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Source: Computer Standards & Interfaces, Vol. 31, No. 4, pp. 723-728, Jun. 2009

An I mproved S mart C ard B ased P assword A uthentication S cheme with P rovable S ecurity. Source: Computer Standards & Interfaces, Vol. 31, No. 4, pp. 723-728, Jun. 2009 Author: Jing Xu, Wen-Tao Zhu and Deng-Guo Feng Speaker: Li-Tzu Chang. Outline. Review of Lee-Chiu’s scheme

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Source: Computer Standards & Interfaces, Vol. 31, No. 4, pp. 723-728, Jun. 2009

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  1. An Improved Smart Card Based Password Authentication Scheme with Provable Security Source: Computer Standards & Interfaces, Vol. 31, No. 4, pp. 723-728, Jun. 2009 Author: Jing Xu, Wen-Tao Zhu and Deng-Guo Feng Speaker: Li-Tzu Chang

  2. Outline • Review of Lee-Chiu’s scheme • Forgery attack on Lee-Chiu’s scheme • Review of Lee et al.’s scheme • Offline password guessing attack on Lee et al.’s scheme • Proposed scheme • Conclusions

  3. Notations • h(.): a one-way hash function • p: a large prime number • g: a primitive root in GF(p) • q:a large prime such that p = 2q+1 • ID: user’s identification • PW: user’s password

  4. Review of Lee-Chiu’s scheme Server User Server’s secret key Registration {ID, PW} Selects ID, PW Computes A = h(ID||x) B = gA．h(PW) mod p {ID, A, B, h(.), p, g} Smart card Smart card Login and Authentication Inputs ID, PW* Verifies B ?= gA．h(PW*) mod p Computes Z = (B . A) mod p C1 = h(T⊕ B) {ID, Z, C1, T} Verifies ID, T Computes A* = h(ID||x) Verifies C1 ?= h(T ⊕ (Z / A* mod p)) No mutual authentication

  5. Forgery attack on Lee-Chiu’s scheme Adversary Steals a smart card and extracts the stored values someway Login and Authentication Computes Z’ = (B . A) mod p C1’= h(T’⊕ B) Server {ID, Z’, C1’, T’} Verifies ID, T’ Computes A* = h(ID||x) Verifies C1’ ?= h(T ⊕ (Z’ / A* mod p))

  6. Review of Lee et al.’s scheme Server User Server’s secret key Registration {ID, PW} Selects ID, PW Computes R = h(ID ⊕ x) ⊕ PW {ID, R, h(.)} Smart card Smart card Login and Authentication Inputs ID, PW* Computes C1 = R ⊕PW* C2 = h(C1 ⊕ T1) {ID, T1, C2} Verifies ID, T1 C2 ?= h( h(ID ⊕ x) ⊕T1) Computes C3 = h(h(ID ⊕ x) ⊕T3) {T3, C3} Verifies T3 C3 ?= h(C1⊕T3)

  7. Offline password guessing attack on Lee et al.’s scheme Adversary Records T1 and C2 from a successful login of a certain user Steals the smart card and reveals R from it Selects a password S Computes C’ = R ⊕S Checks h(C’⊕ T1) ?= C2 Repeats procedure offline until the correct password is yielded

  8. Proposed scheme (1/2) Registration Server’s secret key (x ∈ Zq*) Server User {ID, PW} Selects ID, PW Computes B = (h(ID)x + h(PW)) mod p {ID, B, h(.), p, g} Smart card Smart card

  9. Proposed scheme (2/2) Login and Authentication Server User Inputs ID, PW* Selects w ∈R Zq* Computes B’ = (B – h(PW*))w mod p W = h(ID)w mod p C= h(T||B’||W||ID) {ID, C, W, T} Verifies ID, T Computes B”= Wxmod p Verifies C ?= h(T||B”||W||ID) Selects m ∈R Zq* Computes M = h(ID)mmod p C’ = h(M||B”||T’||ID) {ID, C’, M, T’} Verifies T’ C’ ?= h(M||B’||T’||ID) Key agreement sk = h(ID||M||W||Wm) sk = h(ID||M||W||Mw)

  10. Conclusions • Proposes an improved smart card based password authentication scheme with formal security proof • Provides key agreement

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