Prt rt - - PowerPoint PPT Presentation

❑❡② Pr❡❞✐❝t✐♦♥ ❙❡❝✉r✐t② ♦❢ ❑❡②❡❞ ❙♣♦♥❣❡s

❇❛rt ▼❡♥♥✐♥❦ ❘❛❞❜♦✉❞ ❯♥✐✈❡rs✐t② ✭❚❤❡ ◆❡t❤❡r❧❛♥❞s✮ ❋❛st ❙♦❢t✇❛r❡ ❊♥❝r②♣t✐♦♥ ✷✵✶✾ ▼❛r❝❤ ✷✻✱ ✷✵✶✾

✶ ✴ ✶✽

❙♣♦♥❣❡s ❬❇❉P❱✵✼❪

M pad trunc Z

• uter

inner r c f f f f f f absorbing squeezing

m pad trunc z r π π π π π π c

• ❈r②♣t♦❣r❛♣❤✐❝ ❤❛s❤ ❢✉♥❝t✐♦♥
• ❙❍❆✲✸✱ ❳❖❋s✱ ❧✐❣❤t✇❡✐❣❤t ❤❛s❤✐♥❣✱ ✳ ✳ ✳
• ❇❡❤❛✈❡s ❛s ❘❖ ✉♣ t♦ q✉❡r② ❝♦♠♣❧❡①✐t② ≈ 2c/2 ❬❇❉P❱✵✽❪

✷ ✴ ✶✽

❑❡②❡❞ ❙♣♦♥❣❡s

M pad trunc Z

• uter

inner r c f f f f f f absorbing squeezing

Km pad trunc z r π π π π π π c

• ❖✉t❡r✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❇❉P❱✶✶✱❆❉▼❱✶✺✱◆❨✶✻❪

■♥♥❡r✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❈❉❍❑◆✶✷✱❆❉▼❱✶✺✱◆❨✶✻❪ ❋✉❧❧✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❇❉P❱✶✷✱●P❚✶✺✱▼❘❱✶✺❪

✸ ✴ ✶✽

❑❡②❡❞ ❙♣♦♥❣❡s

M pad trunc Z

• uter

inner r c f f f f f f absorbing squeezing

m pad trunc z r π π π π π π c K

• ❖✉t❡r✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❇❉P❱✶✶✱❆❉▼❱✶✺✱◆❨✶✻❪
• ■♥♥❡r✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❈❉❍❑◆✶✷✱❆❉▼❱✶✺✱◆❨✶✻❪

❋✉❧❧✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❇❉P❱✶✷✱●P❚✶✺✱▼❘❱✶✺❪

✸ ✴ ✶✽

❑❡②❡❞ ❙♣♦♥❣❡s

M pad trunc Z r c f f f f f f absorbing squeezing

m pad trunc z r π π π π π π c K

• ❖✉t❡r✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❇❉P❱✶✶✱❆❉▼❱✶✺✱◆❨✶✻❪
• ■♥♥❡r✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❈❉❍❑◆✶✷✱❆❉▼❱✶✺✱◆❨✶✻❪
• ❋✉❧❧✲❑❡②❡❞ ❙♣♦♥❣❡ ❬❇❉P❱✶✷✱●P❚✶✺✱▼❘❱✶✺❪

✸ ✴ ✶✽

❙❡❝✉r✐t② ♦❢ ❑❡②❡❞ ❙♣♦♥❣❡

π π π π π

• K1

Kλ m1 mµ z1 z2

c′ c′ c′ c′ c c

• F ∈ {OKS, FKS}

✿ ❞❛t❛ ✭❝♦♥str✉❝t✐♦♥✮ ❝♦♠♣❧❡①✐t② ✿ t✐♠❡ ✭♣r✐♠✐t✐✈❡✮ ❝♦♠♣❧❡①✐t② ❙✐♠♣❧✐✜❡❞ ❙❡❝✉r✐t② ❇♦✉♥❞

