❛çõ❡s✳
❈❛♠♣♦s ❋✐♥✐t♦s ❢♦r❛♠ ❞❡s❝♦❜❡rt♦s ❡ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❡❧♦ ❣r❛♥❞❡ ♠❛t❡♠át✐❝♦ ➱✈❛r✐st❡ ●❛❧♦✐s ❬✶❪✳
❆♣ós s❡rá ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❞♦s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❡ ❞♦ ❛❧❣♦r✐t♠♦ ❆❊❙✭❘✐❥♥❞❛❡❧✮✳
❊ ✜♥❛❧♠❡♥t❡ s❡rá ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❞♦s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ❞❡ ❣❡♦❞❡s✐❛ ❡ r❡❝❡♣t♦r❡s ●P❙✳
✷✳✶ ❈❛♠♣♦s ❋✐♥✐t♦s
❉❡✜♥❡✲s❡ ❝❛♠♣♦s ❝♦♠♦ ✉♠ ❣r✉♣♦ ❞❡ ❡❧❡♠❡♥t♦s✭♥ú♠❡r♦s✮ ✜♥✐t♦s ❞❡♥tr♦ ❞❛s ♦♣❡r❛çõ❡s ❞❡ ❛❞✐çã♦✱ s✉❜tr❛çã♦✱ ♠✉❧t✐♣❧✐❝❛çã♦ ❡ ❞✐✈✐sã♦ ♣♦r ♥ú♠❡r♦s ♥ã♦ ♥✉❧♦s✳ ❈♦♥t✉❞♦ ✉♠ ❝❛♠♣♦ é ✉♠ ❣r✉♣♦ ❞❡ ♥ú♠❡r♦s ❝♦♠ ❞✉❛s ♦♣❡r❛çõ❡s ❜✐♥ár✐❛s✿ ❛❞✐çã♦ ❡ ♠✉❧t✐♣❧✐❝❛çã♦❬✷❪✳
❊st❛s ❞✉❛s ♦♣❡r❛çõ❡s ♣♦ss✉❡♠ ❛s s❡❣✉✐♥t❡s ❝❛r❛❝t❡ríst✐❝❛s✿
❼ ❙ã♦ ❛ss♦❝✐❛t✐✈❛s ❡ ❝♦♠✉t❛t✐✈❛s✿(ab)∗c=a∗(bc)❀
❼ P♦ss✉❡♠ ✐❞❡♥t✐❞❛❞❡s✿ ✶
❼ P♦ss✉❡♠ ❛s ♦♣❡r❛çõ❡s ✐♥✈❡rs❛s✿ s✉❜tr❛çã♦ ❡ ❞✐✈✐sã♦❀
❼ P♦ss✉❡♠ ❛s r❡❣r❛s ❞✐str✐❜✉t✐✈❛s ❝♦♠♦✿ a(b+x) =ab+bx
❊st❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s sã♦ ❛s ♠❛✐s ❝♦♠✉♠❡♥t❡ ✉s❛❞❛s✱ ♦✉tr❛s ♣r♦✲ ♣r✐❡❞❛❞❡s ❢❛③❡♠ ♣❛rt❡ ❞❡ ✉♠ ❣r✉♣♦ ♠❡♥♦r ❞❡ ❝❛♠♣♦s ❞❡✈✐❞♦ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❝❡rt♦s ❝❛♠♣♦s sã♦ ♠❡♥♦s ✉s❛❞❛s❬✶❪✳
❯♠ ❞♦s ❣r✉♣♦s ♠❛✐s ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ♦ ❣r✉♣♦ ❞♦s ✐♥t❡✐r♦s Z✱ ♥ã♦ é ✉♠
❝❛♠♣♦✱ ♥❡st❡ ❝❛s♦ ♣♦rq✉❡Z♥ã♦ é ✜♥✐t♦ ♥❛ ❞✐✈✐sã♦✳ ❖s ❝❛♠♣♦s ♠❛✐s ❝♦♠✉♥s
❡stã♦ ❞❡♥tr♦ ❞♦s ❣r✉♣♦s ❞♦s r❛❝✐♦♥❛✐s Q✱ r❡❛✐s R❡ ♦s ♥ú♠❡r♦s ❝♦♠♣❧❡①♦s C
✷✳✶✳✶ ❆❞✐çã♦ ❞❡ ❈❛♠♣♦s ❋✐♥✐t♦s
❆ ❛❞✐çã♦ ❞❡ ❝❛♠♣♦s ✜♥✐t❛s é ❢❡✐t❛ ❛tr❛✈és ❞❛ ❛❞✐çã♦ ❞❛s ♣♦tê♥❝✐❛s ❞♦s ❞♦✐s ♣♦❧✐♥ô♠✐♦s✳ ❖ ♠♦❞♦ ❞❡ ❛❞✐çã♦ ❞❡ ❝❛♠♣♦s ✜♥✐t♦s ❡♠ ❜②t❡s sã♦ ❞✐❢❡r❡♥t❡s ❞♦s ♠ét♦❞♦s ✉s❛❞♦s ❡♠ ♥ú♠❡r♦s✳ ◆❛ ❝♦♠♣✉t❛çã♦ ♣♦r ❜②t❡s ❛ ❛❞✐çã♦ ❞❡ ❝❛♠♣♦s ✜♥✐t♦s é ❢❡✐t❛ ✉t✐❧✐③❛♥❞♦✲s❡ ❛ ♦♣❡r❛çã♦ ❳❖❘✱ s✐♠❜♦❧✐③❛❞❛ ❛q✉✐ ❝♦♠♦ ⊕ ✱ ♥❛ t❛❜❡❧❛ ✶ ❛❜❛✐①♦ é ❞❡♠♦♥str❛❞♦ ♦s s❡✉s r❡s✉❧t❛❞♦s✳
❚❛❜❡❧❛ ✶✿ ❆❞✐çã♦ ❞❡ ❈❛♠♣♦s ❋✐♥✐t♦s ❛ ♦♣❡r❛❞♦r ❜ r❡s✉❧t❛❞♦
✶ ⊕ ✶ ✵
✶ ⊕ ✵ ✶
✵ ⊕ ✶ ✶
✵ ⊕ ✵ ✵
❆✐♥❞❛ ♥❡st❛ ♠❡s♠❛ ❧✐♥❤❛ ❞❡ r❛❝✐♦❝í♥✐♦ é ♣♦ssí✈❡❧ ❞❡s❝r❡✈❡r ❛ ❛❞✐çã♦ ❞❡ ❝❛♠♣♦s ✜♥✐t♦s ❝♦♠♦ ✉♠❛ ❛❞✐çã♦ ❞♦s ❜✐ts ❞❡♥tr♦ ❞♦s ❝♦rr❡s♣♦♥❞❡♥t❡s ❜②t❡s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✿
(x6 +x5+x2) + (x7+x+ 1) =x7+x6+x5+x2 ✭✶✮
00110010⊕01000011 = 01110011 ✭✷✮
✷✳✶✳✷ ▼✉❧t✐♣❧✐❝❛çã♦ ❞❡ ❈❛♠♣♦s ❋✐♥✐t♦s
❖ ♣❛❞rã♦ ❆❊❙ ✉t✐❧✐③❛ ❛ ♠✉❧t✐♣❧✐❝❛çã♦ ♣♦❧✐♥♦♠✐❛❧ ❞❡ ●❋✭28✮✱ s✐♠❜♦❧✐③❛❞❛ ❛q✉✐
♣♦r ”•”✳ ❉❡s❝r❡✈❡✲s❡ ❡st❛ ♦♣❡r❛çã♦ ❝♦♠♦ ✉♠❛ ♠✉❧t✐♣❧✐❝❛çã♦ ❞❡ ♣♦❧✐♥ô♠✐♦s
❝♦♠ ✉♠ ♣♦❧✐♥ô♠✐♦ ✐rr❡❞✉tí✈❡❧ ✭ s♦♠❡♥t❡ ❞✐✈✐sí✈❡❧ ♣♦r ✶ ❡ ♣♦r ❡❧❡ ♠❡s♠♦✮✳ ◆♦ ❝❛s♦ ❞♦ ❆❊❙ ♦ ♣♦❧✐♥ô♠✐♦ ✉t✐❧✐③❛❞♦ é ✿
m(x) =x8+x4+x3+x+ 1 ✭✸✮
✉s❛r❡♠♦s ♦ ❡①❡♠♣❧♦ ❛❜❛✐①♦ ♣❛r❛ ❞❡s❝r❡✈❡r ❡st❛ ♦♣❡r❛çã♦✿
(x6+x4+x2+x+1)(x7+x+1) =x13+x11+x9+x8+x6+x5+x4+x3+1 ✭✹✮
r❡❞✉③✐♥❞♦✲s❡
x13+x11+x9+x8+x6+x5+x4 +x3+ 1
mod(x8+x4+x3+x+ 1) =x7+x6+ 1 ✭✺✮
❆tr❛✈és ❞❡st❛ r❡❞✉çã♦ é ♣♦ssí✈❡❧ ❣❛r❛♥t✐r q✉❡ ♦ ♣♦❧✐♥ô♠✐♦ ✜♥❛❧ s❡rá ❞❡ ♦r❞❡♠ ✐♥❢❡r✐♦r ❛ ✽ ♣❡r♠✐t✐♥❞♦ ❛ss✐♠ s❡r r❡♣r❡s❡♥t❛❞♦ ❛tr❛✈és ❞❡ ✶ ❜②t❡✳ ❆♦ ❝♦♥trár✐♦ ❞❛ ❛❞✐çã♦ ♥ã♦ ❡①✐st❡ ✉♠❛ ♦♣❡r❛çã♦ ❜✐♥ár✐❛ s✐♠♣❧❡s ♣❛r❛ ❡st❡ ♣r♦✲ ❝❡❞✐♠❡♥t♦✳
❊st❛ ♠✉❧t✐♣❧✐❝❛çã♦ é ❛ss♦❝✐❛t✐✈❛ ❡ ❡❧❡♠❡♥t♦ ④✵✶⑥ é ❛ ✐❞❡♥t✐❞❛❞❡ ♥❛ ♠✉❧t✐✲ ♣❧✐❝❛çã♦✳ P❛r❛ q✉❛❧q✉❡r ♣♦❧✐♥ô♠✐♦ ❜✐♥ár✐♦ ♥ã♦✲♥✉❧♦b(x)❞❡ ❣r❛✉ ♠❡♥♦r q✉❡
✽✱ ♦ ✐♥✈❡rs♦ ❛q✉✐ ❞❡♥♦♠✐♥❛❞♦ ❞❡ b−1(x) ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞♦ ❛tr❛✈és ❞♦ ✉s♦
❞♦ ❛❧❣♦r✐t♠♦ ❡st❡♥❞✐❞♦ ❞❡ ❊✉❝❧✐❞❡s ❬✸❪✿
b(x)a(x) +m(x)c(x) = 1 ✭✻✮
❙❡♥❞♦ q✉❡a(x)•b(x)♠♦❞ m(x) = 1✱ ❛ q✉❛❧ s❡ tr❛❞✉③ ♣♦r
b−1(x) =a(x)mod m(x) ✭✼✮
❆✐♥❞❛ ❞❡❞✉③✲s❡ q✉❡ ♣❛r❛ q✉❛❧q✉❡r ✈❛❧♦r ❞❡a(x), b(x), c(x)t❡♠ ❛s s❡❣✉✐♥t❡s
♣r♦♣r✐❡❞❛❞❡s ❛ss♦❝✐❛t✐✈❛s✿
a(x)•(b(x) +c(x)) =a(x)•b(x) +a(x)•c(x) ✭✽✮
P♦r ❝♦♥s❡qüê♥❝✐❛ ♣❛r❛ t♦❞♦s ♦s ✈❛❧♦r❡s ♣♦ssí✈❡✐s ❞❡ ❞❡♥tr♦ ❞❡ ✉♠ ❜②t❡ ✭✷✺✻✮✱ ❝♦♠ ❛ ♦♣❡r❛çã♦ ❞❡ ❳❖❘ ✉s❛❞❛ ❝♦♠♦ ❛❞✐çã♦ ❡ ♠✉❧t✐♣❧✐❝❛çã♦✱ t❡♠ s✉❛
❡str✉t✉r❛ ❞❡✜♥✐❞❛ ♣♦r ●❋✭28).
