Public-seed Pseudorandom Permutations Pratik Soni Stefano Tessaro - PowerPoint PPT Presentation
Public-seed Pseudorandom Permutations Pratik Soni Stefano Tessaro UC Santa Barbara UC Santa Barbara EUROCRYPT 2017 Cryptographic schemes often built from generic building blocks Cryptographic schemes often built from generic building
UCE security π‘ β Gen(1 π ) π β Funcs(π, π) β π‘ π source π πΌ = (π»ππ, β) Bellare Hoang Keelveedhi
UCE security π‘ β Gen(1 π ) π β Funcs(π, π) β π‘ π source π πΌ = (π»ππ, β) Bellare Hoang Keelveedhi
UCE security π‘ β Gen(1 π ) π β Funcs(π, π) β π‘ π source π π πΌ = (π»ππ, β) πΈ distinguisher Bellare Hoang Keelveedhi
UCE security π‘ β Gen(1 π ) π‘ β Gen(1 π ) π β Funcs(π, π) β π‘ π source π π π πΌ = (π»ππ, β) πΈ distinguisher Bellare Hoang Keelveedhi
UCE security π‘ β Gen(1 π ) π β Funcs(π, π) β π‘ π source π π π πΌ = (π»ππ, β) 0/1 πΈ distinguisher Bellare Hoang Keelveedhi
UCE security π‘ β Gen(1 π ) π β Funcs(π, π) β π‘ π β source π π π πΌ = (π»ππ, β) 0/1 πΈ distinguisher Bellare Hoang Keelveedhi
psPRP security π‘ β Gen(1 π ) π β πππ¬π§π(π) π/π βπ βπ π π /π π π π = (π»ππ, π, π β1 ) πΈ
psPRP security π‘ β Gen(1 π ) π β πππ¬π§π(π) π/π βπ βπ π π /π π Makes forward and π π = (π»ππ, π, π β1 ) backward queries! πΈ
psPRP security π‘ β Gen(1 π ) π β πππ¬π§π(π) π/π βπ βπ π π /π π Makes forward and π π = (π»ππ, π, π β1 ) backward queries! π π πΈ
psPRP security π‘ β Gen(1 π ) π β πππ¬π§π(π) π/π βπ βπ π π /π π Makes forward and π π = (π»ππ, π, π β1 ) backward queries! π π 0/1 πΈ
psPRP security π‘ β Gen(1 π ) π β πππ¬π§π(π) π/π βπ βπ π π /π π Makes forward and π π = (π»ππ, π, π β1 ) backward queries! π π 0/1 πΈ π is ππ‘πππ -secure if β PPT π, πΈ , left and right are indistinguishable.
psPRP security π‘ β Gen(1 π ) π β πππ¬π§π(π) π/π βπ βπ π π /π π Makes forward and π π = (π»ππ, π, π β1 ) backward queries! π π 0/1 πΈ π is ππ‘πππ -secure if β PPT π, πΈ , left and right are indistinguishable.
π is ππ‘πππ -secure if β PPT π, πΈ , β¦
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ π
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ (+, 0 π ) (+, 0 π ) π
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ π§ π§ (+, 0 π ) (+, 0 π ) π
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ π§ π§ (+, 0 π ) (+, 0 π ) π π = π§ π πΈ
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ π§ π§ (+, 0 π ) (+, 0 π ) π π = π§ π Outputs 1 iff πΈ π§ = π π‘ 0 π
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ π§ π§ (+, 0 π ) (+, 0 π ) π π = π§ π 1 with prob. 1 Outputs 1 iff πΈ π§ = π π‘ 0 π
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ π§ π§ (+, 0 π ) (+, 0 π ) π π = π§ π 1 with prob. 1 Outputs 1 iff πΈ π§ = π π‘ 0 π with prob. 1/2 π 1
π is ππ‘πππ -secure if β PPT π, πΈ , β¦ π‘ β Gen(1 π ) π β Perms(π) π/π β1 β1 π π‘ /π π‘ β π§ π§ (+, 0 π ) (+, 0 π ) π π = π§ π 1 with prob. 1 Outputs 1 iff πΈ π§ = π π‘ 0 π with prob. 1/2 π 1 ππ‘πππ -security is impossible against all sources!