✲

✹ ✴ ✶✽

− →

c ❢♦r F = OKS ❛♥❞ 0 ❢♦r F = FKS

♣r♦❜❛❜✐❧✐t② t❤❛t ❛❞✈❡rs❛r② ♣r❡❞✐❝ts ❦❡②

❙❡❝✉r✐t② ♦❢ ❑❡②❡❞ ❙♣♦♥❣❡

π π π π π

• K1

Kλ m1 mµ z1 z2

c′ c′ c′ c′ c c

• F ∈ {OKS, FKS}
• M✿ ❞❛t❛ ✭❝♦♥str✉❝t✐♦♥✮ ❝♦♠♣❧❡①✐t②
• N✿ t✐♠❡ ✭♣r✐♠✐t✐✈❡✮ ❝♦♠♣❧❡①✐t②

❙✐♠♣❧✐✜❡❞ ❙❡❝✉r✐t② ❇♦✉♥❞ M2 2c + MN 2c + Advkey✲pre

F

(N)

✹ ✴ ✶✽

− →

c ❢♦r F = OKS ❛♥❞ 0 ❢♦r F = FKS

♣r♦❜❛❜✐❧✐t② t❤❛t ❛❞✈❡rs❛r② ♣r❡❞✐❝ts ❦❡②

❙❡❝✉r✐t② ♦❢ ❑❡②❡❞ ❙♣♦♥❣❡

π π π π π

• K1

Kλ m1 mµ z1 z2

c′ c′ c′ c′ c c

• F ∈ {OKS, FKS}
• M✿ ❞❛t❛ ✭❝♦♥str✉❝t✐♦♥✮ ❝♦♠♣❧❡①✐t②
• N✿ t✐♠❡ ✭♣r✐♠✐t✐✈❡✮ ❝♦♠♣❧❡①✐t②

❙✐♠♣❧✐✜❡❞ ❙❡❝✉r✐t② ❇♦✉♥❞ M2 2c + MN 2c + Advkey✲pre

F

(N)

✹ ✴ ✶✽

− →

c ❢♦r F = OKS ❛♥❞ 0 ❢♦r F = FKS

♣r♦❜❛❜✐❧✐t② t❤❛t ❛❞✈❡rs❛r② ♣r❡❞✐❝ts ❦❡②

❑❡② Pr❡❞✐❝t✐♦♥ ❙❡❝✉r✐t②

π π π π π

• K1

Kλ m1 mµ z1 z2

c′ c′ c′ c′ c c

Advkey✲pre

F

(N)

• ❆❞✈❡rs❛r② ♠❛❦❡s N q✉❡r✐❡s t♦ π
• ❑❡② K r❛♥❞♦♠❧② ❞r❛✇♥
• ❆❞✈❡rs❛r② ✇✐♥s ✐❢ q✉❡r② ❤✐st♦r② ✏❝♦✈❡rs K✑

✺ ✴ ✶✽

❑❡② Pr❡❞✐❝t✐♦♥ ❙❡❝✉r✐t②✿ ❊①✐st✐♥❣ ❇♦✉♥❞s

π π π π π

• K1

m1 m2 mµ z1 z2

c′ c′ c′ c′ c c

❖♥❡ ❑❡② ❇❧♦❝❦

• ❆❞✈❡rs❛r② ♠❛❦❡s N q✉❡r✐❡s
• ◗✉❡r② ❤✐st♦r② ❝♦✈❡rs ❛t ♠♦st N ❦❡②s

Advkey✲pre

F

(N) ≤ N 2k ▼♦r❡ ❚❤❛♥ ❖♥❡ ❑❡② ❇❧♦❝❦ ❇② ●❛➸✐ ❡t ❛❧✳ ❬●P❚✶✺❪ ❯s❡❞ ✐♥ ♠❛♥② s♣♦♥❣❡ ♣r♦♦❢s