✷✳✶✳✸ ▼✉❧t✐♣❧✐❝❛çã♦ ♣♦r x
❯♠ ❜②t❡ ♣♦❞❡ s❡r ❞❡♠♦♥str❛❞♦ ❛tr❛✈és ❞❡ ✉♠ ♣♦❧✐♥ô♠✐♦✱ ❝♦♠ ❛ s❡qüê♥❝✐❛ ❞❡ ❜✐ts✿
b7x7+b6x6+b5x5+b4x4 +b3x3+b2x2+b1x+b0 =
7
X
i=0
bixi ✭✾✮
▼✉❧t✐♣❧✐❝❛♥❞♦✲s❡ ♦ ♣♦❧✐♥ô♠✐♦ ❛❝✐♠❛ ♣♦r ① ✭x •b(x)✮ t❡♠✲s❡ ♦ s❡❣✉✐♥t❡
♣♦❧✐♥ô♠✐♦ r❡s✉❧t❛♥t❡✿
b7x8+b6x7 +b5x6+b4x5+b3x4+b2x3+b1x2+b0x ✭✶✵✮
P❛r❛ ♦❜t❡r✲s❡ ♦ r❡s✉❧t❛❞♦ ❞❛ ♦♣❡r❛çã♦x•b(x)é ♥❡❝❡ssár✐♦ ❢❛③❡r ❛ r❡❞✉çã♦
❞❡ ♠ó❞✉❧♦ ❝♦♠♦ ❞❡✜♥✐❞♦ ♥❛ s❡çã♦ ✶✳✸ ✭♠✉❧t✐♣❧✐❝❛çã♦ ❞❡ ♣♦❧✐♥ô♠✐♦s✮✳ ❈❛s♦ ❜✼ s❡❥❛ ✐❣✉❛❧ ❛ ③❡r♦✱ ♦ ♣♦❧✐♥ô♠✐♦ ❥á s❡ ❡♥❝♦♥tr❛ ♥❛ ❢♦r♠❛ r❡❞✉③✐❞❛✳ ❉♦ ❝♦♥✲ trár✐♦ s❡rá ♥❡❝❡ssár✐❛ ❛ r❡❞✉çã♦ s✉❜tr❛✐♥❞♦ ♦ ♣♦❧✐♥ô♠✐♦ ♠✭①✮✳ ❊st❛ ♦♣❡r❛çã♦ ❞❡ ♠✉❧t✐♣❧✐❝❛çã♦ ♣♦❞❡ s❡r ✐♠♣❧❡♠❡♥t❛❞❛ ❜✐♥❛r✐❛♠❡♥t❡ ❛tr❛✈és ✉♠ ❞❡s❧♦❝❛✲ ♠❡♥t♦ ❞♦ ❜②t❡ ♣❛r❛ ❛ ❡sq✉❡r❞❛ ❡ ✉♠❛ ♦♣❡r❛çã♦ ❳❖❘ ❝♦♥❞✐❝✐♦♥❛❧ ❝♦♠ ④✶❜⑥✳ ❊st❛ ♦♣❡r❛çã♦ é ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞❛ ❝♦♠♦ ①t✐♠❡✭✮✳ ❆ ♦♣❡r❛çã♦ ①t✐♠❡✭✮ ♣❡r♠✐t❡ q✉❡ r❡s✉❧t❛❞♦s ✐♥t❡r♠❡❞✐ár✐♦s s❡❥❛♠ ✉s❛❞♦s ❛té ❛s ♣♦tê♥❝✐❛s ♠❛✐♦r❡s ✜♥❛✐s✳ P♦r ❡①❡♠♣❧♦✿
{57} • {13} ={f e} ✭✶✶✮ {57} • {04} =xtime({ae}) ={47}
{57} • {08} =xtime({47}) ={8e} {57} • {10} =xtime({8e}) ={07}
♣♦r ❝♦♥s❡❣✉✐♥t❡✱
{57} • {13} = {57} •({01} ⊕ {02} ⊕ {10})
{57} ⊕ {ae} ⊕ {07} = f e
✷✳✶✳✹ P♦❧✐♥ô♠✐♦s ❝♦♠ ❈♦❡✜❝✐❡♥t❡s ❡♠ GF(28)
❯♠ ♣♦❧✐♥ô♠✐♦ ❝♦♠ q✉❛tr♦ t❡r♠♦s ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❝♦♠ ❡❧❡♠❡♥t♦s ❞❡ ❝❛♠♣♦ ✜♥✐t♦ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ❡♠ ❣r✉♣♦s ❞❡ ❜②t❡s❬✹❪✳
❯♠ ❝♦♥❥✉♥t♦ ❞❡ ❜②t❡s[a0, a1, a2, a3]♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❛tr❛✈és ❞♦ ♣♦❧✐♥ô♠✐♦✿
a(x) =a3x3+a2x2+a1x+a0 ✭✶✷✮
◆♦ ✉s♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ ❡st❡ ♣♦❧✐♥ô♠✐♦ é ✉s❛❞♦ ✉♠ ♣♦✉❝♦ ❞✐❢❡r❡♥t❡ ❞♦ s❡✉ ✉s♦ ♥♦r♠❛❧✱ ✉t✐❧✐③❛♥❞♦ ❜②t❡s ❝♦♠♦ ❝♦❡✜❝✐❡♥t❡s ❡ ✉s❛♥❞♦ ✉♠ ♣♦❧✐♥ô♠✐♦ ❞❡ r❡❞✉çã♦ ❞✐❢❡r❡♥t❡ t❛♠❜é♠✳
❯♠❛ ♦♣❡r❛çã♦ ❞❡ ❛❞✐çã♦ ❞❡ ❞♦✐s ♣♦❧✐♥ô♠✐♦s ❞❡ q✉❛tr♦ t❡r♠♦s é ❢❡✐t❛ ❛❞✐❝✐♦♥❛♥❞♦✲s❡ ♦s t❡r♠♦s ❞❡ ✐❣✉❛✐s ❝♦❡✜❝✐❡♥t❡s✳ ❆ ❛❞✐çã♦ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ ♦♣❡r❛çã♦ ❜✐♥ár✐❛ ❳❖❘ ❡♥tr❡ ♦s ❜②t❡s ❝♦rr❡s♣♦♥❞❡♥t❡s✳
❙❡❥❛ ♦ s❡❣✉♥❞♦ t❡r♠♦✿
b(x) = b3x3+b2x2+b1x+b0 ✭✶✸✮
❆ ❛❞✐çã♦ s❡r✐❛ ❞❡✜♥✐❞❛ ♣♦r✿
a(x) +b(x) = (a3⊕b3)x3+ (a2⊕b2)x2+ (a1⊕b1)x1+ (a0⊕b0) ✭✶✹✮
❆ ♠✉❧t✐♣❧✐❝❛çã♦ ❞❡st❡s ♣♦❧✐♥ô♠✐♦s é ❢❡✐t❛ ❡♠ ❞♦✐s ♣r♦❝❡ss♦s✱ ♣r✐♠❡✐r❛✲ ♠❡♥t❡ é r❡❛❧✐③❛❞❛ ❛ ♦♣❡r❛çã♦ ❞❡ ❡①♣❛♥sã♦ ❡ ❛❞✐çã♦ ❞❛ ❡q✉❛çã♦ c(x) = a(x)•b(x)❡ s❡✉s ❝♦❡✜❝✐❡♥t❡s ❝♦♠ ♣♦t❡♥❝✐❛s ✐❣✉❛✐s s♦♠❛❞♦s✱ r❡s✉❧t❛♥❞♦ ❡♠ ✿
c(x) = c6x6+c5x5+c4x4+c3x3+c2x2+c1x+c0 ✭✶✺✮
♦♥❞❡
c0 =a0•b0
c1 =a1•b0⊕a0•b0
c2 =a2•b0⊕a1•b1⊕a0•b2
c3 =a3•b0⊕a2•b1⊕a1•b2⊕a0•b3
c4 =a3•b1⊕a2•b2⊕a1•b3
c5 =a3•b2⊕a2•b3
c6 =a3•b3