π = (Gen, π, π β1 ) Sources need to be restricted all sources
π = (Gen, π, π β1 ) Sources need to be restricted all sources π―
π = (Gen, π, π β1 ) Sources need to be restricted π‘ β Gen(1 π ) all sources π β Perms(π) β1 π/π β1 π π‘ /π π‘ π― π π π πΈ 0/1 π is ππ‘πππ[π―] -secure if β π β π― and β PPT πΈ , left and right are indistinguishable.
This talk β unpredictable and reset-secure sources all sources
This talk β unpredictable and reset-secure sources all sources π― π‘π£π unpredictable
This talk β unpredictable and reset-secure sources all sources reset-secure π― π‘π π‘ π― π‘π£π unpredictable
This talk β unpredictable and reset-secure sources all sources reset-secure π― π‘π π‘ π― π‘π£π unpredictable Both restrictions model that πΈ cannot predict the queries made by the sources!
This talk β unpredictable and reset-secure sources all sources reset-secure π― π‘π π‘ π― π‘π£π unpredictable Both restrictions model that πΈ cannot predict the queries made by the sources! π― π‘π£π β π― π‘π π‘
This talk β unpredictable and reset-secure sources all sources reset-secure π― π‘π π‘ π― π‘π£π unpredictable Both restrictions model that πΈ cannot predict the queries made by the sources! ππ‘πππ π― π‘π π‘ is a stronger π― π‘π£π β π― π‘π π‘ βΉ assumption than ππ‘πππ π― π‘π£π
Source restrictions β unpredictability π β Perms(π) π/π β1 π π΅
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π΅
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π β π βͺ { π, π¦ π , (π , π§ π )} π΅
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π§ π π β π βͺ { π, π¦ π , (π , π§ π )} π΅
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π§ π π β π βͺ { π, π¦ π , (π , π§ π )} π π΅
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π§ π π β π βͺ { π, π¦ π , (π , π§ π )} π It should be hard for π΅ to predict any of π βs queries or its inverse π΅ [ π β² β© π β π] = negl(π) Pr π β²
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π§ π π β π βͺ { π, π¦ π , (π , π§ π )} π It should be hard for π΅ to predict any of π βs queries or its inverse π΅ [ π β² β© π β π] = negl(π) Pr π β² π― π‘π£π : π΅ is computationally unbounded β π― ππ£π : π΅ is PPT
Source restrictions β unpredictability π β Perms(π) (π, π¦ π ) π β {+, β} π/π β1 π π§ π π β π βͺ { π, π¦ π , (π , π§ π )} π It should be hard for π΅ to predict any of π βs queries or its inverse π΅ [ π β² β© π β π] = negl(π) Pr π β² π― π‘π£π : π΅ is computationally unbounded β ππ‘πππ[π― ππ£π ] impossible if iO π― ππ£π : π΅ is PPT exists [BFM14]
Source restrictions β reset-security
Source restrictions β reset-security π/π β1 π π β Perms(π) π
Source restrictions β reset-security π/π β1 π π β Perms(π) π
Source restrictions β reset-security π/π β1 π π β Perms(π) π π/π β1 π
Source restrictions β reset-security π/π β1 π π β Perms(π) π π/π β1 π 0/1
Source restrictions β reset-security π/π β1 π/π β1 π π π β Perms(π) π β Perms(π) π π π/π β1 π π β1 π 1 /π 1 π 1 β Perms(π) 0/1 0/1
Source restrictions β reset-security π/π β1 π/π β1 π π π β Perms(π) π β Perms(π) β π π π/π β1 π π β1 π 1 /π 1 π 1 β Perms(π) 0/1 0/1
Source restrictions β reset-security π/π β1 π/π β1 π π π β Perms(π) π β Perms(π) β π π π/π β1 π π β1 π 1 /π 1 π 1 β Perms(π) 0/1 0/1 π― π‘π π‘ : π is computationally unbounded β π― ππ π‘ : π is PPT
Source restrictions β reset-security π/π β1 π/π β1 π π π β Perms(π) π β Perms(π) β π π π/π β1 π π β1 π 1 /π 1 π 1 β Perms(π) 0/1 0/1 π― π‘π π‘ : π is computationally unbounded β π― ππ£π β π― ππ π‘ π― ππ π‘ : π is PPT
Recap ππ‘πππ[π― π‘π π‘ ] ππ‘πππ[π― π‘π£π ]
Recap ππ‘πππ[π― π‘π π‘ ] ππ‘πππ[π― π‘π£π ]
Recap
Recap Central assumption in UCE theory
Recap Central assumption in UCE theory
Roadmap 1.Definitions 2.Constructions & Applications 3.Conclusions
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