✲

✻ ✴ ✶✽

❑❡② Pr❡❞✐❝t✐♦♥ ❙❡❝✉r✐t②✿ ❊①✐st✐♥❣ ❇♦✉♥❞s

π π π π π

• K1

Kλ m1 mµ z1 z2

c′ c′ c′ c′ c c

❖♥❡ ❑❡② ❇❧♦❝❦

• ❆❞✈❡rs❛r② ♠❛❦❡s N q✉❡r✐❡s
• ◗✉❡r② ❤✐st♦r② ❝♦✈❡rs ❛t ♠♦st N ❦❡②s

Advkey✲pre

F

(N) ≤ N 2k ▼♦r❡ ❚❤❛♥ ❖♥❡ ❑❡② ❇❧♦❝❦

• ❇② ●❛➸✐ ❡t ❛❧✳ ❬●P❚✶✺❪
• ❯s❡❞ ✐♥ ♠❛♥② s♣♦♥❣❡ ♣r♦♦❢s

Advkey✲pre

F

(N) bλN 2k/2

✻ ✴ ✶✽

❑❡② Pr❡❞✐❝t✐♦♥ ❙❡❝✉r✐t②✿ ■♠♣❧✐❝❛t✐♦♥ ❢♦r ❖❑❙

π π π π π

• K1

Kλ m1 mµ z1 z2

c c c c c c

❈❛s❡ ♦❢ (b, c, r, k) = (320, 256, 64, 64) M2 2c + MN 2c + N 2k = M2 2256 + MN 2256 + N 264 ❈❛s❡ ♦❢ (b, c, r, k) = (320, 256, 64, 128) M2 2c + MN 2c + N 2k/2 = M2 2256 + MN 2256 + N 264

✼ ✴ ✶✽

◆❡✇ ❆♥❛❧②s✐s

π π π π π

• K1

Kλ m1 mµ z1 z2

c′ c′ c′ c′ c c

Advkey✲pre

F

(N) cλ−1N 2k

• ▲♦ss c ❞✉❡ t♦ ❧✉❝❦② ♠✉❧t✐✲❝♦❧❧✐s✐♦♥s ✭✐♥ ♦❧❞ ❜♦✉♥❞✿ b✮
• 2k ✐♥ ❞❡♥♦♠✐♥❛t♦r ✭✐♥ ♦❧❞ ❜♦✉♥❞✿ 2k/2✮
• ❇❡st ❛tt❛❝❦✿ ❛r♦✉♥❞ 2k q✉❡r✐❡s

✽ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❚r❡❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❛s ✐♥ ❬●P❚✶✺❪✮

V0 V1 V2 V3

• 0b

❣♦❛❧✿ ❜♦✉♥❞ ★ ♣❛t❤s ❢r♦♠ t♦

✾ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❚r❡❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❛s ✐♥ ❬●P❚✶✺❪✮

V0 V1 V2 V3

• 0b
• u

L

❣♦❛❧✿ ❜♦✉♥❞ ★ ♣❛t❤s ❢r♦♠ t♦

✾ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❚r❡❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❛s ✐♥ ❬●P❚✶✺❪✮

V0 V1 V2 V3

• 0b
• u
• L

❣♦❛❧✿ ❜♦✉♥❞ ★ ♣❛t❤s ❢r♦♠ t♦

✾ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❚r❡❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❛s ✐♥ ❬●P❚✶✺❪✮

V0 V1 V2 V3

• 0b
• u
• L

❣♦❛❧✿ ❜♦✉♥❞ ★ ♣❛t❤s ❢r♦♠ t♦

✾ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❚r❡❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❛s ✐♥ ❬●P❚✶✺❪✮

V0 V1 V2 V3

• 0b
• u
• L

❣♦❛❧✿ ❜♦✉♥❞ ★ ♣❛t❤s ❢r♦♠ t♦

✾ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❚r❡❡✲❜❛s❡❞ ❛♣♣r♦❛❝❤ ✭❛s ✐♥ ❬●P❚✶✺❪✮

V0 V1 V2 V3

• 0b
• u
• L
• ❣♦❛❧✿ ❜♦✉♥❞ ★ ♣❛t❤s ❢r♦♠ V0 t♦ V3

✾ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❋✐① ❛♥② q✉❡r② ❢r♦♠ V2 t♦ V3✿ N ♦♣t✐♦♥s

