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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