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slides-nistpqc19-schwabe.pdf

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后量子密码学，量子密码学

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CRYSTALS–Kyber

Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim

Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, Damien Stehlé

authors@pq-crystals.org

https://pq-crystals.org/kyber

August 23, 2019

Reminder: the big picture

Kyber.CPAPKE: LPR encryption or “Noisy ElGamal”

s, e ← χ

sk = s, pk = t = As + e

r, e

, e

← χ

u ← A

r + e

v ← t

r + e

+ Enc(m)

c = (u, v )

m = Dec(v − s

Kyber.CCAKEM: CCA-secure KEM via tweaked FO transform

• Use implicit rejection

• Hash public key into seed and shared key

• Hash ciphertext into shared key

• Use Keccak-based functions for all hashes and XOF

Reminder: the big picture

Kyber.CPAPKE: LPR encryption or “Noisy ElGamal”

s, e ← χ

sk = s, pk = t = As + e

r, e

, e

← χ

u ← A

r + e

v ← t

r + e

+ Enc(m)

c = (u, v )

m = Dec(v − s

Kyber.CCAKEM: CCA-secure KEM via tweaked FO transform

• Use implicit rejection

• Hash public key into seed and shared key

• Hash ciphertext into shared key

• Use Keccak-based functions for all hashes and XOF

Reminder: Kyber in Round 1

• Use MLWE instead of LWE or RLWE

• Use R = Z

[X ]/(X

256

+ 1) with q = 7681

• Use centered binomial noise

• Generate A via XOF(ρ) (“NewHope style”)

• Compress ciphertexts (round oﬀ least-signiﬁcant bits)

• Compress public keys

Reminder: Kyber in Round 1

• Use MLWE instead of LWE or RLWE

• Use R = Z

[X ]/(X

256

+ 1) with q = 7681

• Use centered binomial noise

• Generate A via XOF(ρ) (“NewHope style”)

• Compress ciphertexts (round oﬀ least-signiﬁcant bits)

• Compress public keys

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