❚❤✐s q✉❡r② ✜①❡s ✐♥♥❡r ♣❛rt ♦❢ s❡❝♦♥❞✲❧❛st ❧❛②❡r

❝♦♥✜❣✳ ✿ ❝♦♥✜❣✳ ✿ ❝♦♥✜❣✳ ✿ ❝♦♥✜❣✳ ✿

❈♦♥s✐❞❡r ❝♦♥✜❣✉r❛t✐♦♥s ❢♦r t❤❡s❡ ❧❛②❡rs

❆rr♦✇s ✐♥❞✐❝❛t❡ q✉❡r② ❞✐r❡❝t✐♦♥✱ ❝✐r❝❧❡s ✐♥❞✐❝❛t❡ ✐♥♥❡r ❝♦❧❧✐s✐♦♥s

■♥❞✉❝t✐✈❡ r❡❛s♦♥✐♥❣ ♦♥ ♥♦♥✲♦❝❝✉rr❡♥❝❡ ♦❢ ✲❢♦❧❞ ❝♦❧❧✐s✐♦♥s

✶✵ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❋✐① ❛♥② q✉❡r② ❢r♦♠ V2 t♦ V3✿ N ♦♣t✐♦♥s
• ❚❤✐s q✉❡r② ✜①❡s ✐♥♥❡r ♣❛rt ♦❢ s❡❝♦♥❞✲❧❛st ❧❛②❡r

V0 V1 V2

• 0b
• ⌊v2⌋c

= w ❝♦♥✜❣✳ ✿ ❝♦♥✜❣✳ ✿ ❝♦♥✜❣✳ ✿ ❝♦♥✜❣✳ ✿

❈♦♥s✐❞❡r ❝♦♥✜❣✉r❛t✐♦♥s ❢♦r t❤❡s❡ ❧❛②❡rs

❆rr♦✇s ✐♥❞✐❝❛t❡ q✉❡r② ❞✐r❡❝t✐♦♥✱ ❝✐r❝❧❡s ✐♥❞✐❝❛t❡ ✐♥♥❡r ❝♦❧❧✐s✐♦♥s

■♥❞✉❝t✐✈❡ r❡❛s♦♥✐♥❣ ♦♥ ♥♦♥✲♦❝❝✉rr❡♥❝❡ ♦❢ ✲❢♦❧❞ ❝♦❧❧✐s✐♦♥s

✶✵ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❋✐① ❛♥② q✉❡r② ❢r♦♠ V2 t♦ V3✿ N ♦♣t✐♦♥s
• ❚❤✐s q✉❡r② ✜①❡s ✐♥♥❡r ♣❛rt ♦❢ s❡❝♦♥❞✲❧❛st ❧❛②❡r

V0 V1 V2

• 0b
• ⌊v2⌋c

= w V0 V1 V2

• ❝♦♥✜❣✳ 00✿

❝♦♥✜❣✳ 01✿ ❝♦♥✜❣✳ 10✿ ❝♦♥✜❣✳ 11✿

• ❈♦♥s✐❞❡r ❝♦♥✜❣✉r❛t✐♦♥s ❢♦r t❤❡s❡ ❧❛②❡rs
• ❆rr♦✇s ✐♥❞✐❝❛t❡ q✉❡r② ❞✐r❡❝t✐♦♥✱ ❝✐r❝❧❡s ✐♥❞✐❝❛t❡ ✐♥♥❡r ❝♦❧❧✐s✐♦♥s

■♥❞✉❝t✐✈❡ r❡❛s♦♥✐♥❣ ♦♥ ♥♦♥✲♦❝❝✉rr❡♥❝❡ ♦❢ ✲❢♦❧❞ ❝♦❧❧✐s✐♦♥s

✶✵ ✴ ✶✽

Pr♦♦❢ ■❞❡❛

• ❋✐① ❛♥② q✉❡r② ❢r♦♠ V2 t♦ V3✿ N ♦♣t✐♦♥s
• ❚❤✐s q✉❡r② ✜①❡s ✐♥♥❡r ♣❛rt ♦❢ s❡❝♦♥❞✲❧❛st ❧❛②❡r

V0 V1 V2

• 0b
• ⌊v2⌋c

= w V0 V1 V2

• ❝♦♥✜❣✳ 00✿

❝♦♥✜❣✳ 01✿ ❝♦♥✜❣✳ 10✿ ❝♦♥✜❣✳ 11✿

• ❈♦♥s✐❞❡r ❝♦♥✜❣✉r❛t✐♦♥s ❢♦r t❤❡s❡ ❧❛②❡rs
• ❆rr♦✇s ✐♥❞✐❝❛t❡ q✉❡r② ❞✐r❡❝t✐♦♥✱ ❝✐r❝❧❡s ✐♥❞✐❝❛t❡ ✐♥♥❡r ❝♦❧❧✐s✐♦♥s
• ■♥❞✉❝t✐✈❡ r❡❛s♦♥✐♥❣ ♦♥ ♥♦♥✲♦❝❝✉rr❡♥❝❡ ♦❢ αi✲❢♦❧❞ ❝♦❧❧✐s✐♦♥s