❖ ♣♦❧✐♥ô♠✐♦ ❝✭①✮✱ ♣♦r s✉❛ ❡str✉t✉r❛✱ ♥ã♦ r❡♣r❡s❡♥t❛ ❞❡st❛ ❢♦r♠❛ ✉♠❛ ✈❛r✐á✈❡❧ ❞❡ ✹ ❜②t❡s ❝♦♠♦ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛❧❣✉♠❛s ♦♣❡r❛çõ❡s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝♦♠♦ ❛ ❆❊❙✳ P❛r❛ t❛♥t♦✱ é ♥❡❝❡ssár✐♦ ❡①❡❝✉t❛r ✉♠❛ r❡❞✉çã♦ ❞❡st❡ ♣♦❧✐♥ô♠✐♦ ♣❛r❛ ✉♠ ❣r❛✉ ♠❡♥♦r q✉❡ ✹✳ ❊st❛ r❡❞✉çã♦ ♣♦❞❡ s❡r ❢❡✐t❛ ❝♦♠ ♦ ♣♦❧✐♥ô♠✐♦
x4+ 1 ❞❡s❝r✐t❛ ♣❡❧❛ ❡q✉❛çã♦✿
ximod(x4+ 1) =xi mod4 ✭✶✻✮
❙❡♥❞♦ ❛ss✐♠ ♦ ♣r♦❞✉t♦ ♠♦❞✉❧❛r ❡♥tr❡ ❛✭①✮ ❡ ❜✭①✮ s❡♥❞♦ s✐♠❜♦❧✐③❛❞♦ ♣♦r
a(x)⊗b(x) t❡♠ ❝♦♠♦ r❡s✉❧t❛♥t❡ ♦ ♣♦❧✐♥ô♠✐♦ ❞✭①✮ ❞❡✜♥✐❞♦ ❝♦♠♦✿
d(x) = d3x3+d2x2+d1x+d0 ✭✶✼✮
s❡♥❞♦ q✉❡✱
d0 = (a0 •b0)⊕(a3•b1)⊕(a2•b2)⊕(a1•b3) ✭✶✽✮
d1 = (a1 •b0)⊕(a0•b0)⊕(a3•b2)⊕(a2•b3) ✭✶✾✮
d2 = (a2•b0)⊕(a1•b1)⊕(a0•b2)⊕(a3 •b3) ✭✷✵✮
d3 = (a3•b0)⊕(a2 •b1)⊕(a1•b2)⊕(a0•b3) ✭✷✶✮
✷✳✷ ❈r✐♣t♦❣r❛✜❛
❈r✐♣t♦❣r❛✜❛ ♦r✐❣✐♥❛✲s❡ ❞❛ ♣❛❧❛✈r❛ ❣r❡❣❛ ❝r②♣t♦s ❛♦ q✉❛❧ s✐❣♥✐✜❝❛ s❡❝r❡t♦ ♦✉ ♦❝✉❧t♦✳ ❖ ♦❜❥❡t✐✈♦ ❞♦ ❡st✉❞♦ ❞❛ ❝r✐♣t♦❣r❛✜❛ sã♦ ♦s ♠ét♦❞♦s ❡ ♠❡✐♦s ❞❡ ❝♦❞✐✜❝❛çã♦ ❞❡ ♠❡♥s❛❣❡♥s ♦✉ ❞❛❞♦s ♣❛r❛ q✉❡ s♦♠❡♥t❡ ✉♠ r❡❝❡♣t♦r ❧❡❣ít✐♠♦ ❞❛q✉❡❧❛ ✐♥❢♦r♠❛çã♦ ♣♦ss❛ t❡r ❛❝❡ss♦✳ ❆♦ ♠❡s♠♦ q✉❡ t❡♠♦s ❛ s✉❛ ❝✐ê♥❝✐❛ ✏✐r♠ã✑ ❝❤❛♠❛❞❛ ❝r✐♣t♦❛♥á❧✐s❡✱ q✉❡ ❡st✉❞❛ ♦s ♠❡✐♦s ❞❡ ❞❡❝✐❢r❛r ✉♠❛ ♠❡♥s❛❣❡♠ ❝r✐♣t♦❣r❛❢❛❞❛✱ s❡♠ ❛ t♦t❛❧✐❞❛❞❡ ❞❛s ✐♥❢♦r♠❛çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ❞❡❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠ ❝♦rr❡t❛♠❡♥t❡❬✺❪✳
❉❡♥tr♦ ❞❛ ❝r✐♣t♦❣r❛✜❛ t❡♠✲s❡ ❛s s❡❣✉✐♥t❡s ❝❛r❛❝t❡ríst✐❝❛s ♣r✐♥❝✐♣❛✐s ❛s q✉❛✐s t❡♠ s✐❞♦ ❡✈♦❧✉í❞❛s ♦✉ ♠♦❞✐✜❝❛❞❛s ❝♦♥❢♦r♠❡ ♦s ❛✈❛♥ç♦s t❡❝♥♦❧ó❣✐❝♦s❬✻❪✿
✶✳ ❈♦♥✜❞❡♥❝✐❛❧✐❞❛❞❡✿ ❛ ♠❡♥s❛❣❡♠ ❝r✐♣t♦❣r❛❢❛❞❛ ♥ã♦ ♣♦❞❡ s❡r ❧✐❞❛ ♣♦r ❛❧❣✉é♠ ♥ã♦ ❛✉t♦r✐③❛❞♦❀
✷✳ ■♥t❡❣r✐❞❛❞❡✿ q✉❛♥❞♦ ❝r✐♣t♦❣r❛❢❛❞❛ q✉❛❧q✉❡r t❡♥t❛t✐✈❛ ❞❡ ♠✉❞❛r ❛ ♠❡♥✲ s❛❣❡♠ é ❞❡t❡❝t❛❞❛❀
✸✳ ❙❡♠ r❡♣ú❞✐♦✿ ♦ ❡♥✈✐❛♥t❡ ❞❡♣♦✐s ❞❡ ❛ t❡r ❡♥✈✐❛❞♦ ♥ã♦ ♣♦❞❡ ♥❡❣❛r ♦ ❡♥✈✐♦ ❞❡st❛ ♠❡s♠♦❀
✹✳ ❆✉t❡♥t✐❝✐❞❛❞❡✿ t❛♥t♦ r❡❝❡♣t♦r q✉❛♥t♦ r❡❝❡♣t♦r ♣♦❞❡♠ ❝♦♥✜r♠❛r ❛s s✉❛s ✐❞❡♥t✐❞❛❞❡s✳
✷✳✷✳✶ ❍✐stór✐❝♦
❆ ❝r✐♣t♦❣r❛✜❛ ✈ê♠ ❞❡s❡♠♣❡♥❤❛♥❞♦ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ❞❡s❞❡ ♦s t❡♠♣♦s ♠❛✐s ❛♥t✐❣♦s ❞❛ ❤✉♠❛♥✐❞❛❞❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥❛ tr❛♥s♠✐ssã♦ ❞❡ ♠❡♥s❛❣❡♥s
♠✐❧✐t❛r❡s ♦✉ ❛té ♠❡s♠♦ ♣❛r❛ ❢ór♠✉❧❛s s❡❝r❡t❛s✳ ❆❜❛✐①♦ t❡♠♦s ♦s ♣r✐♥❝✐♣❛✐s ✉s♦s ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡♥tr♦ ❞❛ ❧✐♥❤❛ ❞♦ t❡♠♣♦✿
❼ ✶✾✵✵ ❆✳❈✿ ❡s❝r✐t♦s ❡❣í♣❝✐♦s ❞❡ ❢♦r♠❛ ♥ã♦ ♣❛❞rã♦ sã♦ ✉s❛❞♦s ♣♦r ✉♠ ❡s❝r✐❜❛ ❞❡s❝♦♥❤❡❝✐❞♦❀
❼ ✶✺✵✵ ❆✳❈✳✿ é ❡♥❝♦♥tr❛❞❛ ✉♠❛ ❢♦r♠✉❧❛ ❡♥❝r✐♣t❛❞❛ ❞❡ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ♣✐♥t✉r❛ ❞❡ ♣♦t❡s ❞❡ ❜❛rr♦❀
❼ ✺✵✵ ❛ ✻✵✵ ❆✳❈✳✿ ❡s❝r✐❜❛s ❤❡❜r❡✉s ✉s❛♠ ✉♠❛ ❢♦r♠❛ ❞❡ ❝r✐♣t♦❣r❛✜❛ ♥♦ ❧✐✈r♦ ❞❡ ❏❡r❡♠✐❛s❀
❼ ✹✽✼ ❆✳❈✳✿ ✉s♦ ❞♦ ❛♣❛r❡❧❤♦ s❦②t❡❧ ♣❡❧♦s ❣r❡❣♦s✱ ❡r❛ ❝♦♠♣♦st❛ ❞❡ ✉♠ ❝✐♥t♦ ❞❡ s❡❞❛ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ✉♠ ♣❡❞❛ç♦ ❞❡ ♠❛❞❡✐r❛✳ Pr✐♠❡✐r♦ ✉s♦ ❞❡ ❡st❡❣❛♥♦❣r❛✜❛ r❡❣✐str❛❞♦✱ ♦s ♠❡♥s❛❣❡✐r♦s t✐♥❤❛♠ s✉❛s ❝❛❜❡ç❛s r❛s✲ ♣❛❞❛s✳ ❊ ❡r❛ ❡s❝r✐t❛ ❛ ♠❡♥s❛❣❡♠ ❡♠ s✉❛s ❝❛❜❡ç❛s ❡ q✉❛♥❞♦ ♦ ❝❛❜❡❧♦ ❝r❡s❝✐❛♠ ❡❧❡s ❡r❛♠ ❡♥✈✐❛❞♦s ♣❛r❛ tr❛♥s♠✐t✐r ❛ ♠❡♥s❛❣❡♠❀