✶✵ ✴ ✶✽

❋✉rt❤❡r ❆♣♣❧✐❝❛t✐♦♥ t♦ ❉✉♣❧❡①

r c

• uter

inner initialize pad trunc f duplexing σ0 Z0 pad trunc f duplexing σ1 Z1 pad trunc f duplexing σ2 Z2 …

σ0 z0 σ1 z1 σ2 z2 pad trunc pad trunc pad trunc r π π π c

• ❯♥❦❡②❡❞ ❉✉♣❧❡① ❬❇❉P❱✶✶❪

❖✉t❡r✲❑❡②❡❞ ❉✉♣❧❡① ❬❇❉P❱✶✶❪ ❋✉❧❧✲❑❡②❡❞ ❉✉♣❧❡① ❬▼❘❱✶✺✱❉▼❱✶✼❪

✶✶ ✴ ✶✽

❋✉rt❤❡r ❆♣♣❧✐❝❛t✐♦♥ t♦ ❉✉♣❧❡①

r c

• uter

inner initialize pad trunc f duplexing σ0 Z0 pad trunc f duplexing σ1 Z1 pad trunc f duplexing σ2 Z2 …

Kσ0 z0 σ1 z1 σ2 z2 pad trunc pad trunc pad trunc r π π π c

• ❯♥❦❡②❡❞ ❉✉♣❧❡① ❬❇❉P❱✶✶❪
• ❖✉t❡r✲❑❡②❡❞ ❉✉♣❧❡① ❬❇❉P❱✶✶❪

❋✉❧❧✲❑❡②❡❞ ❉✉♣❧❡① ❬▼❘❱✶✺✱❉▼❱✶✼❪

✶✶ ✴ ✶✽

❋✉rt❤❡r ❆♣♣❧✐❝❛t✐♦♥ t♦ ❉✉♣❧❡①

r c initialize pad trunc f duplexing σ0 Z0 pad trunc f duplexing σ1 Z1 pad trunc f duplexing σ2 Z2 … …

∀i : τi ≤ r

σ0 z0 σ1 z1 σ2 z2 pad

truncτ0

pad

truncτ1

pad

truncτ2

r π π π c K

• ❯♥❦❡②❡❞ ❉✉♣❧❡① ❬❇❉P❱✶✶❪
• ❖✉t❡r✲❑❡②❡❞ ❉✉♣❧❡① ❬❇❉P❱✶✶❪
• ❋✉❧❧✲❑❡②❡❞ ❉✉♣❧❡① ❬▼❘❱✶✺✱❉▼❱✶✼❪

✶✶ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❉✉♣❧❡①

❇♦✉♥❞s ❘❡❞✉❝❡ ❇✐✲❉✐r❡❝t✐♦♥❛❧❧② ❬▼❘❱✶✺✱❉▼❱✶✼❪ OKS ❛♥❞ OKD: M2 2c + MN 2c + Advkey✲pre

OKS

(N) FKS ❛♥❞ FKD: M2 2c + MN 2c + Advkey✲pre

FKS

(N) ❙❛♠❡ ❢♦r ◆♦♥❝❡✲❘❡s♣❡❝t✐♥❣ ❙❡tt✐♥❣ ❬❏▲▼✶✹✱❉▼❱✶✼❪ OKS ❛♥❞ OKD: M2 2b + N 2c + Advkey✲pre

OKS

(N) FKS ❛♥❞ FKD: M2 2b + N 2c + Advkey✲pre

FKS

(N)

✶✷ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❈❆❊❙❆❘

❈❆❊❙❆❘ ❈♦♠♣❡t✐t✐♦♥

• ❋♦✉r t❤✐r❞✲r♦✉♥❞ ❝❛♥❞✐❞❛t❡s ❜❛s❡❞ ♦♥ ❞✉♣❧❡①

s❝❤❡♠❡ b c r k ❆s❝♦♥ ❬❉❊▼❙✶✻❪ ✸✷✵ ✷✺✻ ✻✹ ✶✷✽ ✸✷✵ ✶✾✷ ✶✷✽ ✶✷✽ ❑❡t❥❡ ❬❇❉P✰✶✻❪ ✷✵✵ ✶✽✹ ✶✻ ✾✷ ✹✵✵ ✸✻✽ ✸✷ ✶✷✽ ❑❡②❛❦ ❬❇❉P✰✶✻❪ ✽✵✵ ✷✺✻ ✺✹✹ ✶✷✽✳✳✷✷✹ ✶✻✵✵ ✷✺✻ ✶✸✹✹ ✶✷✽✳✳✷✷✹ ◆❖❘❳ ❬❆❏◆✶✻❪ ✺✶✷ ✶✷✽ ✸✽✹ ✶✷✽ ✶✵✷✹ ✷✺✻ ✼✻✽ ✷✺✻

■♥✐t✐❛❧✐③❡ ❡♥t✐r❡ st❛t❡ ✉s✐♥❣ ❦❡② ✭ ❢♦r ❦❡②✮

✶✸ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❈❆❊❙❆❘

❈❆❊❙❆❘ ❈♦♠♣❡t✐t✐♦♥

• ❋♦✉r t❤✐r❞✲r♦✉♥❞ ❝❛♥❞✐❞❛t❡s ❜❛s❡❞ ♦♥ ❞✉♣❧❡①

s❝❤❡♠❡ b c r k ❆s❝♦♥ ❬❉❊▼❙✶✻❪ ✸✷✵ ✷✺✻ ✻✹ ✶✷✽ ✸✷✵ ✶✾✷ ✶✷✽ ✶✷✽ ❑❡t❥❡ ❬❇❉P✰✶✻❪ ✷✵✵ ✶✽✹ ✶✻ ✾✷ ✹✵✵ ✸✻✽ ✸✷ ✶✷✽ ❑❡②❛❦ ❬❇❉P✰✶✻❪ ✽✵✵ ✷✺✻ ✺✹✹ ✶✷✽✳✳✷✷✹ ✶✻✵✵ ✷✺✻ ✶✸✹✹ ✶✷✽✳✳✷✷✹ ◆❖❘❳ ❬❆❏◆✶✻❪ ✺✶✷ ✶✷✽ ✸✽✹ ✶✷✽ ✶✵✷✹ ✷✺✻ ✼✻✽ ✷✺✻

• ■♥✐t✐❛❧✐③❡ ❡♥t✐r❡ st❛t❡ ✉s✐♥❣ ❦❡② ✭FKS ❢♦r ❦❡②✮

✶✸ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❈❆❊❙❆❘ P♦rt❢♦❧✐♦✿ ❆s❝♦♥

❉♦❜r❛✉♥✐❣✱ ❈✳✱ ❊✐❝❤❧s❡❞❡r✱ ▼✳✱ ▼❡♥❞❡❧✱ ❋✳✱ ❙❝❤❧ä✛❡r✱ ▼✳✿ ❆s❝♦♥ ✈✶✳✷

1.4 Mode of Operation

The mode of operation of Ascon is based on duplex sponge modes like MonkeyDuplex [13], but uses a stronger keyed initialization and keyed finalization function. The core permu- tations pa and pb operate on a sponge state S of size 320 bits, with a rate of r bits and a capacity of c = 320 − r bits. For a more convenient notation, the rate and capacity parts of the state S are denoted by Sr and Sc, respectively. The encryption and decryption

• perations are illustrated in Figure 1a and Figure 1b and specified in Algorithm 1.

IVKN

320 pa

⊕ 0∗K

c

⊕

r

A1 pb ⊕ As

c

pb ⊕ 0∗1

c

⊕

r

P1 C1 pb

c

⊕ Pt

− 1 Ct − 1

pb ⊕ Pt Ct

r

⊕ K0∗

c

pa ⊕ K

k

T Initialization Associated Data Plaintext Finalization

(a) Encryption

✶✹ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❈❆❊❙❆❘ P♦rt❢♦❧✐♦✿ ❆s❝♦♥✲✶✷✽ P❛r❛♠❡t❡rs⋆