❼ ✺✵ ❛ ✻✵ ❆✳❈✳✿ ❏✉❧✐✉s ❈❛❡s❛r ❞❡s❡♥✈♦❧✈❡ ♦ ❛❧❣♦r✐t♠♦ ❞❡ tr♦❝❛ ❡ s✉❜st✐✲ t✉✐çã♦ q✉❡ s❡r✐❛ ♥♦ ❢✉t✉r♦ ❝♦♥❤❡❝✐❞♦ ♣❡❧♦ s❡✉ ♥♦♠❡❀
❼ ✶ ❛ ✹✵✵ ❉✳❈ ✿ ▼❛❧❧❛♥❛❣❛ ❱❛ts❛②❛♥❛ ❞❛ ❮♥❞✐❛ ❞❡s❝r❡✈❡ ❛ ❝r✐♣t♦❣r❛✜❛ ❝♦♠♦ ✉♠❛ ❢♦r♠❛ ❞❡ ②♦❣❛✱ ❞❡♥tr♦ ❞❡ s❡✉ ❝♦♠♣ê♥❞✐♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦s ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❑❛♠❛ ❙✉tr❛❀
❼ ✷✵✵ ❉✳❈ ✿ ❖s ♣❛♣✐r♦s ❞❡ ▲❡✐❞❡♥ sã♦ ❡♥❝♦♥tr❛❞♦s ❝♦♠ s✉♣♦st❛s ❢ór♠✉❧❛s ♠á❣✐❝❛s❀
❼ ✼✷✺ ❛ ✽✺✺ ❉✳❈✿ ✈ár✐❛s ❡s❝r✐t✉r❛s ❡ ♣❛♣✐r♦s ♣❡rs❛s sã♦ ✉s❛❞♦s ♣❛r❛ ❝♦✲ ♠✉♥✐❝❛çõ❡s ♠✐❧✐t❛r❡s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♥tr❡ ❛s ✏❡♠❜❛✐①❛❞❛s✑ ❡♠ ár❡❛s ♠✐❧✐t❛r✐③❛❞❛s ❞♦ ♠✉♥❞♦ ár❛❜❡❀
❼ ✶✷✷✻✿ ◆♦s ❛rq✉✐✈♦s ❞❡ ❱❡♥❡③❛ é ❡♥❝♦♥tr❛❞❛ ✉♠❛ ❢♦r♠❛ s✐♠♣❧❡s ❞❡ ❝r✐♣t♦❣r❛✜❛ ♦♥❞❡ ♣♦♥t♦s ❡ ❝r✉③❡s s✉❜st✐t✉í❛♠ ✈♦❣❛✐s❀
❼ ✶✷✺✵✿ ❘♦❣❡r ❇❛❝♦♥✱ ❡s❝r❡✈❡ q✉❡ ✏é ❧♦✉❝♦ ❛q✉❡❧❡ q✉❡ ❡s❝r❡✈❡ ✉♠ s❡❣r❡❞♦ ❞❡ ♦✉tr❛ ❢♦r♠❛ q✉❡ ♥ã♦ ❛ ❞❡ ♠❛♥t❡r s❡❣r❡❞♦ ❞♦ ♣r♦❢❛♥♦✑❀
❼ ✶✸✼✾✿ ●❛❜r✐❡❧✐ ❞✐ ▲❛✈✐♥❞❡ ❛ ♣❡❞✐❞♦ ❞♦ P❛♣❛ ❈❧❡♠❡♥t❡ ❱■■ ❞❡s❡♥✈♦❧✈❡ ✉♠ ♠ét♦❞♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ✉s❛♥❞♦ s✉❜st✐t✉✐çã♦ ❞❡ ❛❧❢❛❜❡t♦ ❡ ❝ó❞✐❣♦s❀
❼ ✶✹✶✷✿ ◆✉♠❛ ❡♥❝✐❝❧♦♣é❞✐❛ ár❛❜❡ é ❡♥❝♦♥tr❛❞♦ ✉♠ ❝❛♣ít✉❧♦ ✐♥t❡✐r♦ s♦❜r❡ ❝r✐♣t♦❣r❛✜❛✱ ❢❛❧❛♥❞♦ ❡s♣❡❝✐❛❧♠❡♥t❡ ❞❡ s✉❜st✐t✉✐çã♦ ❡ ❥✉st❛♣♦s✐çã♦✱ ❝♦♠ ❡①❡♠♣❧♦s ❡ ❞❡♠♦♥str❛çõ❡s ❞❡ ✉s♦❀
❼ ✶✹✻✻✿ ▲❡♦♥ ❇❛tt✐st❛ ❆❧❜❡rt✐ ❞❡s❡♥✈♦❧✈❡ ♦ ♣r✐♠❡✐r♦ ❡♥❝r✐♣t❛❞♦r ♣♦❧✐✲ ❛❧❢❛❜ét✐❝♦ ❡ ❝♦♥stró✐ ✉♠ ❞✐s❝♦ ❞❡ ❡♥❝r✐♣t❛çã♦❀
❼ ✶✺✶✽✿ ❏♦❤❛♥♥❡s ❚r✐t❤❡♠✐✉s ❡s❝r❡✈❡ ❡ ♣✉❜❧✐❝❛ ♦ ♣r✐♠❡✐r♦ ❧✐✈r♦ s♦❜r❡ ❝r✐♣t♦❣r❛✜❛ ❝❤❛♠❛❞♦ P♦❧✐❣r❛♣❤✐❛❡ ▲✐❜r✐ ❙❡①❀
❼ ✶✺✺✸✿ ●✐♦✈❛♥ ❇❛t✐st❛ ❇❡❧❛s♦ ❛❞✐❝✐♦♥❛ ✉♠❛ ❝❤❛✈❡ ❛♦ ♠ét♦❞♦ ❞❡ ❏♦✲ ❤❛♥♥❡s ❚r✐t❤❡♠✐✉s❀
❼ ✶✻✷✸✿ ❙✐r ❋r❛♥❝✐s ❇❛❝♦♥✿ ❞❡s❝r❡✈❡ ✉♠ s✐st❡♠❛ ❜✐❧❛t❡r❛❧ ❞❡ ❝r✐♣t♦❣r❛✜❛✱ q✉❡ ❝♦♥s✐❞❡r❛✈❛ ✉♠❛ ❢♦r♠❛ ❞❡ ❡st❡❣❛♥♦❣r❛✜❛✳
❼ ✶✼✾✵✿ ❚❤♦♠❛s ❏❡✛❡rs♦♥ ✐♥✈❡♥t❛ s❡✉ ❞✐s❝♦ ❞❡ ❝r✐♣t♦❣r❛✜❛❀
❼ ✶✽✶✼✿ ❈♦r♦♥❡❧ ❉❡❝✐✉s ❲❛❞s✇♦rt❤ ❝♦♥stró✐ ✉♠ s✐st❡♠❛ ❞❡ ❞✐s❝♦ ❝r✐♣✲ t♦❣rá✜❝♦ ❝♦♠ ♥ú♠❡r♦s ❞✐❢❡r❡♥t❡s ❞❡ ❧❡tr❛s ❡ ♥ú♠❡r♦s✱ r❡s✉❧t❛♥❞♦ ♥✉♠❛ ❢♦r♠❛ ♣r♦❣r❡ss✐✈❛ ❞❡ ♣❡r♠✉t❛çã♦ ❡ ❝r✐♣t♦❣r❛✜❛❀
❼ ✶✽✺✹✿ ❈❤❛r❧❡s ❲❤❡❛tst♦♥❡ ❞❡s❡♥✈♦❧✈❡ ♦ s✐st❡♠❛ P❧❛②❋❛✐r ❞❡ ❝r✐♣t♦❣r❛✜❛❀
❼ ✶✽✺✾✿ P❧✐♥② ❊❛r❧❡ ❈❤❛s❡ ♣✉❜❧✐❝❛ ❛ ♣r✐♠❡✐r❛ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❢r❛❝✐♦♥❛✲ ♠❡♥t♦❀
❼ ✶✽✻✶✿ ❋r✐❡❞❡r✐❝❤ ❲✳ ❑❛s✐s❦✐ ♣✉❜❧✐❝❛ ❛ s♦❧✉çã♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ ♣♦❧✐✲ ❛❧❢❛❜ét✐❝❛ ❝♦♠ ❝❤❛✈❡s ✐❞ê♥t✐❝❛s❀
❼ ✶✽✾✺✿ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❝♦♠❡r❝✐❛❧ ❞♦ rá❞✐♦ ♣♦r ●✉❣❧✐❡❧♠♦ ▼❛r✲ ❝♦♥✐✱ ❝❛✉s♦✉ ✉♠❛ ❣r❛♥❞❡ ❡✈♦❧✉çã♦ ♥♦ ❝❛♠♣♦ ❞❛ ❝r✐♣t♦❣r❛✜❛✳ ◆ã♦ ♥❡✲ ❝❡ss✐t❛♥❞♦ ♠❛✐s ❞❡ ✜♦s ♣❛r❛ ❛ tr❛♥s♠✐ssã♦ ❞❡ ♠❡♥s❛❣❡♥s ♣❛r❛ ❛ tr❛♥s✲ ♠✐ssã♦ ❡ r❡❝❡♣çã♦ ♦ ❝❛♠♣♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ s❡ ❞❡s❡♥✈♦❧✈❡✉ ❜❛st❛♥t❡❀