❖❧❞ ❇♦✉♥❞ ✭❙✐♠♣❧✐✜❡❞✮ M2 2320 + N 2256 + N 264

• ■❢ M ≤ 2160✱ s❡❝✉r✐t② ❛s ❧♦♥❣ ❛s N ≤ 264

◆❡✇ ❇♦✉♥❞ ✭❙✐♠♣❧✐✜❡❞✮ M2 2320 + N 2256 + N 2128

• ■❢ M ≤ 2160✱ s❡❝✉r✐t② ❛s ❧♦♥❣ ❛s N ≤ 2128

✶✺ ✴ ✶✽

(b, c, r, k) = (320, 256, 64, 128)

⋆ ❘❡❛s♦♥✐♥❣ ❞♦❡s ♥♦t ❛♣♣❧② t♦ ❆s❝♦♥✲✶✷✽ ✐ts❡❧❢

❆♣♣❧✐❝❛t✐♦♥ t♦ ❙❚❘❖❇❊

❙❚❘❖❇❊ Pr♦t♦❝♦❧ ❋r❛♠❡✇♦r❦ ❬❍❛♠✶✼❪

• ▲✐❣❤t✇❡✐❣❤t ❢r❛♠❡✇♦r❦ ❢♦r ♥❡t✇♦r❦ ♣r♦t♦❝♦❧s
• ●♦❛❧✿ s✐♠♣❧❡ ❢r❛♠❡✇♦r❦ ✇✐t❤ s♠❛❧❧ ❝♦❞❡ s✐③❡

❍❛s❤✐♥❣✱ ❛✉t❤❡♥t✐❝❛t✐♦♥✱ ❛♥❞ ❡♥❝r②♣t✐♦♥✿ ❛❧❧ ✉s✐♥❣ s♣♦♥❣❡ ❛♥❞ ♦✉t❡r✲❦❡②❡❞ s♣♦♥❣❡✴❞✉♣❧❡①

s❝❤❡♠❡ ❙❚❘❖❇❊✲✶✷✽✴✶✻✵✵ ✶✻✵✵ ✷✺✻ ✶✸✹✹ ✷✺✻ ❙❚❘❖❇❊✲✷✺✻✴✶✻✵✵ ✶✻✵✵ ✺✶✷ ✶✵✽✽ ✷✺✻ ❙❚❘❖❇❊✲✶✷✽✴✽✵✵ ✽✵✵ ✷✺✻ ✺✹✹ ✷✺✻ ❙❚❘❖❇❊✲✷✺✻✴✽✵✵ ✽✵✵ ✺✶✷ ✷✽✽ ✷✺✻ ❙❚❘❖❇❊✲✶✷✽✴✹✵✵ ✹✵✵ ✷✺✻ ✶✹✹ ✷✺✻

✶✻ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❙❚❘❖❇❊

❙❚❘❖❇❊ Pr♦t♦❝♦❧ ❋r❛♠❡✇♦r❦ ❬❍❛♠✶✼❪

• ▲✐❣❤t✇❡✐❣❤t ❢r❛♠❡✇♦r❦ ❢♦r ♥❡t✇♦r❦ ♣r♦t♦❝♦❧s
• ●♦❛❧✿ s✐♠♣❧❡ ❢r❛♠❡✇♦r❦ ✇✐t❤ s♠❛❧❧ ❝♦❞❡ s✐③❡
• ❍❛s❤✐♥❣✱ ❛✉t❤❡♥t✐❝❛t✐♦♥✱ ❛♥❞ ❡♥❝r②♣t✐♦♥✿

❛❧❧ ✉s✐♥❣ s♣♦♥❣❡ ❛♥❞ ♦✉t❡r✲❦❡②❡❞ s♣♦♥❣❡✴❞✉♣❧❡①

s❝❤❡♠❡ ❙❚❘❖❇❊✲✶✷✽✴✶✻✵✵ ✶✻✵✵ ✷✺✻ ✶✸✹✹ ✷✺✻ ❙❚❘❖❇❊✲✷✺✻✴✶✻✵✵ ✶✻✵✵ ✺✶✷ ✶✵✽✽ ✷✺✻ ❙❚❘❖❇❊✲✶✷✽✴✽✵✵ ✽✵✵ ✷✺✻ ✺✹✹ ✷✺✻ ❙❚❘❖❇❊✲✷✺✻✴✽✵✵ ✽✵✵ ✺✶✷ ✷✽✽ ✷✺✻ ❙❚❘❖❇❊✲✶✷✽✴✹✵✵ ✹✵✵ ✷✺✻ ✶✹✹ ✷✺✻

✶✻ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❙❚❘❖❇❊

❙❚❘❖❇❊ Pr♦t♦❝♦❧ ❋r❛♠❡✇♦r❦ ❬❍❛♠✶✼❪

• ▲✐❣❤t✇❡✐❣❤t ❢r❛♠❡✇♦r❦ ❢♦r ♥❡t✇♦r❦ ♣r♦t♦❝♦❧s
• ●♦❛❧✿ s✐♠♣❧❡ ❢r❛♠❡✇♦r❦ ✇✐t❤ s♠❛❧❧ ❝♦❞❡ s✐③❡
• ❍❛s❤✐♥❣✱ ❛✉t❤❡♥t✐❝❛t✐♦♥✱ ❛♥❞ ❡♥❝r②♣t✐♦♥✿

❛❧❧ ✉s✐♥❣ s♣♦♥❣❡ ❛♥❞ ♦✉t❡r✲❦❡②❡❞ s♣♦♥❣❡✴❞✉♣❧❡①

s❝❤❡♠❡ b c r k ❙❚❘❖❇❊✲✶✷✽✴✶✻✵✵ ✶✻✵✵ ✷✺✻ ✶✸✹✹ ✷✺✻ ❙❚❘❖❇❊✲✷✺✻✴✶✻✵✵ ✶✻✵✵ ✺✶✷ ✶✵✽✽ ✷✺✻ ❙❚❘❖❇❊✲✶✷✽✴✽✵✵ ✽✵✵ ✷✺✻ ✺✹✹ ✷✺✻ ❙❚❘❖❇❊✲✷✺✻✴✽✵✵ ✽✵✵ ✺✶✷ ✷✽✽ ✷✺✻ ❙❚❘❖❇❊✲✶✷✽✴✹✵✵ ✹✵✵ ✷✺✻ ✶✹✹ ✷✺✻

✶✻ ✴ ✶✽

❆♣♣❧✐❝❛t✐♦♥ t♦ ❙❚❘❖❇❊✲✶✷✽✴✹✵✵

❖❧❞ ❇♦✉♥❞ ✭❙✐♠♣❧✐✜❡❞✮ M2 2256 + MN 2256 + N 2128

• ■❢ M ≤ 2100 =: 2a✱ s❡❝✉r✐t② ❛s ❧♦♥❣ ❛s N ≤ 2128

◆❡✇ ❇♦✉♥❞ ✭❙✐♠♣❧✐✜❡❞✮ M2 2256 + MN 2256 + N 2256

• ■❢ M ≤ 2100 =: 2a✱ s❡❝✉r✐t② ❛s ❧♦♥❣ ❛s N ≤ 2156

✶✼ ✴ ✶✽

(b, c, r, k) = (400, 256, 144, 256)

❈♦♥❝❧✉s✐♦♥

❚✐❣❤t ❑❡② Pr❡❞✐❝t✐♦♥ ❙❡❝✉r✐t②

• ▲❛st ✏♠✐ss✐♥❣ ❧✐♥❦✑ ✐♥ ❦❡②❡❞ s♣♦♥❣❡ ♣r♦♦❢s
• ❈❧♦s❡ t♦ ♦♣t✐♠❛❧ ❜♦✉♥❞

❆♣♣❧✐❝❛t✐♦♥s

• ❊✈❡r② ✉s❡ ♦❢ ♦✉t❡r✲❦❡②❡❞ s♣♦♥❣❡✴❞✉♣❧❡① ✇✐t❤ k > r
• ❍▼❆❈✲❙❍❆✲✸ ❬◆❨✶✻❪ ❛♥❞ s❛♥❞✇✐❝❤ s♣♦♥❣❡ ❬◆❛✐✶✻❪
• ❙❚❘❖❇❊ ♣r♦t♦❝♦❧ ❢r❛♠❡✇♦r❦
• ▲✐❣❤t✇❡✐❣❤t ♣❡r♠✉t❛t✐♦♥s

❚❤❛♥❦ ②♦✉ ❢♦r ②♦✉r ❛tt❡♥t✐♦♥✦

✶✽ ✴ ✶✽