❼ ✶✾✶✼✲✶✾✶✽✿ é ❝r✐❛❞♦ ♦ ❇✉r❡❛✉ ❞❡ ❈r✐♣t♦❣r❛✜❛ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ❝♦♠♦ ♣❛rt❡ ❞❛ ✐♥t❡❧✐❣ê♥❝✐❛ ♠✐❧✐t❛r❀
❼ ✶✾✸✾✿ ♦ s✐st❡♠❛ ❞❡ ❈r✐♣t♦❣r❛✜❛ ❊♥✐❣♠❛ é q✉❡❜r❛❞♦
❼ ✶✾✼✻✿ ♦ s✐st❡♠❛ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧❛ ■❇▼ ❝❤❛♠❛❞♦ ❞❡ ❉❊❙ é s❡❧❡❝✐♦♥❛❞♦ ❝♦♠♦ ♦ ♣❛❞rã♦ ♣❛r❛ ♦s ❊st❛❞♦s ❯♥✐❞♦s❀
❼ ✶✾✼✻✿ ❲✐t❤✜❡❧❞ ❉✐✣❡ ❡ ▼❛rt✐♥ ❍❡❧❧♠❛♥♥ ♣✉❜❧✐❝❛♠ ✏◆❡✇ ❉✐r❡❝t✐♦♥s ✐♥ ❈r②♣t♦❣r❛♣❤②✑ ❛❜r✐♥❞♦ ❝❛♠✐♥❤♦ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s❀
❼ ✶✾✼✼✿ ❘♦♥❛❧❞ ❘✐✈❡st✱ ❆❞✐ ❙❤❛♠✐r ❡ ▲❡♦♥❛r❞ ❆❞❧❡♠❛♥ ❝r✐❛♠ ♦ ♠ét♦❞♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❝❤❛♠❛❞♦ ❞❡ ❘❙❆✱ ❜❛s❡❛❞♦ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❲✐t❤✜❡❧❞ ❉✐✣❡ ❡ ▼❛rt✐♥ ❍❡❧❧♠❛♥♥✳ ❙✉❛ s❡❣✉r❛♥ç❛ é ❜❛s❡❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥❛ ❞✐✜❝✉❧❞❛❞❡ ❞❡ s❡ ❢❛t♦r❛r ♥ú♠❡r♦s ❣r❛♥❞❡s❀
❼ ✶✾✽✷✿ ❈r✐❛çã♦ ❞❛ ❝r✐♣t♦❣r❛✜❛ q✉â♥t✐❝❛ ♣♦r ●✐❧❧❡s ❇r❛ss❛r❞ ❡ ❈❤❛r❧❡s ❇❡♥♥❡tt❀
❼ ✶✾✾✶✿ P❤✐❧ ❩✐♠♠❡r♠❛♥♥ ❧❛♥ç❛ ❛ ♣r✐♠❡✐r❛ ✈❡rsã♦ ❞♦ P●P✱ ❝r✐❛♥❞♦ ✉♠ ♠❡✐♦ ❢á❝✐❧ ♣❛r❛ q✉❡ ♣❡ss♦❛s ❝♦♠✉♥s ♣✉❞❡ss❡♠ t❡r ✉♠❛ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❜♦♠ ♥í✈❡❧❀
❼ ✷✵✵✶✿ P✉❜❧✐❝❛çã♦ ❞❛ ❆❊❙ ❝♦♠♦ ❡s❝♦❧❤❛ ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ ❞♦s ór❣ã♦s ❣♦✈❡r♥❛♠❡♥t❛✐s ❛♠❡r✐❝❛♥♦s✳
✷✳✷✳✷ ❙✐st❡♠❛s ❆ss✐♠étr✐❝♦s ❡ ❙✐♠étr✐❝♦s
◆♦ ❝❛s♦ ❞❡ s✐st❡♠❛s s✐♠étr✐❝♦s✱ ❛s ❝❤❛✈❡s ❞❡ ❡♥❝r✐♣t❛çã♦ sã♦ ✐❣✉❛✐s ❛ ❞❡ ❞❡❝♦❞✐✜❝❛çã♦✱ ❝❛✉s❛♥❞♦ ❛ss✐♠✱ q✉❡ ❡❧❛s t❡♥❤❛♠ q✉❡ s❡r tr❛♥s♠✐t✐❞❛s ❛♥t❡s ❞❛ ❝♦♠✉♥✐❝❛çã♦ ❞❛ ♠❡♥s❛❣❡♠ ❡♥✈✐❛❞❛✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❛s ❝❤❛✈❡s s❡r❡♠ ✐❣✉❛✐s ♦ s✐st❡♠❛ é ❝❤❛♠❛❞♦ ❞❡ s✐♠étr✐❝♦✳
◆♦s s✐st❡♠❛s ❛ss✐♠étr✐❝♦s ❛s ❝❤❛✈❡s ❞❡♥♦♠✐♥❛❞❛s ❉ ❡ ❋ sã♦ ❞✐st✐♥t❛s ❡ ❞❡ ❞✐❢í❝✐❧ ❝♦♠♣✉t❛❜✐❧✐❞❛❞❡✳ ◆❡st❡ ❝❛s♦✱ ❛ ❝❤❛✈❡ ❞❡ ❡♥❝r✐♣t❛çã♦ ♣♦❞❡ s❡r ♣ú❜❧✐❝❛✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❝❤❛✈❡ ❞❡ ❞❡❝♦❞✐✜❝❛çã♦ é ❣✉❛r❞❛❞❛✳ ◆✉♠ ❡①❡♠♣❧♦✱ ♦s ✉s✉ár✐♦s ❳ ❡ ❨ tr❛♥s♠✐t❡♠ ✉♠ ❛♦ ♦✉tr♦ s✉❛s ❝❤❛✈❡s ❞❡ ❡♥❝r✐♣t❛çã♦ ♠❛s ❣✉❛r❞❛♠ ❛s s✉❛s ❝❤❛✈❡s ❞❡ ❞❡❝r✐♣t❛çã♦ ❡♠ s❡❣r❡❞♦✳ ❆ss✐♠ s❡♥❞♦ ❛ ♦✉tr❛
♣❛rt❡ ❡♥✈♦❧✈✐❞❛ s❛❜❡ ❝♦♠♦ ❡♥❝r✐♣t❛r ❛ ♠❡♥s❛❣❡♠✱ ♣♦ré♠ ♥ã♦ t❡♠ ❛❝❡ss♦ à ❢✉♥çã♦ ❞❡ ❞❡❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠ ❞❛ ♦✉tr❛ ♣❛rt❡✳❬✼❪
❊st❡ s✐st❡♠❛ ❞❡ ✏tr♦❝❛s✑ ❞❡ ❝❤❛✈❡s é ❝♦♠✉♠❡♥t❡ ❝❤❛♠❛❞♦ ❞❡ s✐st❡♠❛s ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ♦✉ P❑■❬✻❪✳
✷✳✷✳✸ ❙✐st❡♠❛ ❞❡ ❈r✐♣t♦❣r❛✜❛ ❞❡ ❈❤❛✈❡s Pú❜❧✐❝❛s ❡ Pr✐✈❛❞❛s ✭❘❙❆✮
❯♠ ❞♦s s✐st❡♠❛s ❝r✐♣t♦❣rá✜❝♦s ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ❡ ♣r✐✈❛❞❛s ♠❛✐s ❝♦♥❤❡❝✐❞♦ é ♦ ❘❙❆✳ ❙❡✉ ♥♦♠❡ ♣r♦✈ê♠ ❞♦s ❛✉t♦r❡s ❞❡st❡ s✐st❡♠❛ ♦s três ❝♦❧❡❣❛s ❘✳ ▲✳ ❘✐✈❡st✱ ❆✳ ❙❤❛♠✐r ❡ ▲✳ ❆❞❧❡♠❛♥♥ q✉❡ ❡♠ ✶✾✼✽ ❝r✐❛r❛♠ ♦ s✐st❡♠❛ ❞❡♥tr♦ ❞♦ ▼❛ss❛❝❤✉s❡tts ■♥st✐t✉t❡ ♦❢ ❚❡❝❤♥♦❧♦❣②✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡♣♦✐s ❞❛ ❞✐❢✉sã♦ ❞♦ ✉s♦ ❞❛ ✐♥t❡r♥❡t✱ ❡st❡ s❡ t♦r♥♦✉ ♦ ♣r♦t♦❝♦❧♦ ♠❛✐s ✉s❛❞♦✱ s❡♥❞♦ ✉s❛❞♦ ♣r✐♥❝✐✲ ♣❛❧♠❡♥t❡ ❡♠ ♥❛✈❡❣❛❞♦r❡s ❞❡ ✐♥t❡r♥❡t❬✺❪✳
P♦❞❡✲s❡ ❞❡✜♥✐r ✉♠ s✐st❡♠❛ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❞❡ ❝❤❛✈❡s ♣ú❜❧✐❝❛s ❡ ♣r✐✈❛❞❛s ❛tr❛✈és ❞♦s s❡❣✉✐♥t❡s ❝♦♠♣♦♥❡♥t❡s ✭P✱ ❈✱ ❑✱ ❊✱ ❉✮✱ ❝♦♠ ❛s s❡❣✉✐♥t❡s ❞❡✜♥✐çõ❡s✿
✶✳ P é ❝♦♥s✐❞❡r❛❞♦ ♦ ❝♦♥❥✉♥t♦ ♣❧❛✐♥t❡①t ♦✉ ♦ t❡①t♦ ♥ã♦ ❝r✐♣t♦❣r❛❢❛❞♦❀
✷✳ ❈ é ♦ ❝♦♥❥✉♥t♦ ❞❡ t❡①t♦ ❝r✐♣t♦❣r❛❢❛❞♦❀
✸✳ ❑ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❝❤❛✈❡s ✉s❛❞❛s❀
✹✳ ❊ sã♦ ❢❛♠í❧✐❛s ❞❡ ❢✉♥çõ❡s q✉❡ ♥❡st❡ ❝❛s♦ ❡①❡❝✉t❛♠ ♦✉ tr❛♥s❢♦r♠❛♠ ♦ t❡①t♦ ♥ã♦ ❝r✐♣t♦❣r❛❢❛❞♦ ❡♠ t❡①t♦ ❝r✐♣t♦❣r❛❢❛❞♦❀
✺✳ ❉ sã♦ ❢❛♠í❧✐❛s ❞❡ ❢✉♥çõ❡s q✉❡ ♣❡r♠✐t❡♠ ❛ tr❛♥s❢♦r♠❛çã♦ ❞♦ t❡①t♦ ❝r✐♣✲ t♦❣r❛❢❛❞♦ ❡♠ t❡①t♦ ♥ã♦ ❝r✐♣t♦❣r❛❢❛❞♦❀
P❛r❛ ❝❛❞❛ ❢✉♥çã♦ ❞❡ ❝r✐♣t♦❣r❛✜❛ ❡①✐st❡ ✉♠❛ ❢✉♥çã♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ♣❛r❛ ❞❡✲ ❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠✳
P❛r❛ ❡①❡♠♣❧✐✜❝❛r ✉♠ ❞❡st✐♥❛tár✐♦ ❞❡♥♦♠✐♥❛❞♦ ❳ q✉❡r tr❛♥s♠✐t✐r ❛ ♠❡♥✲ s❛❣❡♠ ❞❡♥tr♦ ❞♦ ❝♦♥❥✉♥t♦ ✭P✮ ♣❛r❛ ♦ ❞❡st✐♥❛tár✐♦ ❨✳ P❛r❛ tr❛♥s♠✐t✐r ❡❧❡ ✐r✐❛ ✉s❛r ❛ ❢✉♥çã♦ ✭❊✮ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❛s ❝❤❛✈❡s ✭❦✮ ♣❛r❛ tr❛♥s♠✐t✐r✳ ❊♥q✉❛♥t♦ q✉❡ ♥♦ ♦✉tr♦ ❧❛❞♦ s❡r✐❛ ✉s❛❞❛ ❛s ❢✉♥çõ❡s ✭❉✭❡▼✮✮ ♣❛r❛ ❞❡❝♦❞✐✜❝❛r❬✽❪
✷✳✷✳✹ ❆t❛q✉❡s ♥❛ ❈r✐♣t♦❣r❛✜❛
❉❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❛ ❝r✐♣t♦❣r❛✜❛ t❡♠ ❝♦♠♦ ✐♥t❡r❡ss❡ ♠❛♥t❡r ❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥✜❞❡♥❝✐❛s✱ ❡①✐st❡ t♦❞❛ ✉♠❛ ❝❧❛ss❡ ❡ ✉♠ ❣r✉♣♦ ❞❡ ❛t❛q✉❡s ❞❡st✐♥❛❞♦s ❛ ❞❡❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠ ✱❝♦♠ ♥❡♥❤✉♠❛ ♦✉ ❛❧❣✉♠❛ ✐♥❢♦r♠❛çã♦✱ ❞❛s ❝❤❛✈❡s ❡ ♠ét♦❞♦s ❞❡ ❝r✐♣t♦❣r❛✜❛❬✸❪✳
❖s ♣r✐♥❝✐♣❛✐s t✐♣♦s ❞❡ ❛t❛q✉❡s sã♦✿
❼ ❆t❛q✉❡ ❞❡ t❡①t♦ ❝r✐♣t♦❣r❛❢❛❞♦✿ ♥❡st❡ ❝❛s♦ ♦ ❛t❛❝❛♥t❡ t❡♥t❛ ❞❡s❝♦❜r✐r ❛ ❝❤❛✈❡ ♦✉ t❡①t♦ ❞❡❝♦❞✐✜❝❛❞♦ s♦♠❡♥t❡ ❛tr❛✈és ❞♦ t❡①t♦ ❝r✐♣t♦❣r❛❢❛❞♦❀
❼ ❆t❛q✉❡ ❝♦♠ t❡①t♦ ❞❡s❝r✐♣t♦❣r❛❢❛❞♦ ❝♦♥❤❡❝✐❞♦✿ ♥❡st❡ ❝❛s♦ ♦ ❛t❛❝❛♥t❡ ♣♦ss✉✐ ✉♠❛ ♣❛rt❡ ♦✉ t❡①t♦ ❞❡❝♦❞✐✜❝❛❞♦ ❡ s❡✉ ❝♦rr❡s♣♦♥❞❡♥t❡ t❡①t♦ ❝r✐♣✲ t♦❣r❛❢❛❞♦❀
❼ ❆t❛q✉❡ ❝♦♠ t❡①t♦ ❞❡❝♦❞✐✜❝❛❞♦ ❡s❝♦❧❤✐❞♦✿ ♥❡st❡ ❛t❛q✉❡ é ❡s❝♦❧❤✐❞♦ ✉♠ t❡①t♦ ❞❡❝♦❞✐✜❝❛❞♦ ❡ ❛tr❛✈és ❞❡ ❛t❛q✉❡s sã♦ ❢♦r♥❡❝✐❞♦s t❡①t♦s ❝♦rr❡s♣♦♥✲ ❞❡♥t❡s ❝♦❞✐✜❝❛❞♦s✳ ❆tr❛✈és ❞❡st❡ ♠ét♦❞♦ é t❡♥t❛❞♦ ❞❡s❝♦❜r✐r ♦s ❞❛❞♦s ❞❡ ♦✉tr♦s t❡①t♦s ❞❡❝♦❞✐✜❝❛❞♦s❀
❼ ❆t❛q✉❡ ❝♦♠ t❡①t♦ ❞❡❝♦❞✐✜❝❛❞♦ ❡s❝♦❧❤✐❞♦ ❛❞❛♣t❛❞♦✿ é ❡s❝♦❧❤✐❞♦ ✉♠ t❡①t♦ ❡s♣❡❝í✜❝♦ ❞✉r❛♥t❡ ♦s ❛t❛q✉❡s ♣❡r♠✐t✐♥❞♦ ✉♠❛ ♠❡❧❤♦r ❛♥á❧✐s❡ ❡♠ ❛❧❣✉♥s ❝❛s♦s❀
❼ ❆t❛q✉❡ ❝♦♠ t❡①t♦ ❝♦❞✐✜❝❛❞♦ ❡s❝♦❧❤✐❞♦✿ ♥❡st❡ ❛t❛q✉❡ é s❡❧❡❝✐♦♥❛❞♦ ❡s✲ ♣❡❝✐✜❝❛♠❡♥t❡ ✉♠ t❡①t♦ ❛ s❡r ❝♦❞✐✜❝❛❞♦ ❡ é r❡❝❡❜✐❞♦ ♦ t❡①t♦ ❞❡❝♦❞✐✜✲ ❝❛❞♦✳ ❯s❛❞♦ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❛r❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❝♦❞✐✲ ✜❝❛çã♦ ❛♦♥❞❡ ♥ã♦ s❡ t❡♠ ❛ ❝❤❛✈❡ ❞❡ ❞❡❝♦❞✐✜❝❛çã♦✳ ●❡r❛❧♠❡♥t❡ ✉s❛❞♦ q✉❛♥❞♦ s❡ t❡♠ ❛❝❡ss♦ ❛♦ ❡q✉✐♣❛♠❡♥t♦ ❞❡ ❞❡❝♦❞✐✜❝❛çã♦❀
❼ ❆t❛q✉❡ ❝♦♠ t❡①t♦ ❝♦❞✐✜❝❛❞♦ ❛❞❛♣tá✈❡❧✿ ♥❡st❛ ❝❛s♦ ♦ ❛t❛q✉❡ sã♦ ❢❡✐t♦s ❝♦♠ t❡①t♦s ❝♦❞✐✜❝❛❞♦s ❡s♣❡❝í✜❝♦s ❡ ❝♦♥❢♦r♠❡ s❡ ♣r♦❣r❡❞✐ ♥♦s ❛t❛q✉❡s ❡st❡s t❡①t♦s sã♦ ♠✉❞❛❞♦s ♣❛r❛ ♠❡❧❤♦r ✐♥t❡r♣r❡t❛çã♦ ❞♦s ❞❛❞♦s r❡❝❡✲ ❜✐❞♦s✳
❊st❡s ❛t❛q✉❡s s❡ ❝♦♥❝❡♥tr❛♠ ❜❛s✐❝❛♠❡♥t❡ ♥♦ ♠♦❞❡❧♦ ❞❡ ❝♦❞✐✜❝❛çã♦ ❞❡ t❡①t♦s✱ ❝❛s♦ ♦ ❛t❛q✉❡ s❡❥❛ ❢❡✐t❛ ❡♠ ♣r♦t♦❝♦❧♦s✱ t❡♠✲s❡ ♦s s❡❣✉✐♥t❡s ♠ét♦❞♦s ❞❡ ❛t❛q✉❡✿
❼ ❈❤❛✈❡s ❥á ♣r❡✈✐❛♠❡♥t❡ ❝♦♥❤❡❝✐❞❛s✿ ♥❡st❡ ❛t❛q✉❡ ❥á s❡ ♣♦ss✉✐ ❛❧❣✉♠❛s ❝❤❛✈❡s ♣r❡✈✐❛♠❡♥t❡ ✉s❛❞❛s✱ ❡ ❡❧❛s sã♦ ✉s❛❞❛s ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛s ❝❤❛✈❡s ❞❡ ❞❡❝♦❞✐✜❝❛çã♦ ♥♦✈❛s❀
❼ ❘❡♣r♦❞✉çã♦✿ ♥❡st❡ ❝❛s♦ ✉♠❛ s❡ssã♦ ❞❡ ❝♦❞✐✜❝❛çã♦ é ❣r❛✈❛❞❛ ❡ ✉s❛❞❛ ♣♦st❡r✐♦r♠❡♥t❡ ♣❛r❛ ❛♥á❧✐s❡ ♦✉ ❛t❛q✉❡❀
❼ ■♠♣❡rs♦♥✐✜❝❛çã♦✿ ♥❡st❡ ❛t❛q✉❡ ♦ ❛t❛❝❛♥t❡ s❡ ✐❞❡♥t✐✜❝❛ ❝♦♠♦ ✉♠❛ ♣❛rt❡ ❧❡❣ít✐♠❛ ❞♦ ♣r♦❝❡ss♦✱ ♦❜t❡♥❞♦ ✈❛♥t❛❣❡♥s❀
❼ ❆t❛q✉❡ ♣♦r ❞✐❝✐♦♥ár✐♦✿ ♥❡st❡ ❝❛s♦ ✉♠ ❣r❛♥❞❡ ❞✐❝✐♦♥ár✐♦ ❝♦♠ ❛❧❣✉♠❛s ✈❛r✐❛♥t❡s é ✉s❛❞♦ ♣❛r❛ ❛t❛❝❛r ♦ ♣r♦t♦❝♦❧♦ ❞❡ s❡❣✉r❛♥ç❛❀
❼ ❍♦♠❡♠ ♥♦ ♠❡✐♦✿ ♥❡st❡ ❛t❛q✉❡ ♦ ❛t❛❝❛♥t❡ s❡ ❞✐s❢❛rç❛ ❞❡ ✉♠❛ ♣❛rt❡ ❧❡❣ít✐♠❛ ❡ ❛❣❡ ❝♦♠♦ ✐♥t❡r♠❡❞✐ár✐♦❀
❼ ❆t❛q✉❡ ♣♦r ❞✐❢❡r❡♥ç❛ ❞❡ t❡♠♣♦✿ ❡♠ ❛❧❣✉♠❛s ♦♣❡r❛çã♦ ❞❡ ❝♦❞✐✜❝❛çã♦ ❡ ❞❡❝♦❞✐✜❝❛çã♦ ♦ t❡♠♣♦ ❞❡ ✉♠❛ ❝❤❛✈❡ ❡rr❛❞❛ é ❞✐❢❡r❡♥t❡ ❞❛ ❝❤❛✈❡ ❝❡rt❛✱ ❞❡st❡ ♠♦❞♦ ♦ ❛t❛❝❛♥t❡ ❢❛③ ✉♠❛ ❛♥á❧✐s❡ ❞♦s t❡♠♣♦s ♣❛r❛ ♦❜t❡r ✉♠❛ ✈❛♥t❛❣❡♠❬✾✱ ✸❪❀
❊st❡s sã♦ ♦s ♠♦❞♦s ♣r✐♥❝✐♣❛✐s ❞❡ ❛t❛q✉❡ ✐♠♣♦rt❛♥t❡ ❞❡ s❡ ♥♦t❛r✱ q✉❡ ❝♦♥❢♦r♠❡ ❛s t❡❝♥♦❧♦❣✐❛s ❛✈❛♥ç❛♠✱ ♦✉tr♦s ❛t❛q✉❡s s❡rã♦ ❝r✐❛❞♦s✳
✷✳✷✳✺ ❆✈❛❧✐❛çã♦ ❞❛ ❙❡❣✉r❛♥ç❛ ❞❡ ❙✐st❡♠❛s ❈r✐♣t♦❣rá✜❝♦s
❆ s❡❣✉r❛♥ç❛ ❞♦s s✐st❡♠❛s ❝r✐♣t♦❣rá✜❝♦s ❡ ♣r♦t♦❝♦❧♦s ♣♦❞❡♠ s❡r r❡❛❧✐③❛❞❛s ❞❡ ✈ár✐❛s ❢♦r♠❛s✳ ❆ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✱ ❛tr❛✈és ❞❡ ♣❡sq✉✐s❛s✱ t❡♥t❛ ❛✈❛❧✐❛r ❛ s❡❣✉r❛♥ç❛ ❞❡ ✉♠ s✐st❡♠❛ ❝r✐♣t♦❣rá✜❝♦ ❞❡ ❞✐✈❡rs❛s ❢♦r♠❛s✳ ❚❡♠✲s❡ ❝♦♠♦ ❛s ♣r✐♥❝✐♣❛✐s✱ ♦s s❡❣✉✐♥t❡s ♠♦❞❡❧♦s ❞❡ ❛✈❛❧✐❛çã♦❬✸❪✿
❼ ❙❡❣✉r❛♥ç❛ ✐♥❝♦♥❞✐❝✐♦♥❛❧ ♦✉ ❝♦♥✜❞❡♥❝✐❛❧✐❞❛❞❡ ♣❡r❢❡✐t❛✿ ♥❡st❡ ❝❛s♦ é ✉♠❛ ❢♦r♠❛ ❞❡ ♠♦❞❡❧❛❣❡♠ t❡ór✐❝❛ q✉❡ t❡♥t❛ ❛✈❛❧✐❛r q✉❡ ♦ ❛t❛❝❛♥t❡ ♣♦ss✉✐ ✐♥✜♥✐t♦s r❡❝✉rs♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ ❡ s❡ ❡❧❡ ❝♦♥s❡❣✉❡ ♦✉ ♥ã♦ ❞❡❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠ ❛tr❛✈és s♦♠❡♥t❡ ❞♦ t❡①t♦ ❝♦❞✐✜❝❛❞♦✳ ◆❡st❡ ❝❛s♦✱ ♣r✐♥✲ ❝✐♣❛❧♠❡♥t❡ ❛ ♦❜s❡r✈❛çã♦ ❞♦ t❡①t♦ ❝r✐♣t♦❣r❛❢❛❞♦ ♥ã♦ ♣r♦❞✉③ ♥❡♥❤✉♠
♣❛❞rã♦ ♣❡r❝❡♣tí✈❡❧ ♣❛r❛ ❛ ❞❡❝♦❞✐✜❝❛çã♦ ❞♦ t❡①t♦✳ ❊st❛ ♣❡r❢❡✐t❛ ❝♦♥✜✲ ❞❡♥❝✐❛❧✐❞❛❞❡ s❡ t♦r♥❛ ❝❛❞❛ ✈❡③ ♠❛✐s ❢r❛❝❛ ❝♦♥❢♦r♠❡ ♦ ♥ú♠❡r♦ ❞❡ t❡①t♦s ❝r✐♣t♦❣r❛❢❛❞♦s ❛✉♠❡♥t❛♠❀
❼ ❈♦♠♣❧❡①✐❞❛❞❡ t❡ór✐❝❛✿ ♥❡st❡ ♠♦❞❡❧♦ ❛ ❝♦❞✐✜❝❛çã♦ s❡ ✉t✐❧✐③❛ ❞❡ ♠ét♦❞♦s ♠❛t❡♠át✐❝♦s ♦♥❞❡ ✱♥♦ ♣✐♦r ❞♦s ❝❛s♦s✱ ❛ss✉♠❡ q✉❡ ♦ ❛t❛❝❛♥t❡ t❡♠ ✉♠ ❛❧t♦ ❣r❛✉ ❞❡ ❝❛♣❛❝✐❞❛❞❡ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❛✐♥❞❛ é ✐♠♣r❛t✐❝á✈❡❧ ❛ ❞❡❝♦❞✐✲ ✜❝❛çã♦ ♦✉ ❛t❛q✉❡ ❞♦ s✐st❡♠❛ ❝r✐♣t♦❣rá✜❝♦❀
❼ ❙❡❣✉r❛♥ç❛ ♣r♦✈á✈❡❧✿ ♥❡st❡ ❝❛s♦ ♦ s✐st❡♠❛ ❝r✐♣t♦❣rá✜❝♦ é ❝♦♥s✐❞❡r❛❞♦ s❡✲ ❣✉r♦ ♣❡❧♦ ❢❛t♦ ❞❡ s❡r s✉♣♦st❛♠❡♥t❡ tã♦ ❞✐❢í❝✐❧ ❞❡ s❡r ❝♦♠♣✉t❛❞♦ q✉❛♥t♦ ❛ ✉♠ ♦✉tr♦ ♣r♦❜❧❡♠❛ ❞❡ ❞✐❢í❝✐❧ ❝♦♠♣✉t❛❜✐❧✐❞❛❞❡❀
❼ ❙❡❣✉r❛♥ç❛ ❝♦♠♣✉t❛❝✐♦♥❛❧✿ é ♠❡❞✐❞❛ ❛ ♠❡❧❤♦r ❝❛♣❛❝✐❞❛❞❡ ❝♦♠♣✉t❛✲ ❝✐♦♥❛❧✱ ❞❡♥tr♦ ❞♦s ♠❡❧❤♦r❡s ♠ét♦❞♦s ❡ ❡♥tã♦ ❛tr❛✈és ❞❡ ✉♠❛ ❣r❛♥❞❡ ♠❛r❣❡♠ ❞❡ s❡❣✉r❛♥ç❛ é ❞❡✜♥✐❞❛ ❛ s❡❣✉r❛♥ç❛ ❞♦ s✐st❡♠❛ ❢r❡♥t❡ ❛ ✉♠ ❛t❛❝❛♥t❡✳ ❊st❛ ❝❛r❛❝t❡ríst✐❝❛ é ♠❛✐s ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ s❡❣✉r❛♥ç❛ ♣rát✐❝❛✳ ■♠♣♦rt❛♥t❡ ♥♦t❛r ✐ss♦ ❛tr❛✈és ❞♦ ❛✈❛♥ç♦ ❞❛ t❡❝♥♦❧♦❣✐❛ ❡ ❞❡ ♥♦✈❛s ❢♦r♠❛s ❞❡ ❝♦♠♣✉t❛çã♦❀
❼ ❙❡❣✉r❛♥ç❛ ❆❞ ❍♦❝✿ ♥❡st❡ ♠♦❞❡❧♦ ❞❡ s❡❣✉r❛♥ç❛✱ s❡ s✉♣õ❡ q✉❡ ♦ ❛t❛❝❛♥t❡ ❞❡✈❡rá t❡r ❛❧❣✉♠ r❡❝✉rs♦ ❝♦♠♦ t❡♠♣♦ ♦✉ ❡s♣❛ç♦ s✉♣❡r✐♦r ❛♦ t❡♠♣♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❞❡❝♦❞✐✜❝❛r ❛ ♠❡♥s❛❣❡♠✳
✷✳✷✳✻ Pr♦❝❡ss♦ ❞❡ ❡s❝♦❧❤❛ P❛❞rã♦ ❆❊❙
❉❡♣♦✐s ❞❡ ❛❧❣✉♠❛s ♣❡sq✉✐s❛s ✐♥❞✐❝❛♥❞♦ q✉❡ ♦ ❉❊❙ ✭❉❛t❛ ❊♥❝r②♣t✐♦♥ ❙t❛♥✲ ❞❛r❞✮✱ ♣❛❞rã♦ ✉s❛❞♦ ♣❡❧♦ ❣♦✈❡r♥♦ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ♣❛r❛ ❝r✐♣t♦❣r❛✜❛ ❡♠ ❞♦❝✉♠❡♥t♦s ♥ã♦ ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦ ❞❡ ❛❧tíss✐♠❛ s❡❣✉r❛♥ç❛✱ ❢♦r❛♠ ♣✉❜❧✐❝❛❞❛s❬✶✵❪ ♦ ❣♦✈❡r♥♦ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ♥✉♠ ❡s❢♦rç♦ ❝♦♠ ❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ❣❧♦❜❛❧✱ ❧❛♥ç♦✉ ♦ ❞❡s❛✜♦ ❝❤❛♠❛❞♦ ❆❊❙ ✭❆❞✈❛♥❝❡❞ ❊♥❝r②♣t✐♦♥ ❙t❛♥❞❛r❞✮ q✉❡ ✐r✐❛ ❡s❝♦❧❤❡r ♦ s✉❝❡ss♦r ❞♦ ❉❊❙❬✹❪✳
❊st❡ ♣r♦❝❡ss♦ ❞❡ ❡s❝♦❧❤❛ ✐♥✐❝✐♦✉✲s❡ ❡♠ ✶✾✾✼ ❝♦♠ ✐♥✐❝✐❛t✐✈❛ ❞♦ ◆■❙❚✱ ❞❡✲ ♣❛rt❛♠❡♥t♦ r❡s♣♦♥sá✈❡❧ ♣❡❧❛s ♣❛❞r♦♥✐③❛çõ❡s ❡ ♣r♦❝❡ss♦s ❞❡st❡ t✐♣♦✳ ❉❡♥✲ tr♦ ❞❡st❛ ♣r✐♠❡✐r❛ ❝❤❛♠❛❞❛ ❢♦r❛♠ ❡st❛❜❡❧❡❝✐❞♦s ❛❧❣✉♥s ♣❛râ♠❡tr♦s ♠í♥✐♠♦s ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✿
✶✳ ❇❧♦❝♦ ♠í♥✐♠♦ ❞❡ ❞❛❞♦s✿ ✶✷✽ ❜✐ts❀
✷✳ ❚❛♠❛♥❤♦ ♠í♥✐♠♦ ❞❡ ❝❤❛✈❡s✿ ✶✷✽✱ ✶✾✷ ❡ ✷✺✻ ❜✐ts❀
✸✳ ❙❡♠ ❝♦❜r❛♥ç❛ ❞❡ ❘♦②❛❧t✐❡s ♦✉ ❧✐❝❡♥ç❛s❀
✹✳ P❛r❛ ✉s♦ ♣ú❜❧✐❝♦ ❡ ❞❡ ❣r❛ç❛❀
■♥✐❝✐❛❞♦ ♦ ♣r♦❝❡ss♦✱ ❢♦r❛♠ s✉❜♠❡t✐❞♦s q✉✐♥③❡ ❝❛♥❞✐❞❛❞♦s ❞❡ ❞✐✈❡rs♦s ♣❛ís❡s ❝♦♥❢♦r♠❡ t❛❜❡❧❛ ✷✳
❚❛❜❡❧❛ ✷✿ ❈❛♥❞✐❞❛❞♦s ■♥✐❝✐❛s ♣❛r❛ ♦ ❆❊❙ P❛ís ❆❧❣♦r✐t♠♦ ❆✉t♦r
❆✉strá❧✐❛ ▲❖❑■✾✼ ▲❛✇r✐❡ ❇r♦✇♥✱ ❏♦s❡❢ P✐❡♣r③②❦✱ ❏❡♥♥✐❢❡r ❙❡❜❡rr② ❇é❧❣✐❝❛ ❘■❏◆❉❆❊▲ ❏♦❛♥ ❉❛❡♠❡♥✱ ❱✐♥❝❡♥t
❘✐❥♠❡♥
❈❛♥❛❞❛ ❈❆❙❚✲✷✺✻ ❊♥tr✉st ❚❡❝❤♥♦❧♦❣✐❡s✱ ■♥❝✳ ❈❛♥❛❞❛ ❉❊❆▲ ❘✐❝❤❛r❞ ❖✉t❡r❜r✐❞❣❡✱ ▲❛rs
❑♥✉❞s❡♥
❈♦st❛ ❘✐❝❛ ❋❘❖● ❚❡❝❆♣r♦ ■♥t❡r♥❛❝✐♦♥❛❧ ❙✳❆✳ ❋r❛♥ç❛ ❉❋❈ ❈❡♥tr❡ ◆❛t✐♦♥❛❧ ♣♦✉r ❧❛
❘❡❝❤❡r❝❤❡ ❙❝✐❡♥t✐✜q✉❡ ✭❈◆❘❙✮
❆❧❡♠❛♥❤❛ ▼❆●❊◆❚❆ ❉❡✉ts❝❤❡ ❚❡❧❡❦♦♠ ❆● ❏❛♣ã♦ ❊✷ ◆✐♣♣♦♥ ❚❡❧❡❣r❛♣❤ ❛♥❞ ❚❡❧❡♣❤♦♥❡ ❈♦r♣♦r❛t✐♦♥ ✭◆❚❚✮
❈♦ré✐❛ ❈❘❨P❚❖◆ ❋✉t✉r❡ ❙②st❡♠s✱ ■♥❝✳
❊❯❆ ❍P❈ ❘✐❝❤ ❙❝❤r♦❡♣♣❡❧
❊❯❆ ▼❆❘❙ ■❇▼
❊❯❆ ❘❈✻ ❘❙❆ ▲❛❜♦r❛t♦r✐❡s
❊❯❆ ❙❆❋❊❘✰ ❈②❧✐♥❦ ❈♦r♣♦r❛t✐♦♥ ❊❯❆ ❚❲❖❋■❙❍ ❇r✉❝❡ ❙❝❤♥❡✐❡r✱ ❏♦❤♥
❑❡❧s❡②✱ ❉♦✉❣ ❲❤✐t✐♥❣✱✳ ❉❛✈✐❞ ❲❛❣♥❡r✱ ❈❤r✐s ❍❛❧❧✱ ◆✐❡❧s ❋❡r❣✉s♦♥
❯❑✱ ■sr❛❡❧✱ ◆♦r✉❡❣❛ ❙❊❘P❊◆❚ ❘♦ss ❆♥❞❡rs♦♥✱ ❊❧✐ ❇✐❤❛♠✱ ◆♦r✇❛② ▲❛rs ❑♥✉❞s❡♥
