IDbased Cryptography and SmartCards


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1 IDbased Cryptography and SmartCards Survol des techniques cryptographiques basées sur l identité et implémentation sur carte à puce The Need for Cryptography Encryption! Transform a message so that only the intended recipient can read it! Privacy concerns Digital signature! Relate a message to an individual! Publicly verifiable and (computationally) impossible to forge Nonrepudiation
2 SecretKey Cryptography Cytale, Caesar, Vernam, DES,! Symmetric encryption Symmetric Encryption Alice m C C m Enc Dec Alice and share the same key:
3 SecretKey Cryptography Cytale, Caesar, Vernam, DES,! Symmetric encryption Limitations! Number of keys: n (n  1)/2 n 2! Key distribution PublicKey Cryptography Inventors! Whitfield Diffie! Martin Hellman! Ralph Merkle Publications! W. Diffie & M. Hellman, New directions in cryptography, IEEE TIT, 22 : , 1976! R. Merkle, Secure communications over insecure channels, CACM, 21: , 1978
4 Analogy Privacy! Exchange of encrypted mail Analogy to padlocked boxes Padlocked Boxes Alice Order is important
5 DiffieHellman Key Exchange Alice? x A? x B K A = g x A mod p K B = g x B mod p K AB = (K B ) x A mod p K BA = (K A ) x B mod p K AB = K BA Cryptographic Assumptions CDH problem! Given (g x mod p, g y mod p, g, p), compute g xy mod p DL problem! Given (g x mod p, g, p), compute x
6 PublicKey Cryptosystems DiffieHellman allows to exchange a secret over an insecure channel Limitations! Delays! Maninthemiddle attack Publickey cryptography! Asymmetric encryption! Exchange of encrypted mails (2) RivestShamirAdleman 3 M.I.T. researchers! Leonard Adleman! Ronald Rivest! Adi Shamir Publication! R. Rivest, A. Shamir & L. Adleman, A method for obtaining digital signatures and publickey cryptosystems, CACM, 21 : , 1978
7 RSA Cryptosystem (1/3) Dec SKB (Enc PKB (m)) = m Group (!/N!)*! Modular exponentiation in (!/N!)* Permutation iff gcd(e, φ(n)) = 1! Euler theorem Security based on factoring N RSA Cryptosystem (2/3) Key generation ()! p B et q B, N B = p B q B, e B s.t. gcd(e B, φ(n B )) = 1! PK = {e B, N B }! SK = {p B, q B, d B } with d B = e B 1 mod φ(n B ) Encryption (Alice)! C = m e B mod N B Decryption ()! C d B mod N B (Paddings)
8 RSA Cryptosystem (3/3) Alice e B, N B C = m e B mod N B m = C d B mod N B s certificate needs to be verified Other Applications RSA signature (1978)! Based on factoring! Dual function of RSA encryption ElGamal encryption/signature (1985)! Based on DL! Other groups (e.g., elliptic curves)
9 IdentityBased Cryptography Inventor! Adi Shamir, 1984 Key idea! Identity serves as publickey! Certificates become implicit (inside a domain) No known solution for encryption IndentityBased Encryption (1/2) Y. Desmedt and J.J. Quisquater, 1986 Security assumptions! Enc(Dec(m)) = m! Enc Dec! Tamper resistance
10 IdentityBased Encryption (2/2) Alice m Master key is present in all cards C C Enc = master key = s secret key Dec m Dec Id () Dec BonehFranklin Stanford/UC Davis researchers! Dan Boneh! Matt Franklin Publication! D. Boneh & M. Franklin, Identity based encryption from the Weil pairing, SIAM J. on Computing 32: , 2003
11 BonehFranklin IBE (1/3) Dec SKB (Enc IDB (m)) = m Admissible bilinear map e: " 1 " 1 " 2, i.e.,! [bilinear] e(ap, bq) = e(p, Q) ab! [nondegenerate] e(p, P) 1! [computable] efficient algorithm for e Security based on BDH problem! Given (P, ap, bp, cp), compute e(p, P) abc BonehFranklin IBE (2/3) Setup (TTP)! e: " 1 " 1 " 2, h: {0,1}* " 1, H: " 2 {0,1} m! master SK: s! PK = {P pub = s P, P, e, h, H} Extract (TTP) e.g., for! d IDB = s Q IDB where Q IDB = h(id B ) Encryption (Alice)! Q IDB = h(id B ) and g IDB = e(q IDB, P pub )! (C 1, C 2 ) = (rp, m H(g IDBr )) Decryption ()! m = C 2 H(e(d IDB, C 1 ))
12 BonehFranklin IBE (3/3) Alice Sytem parameters Q IDB = h(id B ) g IDB = e(q IDB, P pub ) (C 1, C 2 ) = (rp, m H(g IDBr )) m = C 2 H(e(d IDB, C 1 )) Verification of certificates is implicit (inside the domain) Smart IBE BonehFranklin protocol on smart cards Prototype library! allowing to perform encryption/decryption First solution with the entire pairing computation performed on the smart card
13 Summary & Perspectives State of the art! Symmetric encryption (3DES, AES)! Asymmetric encryption (RSA, ECC)! IDbased encryption (BonehFranklin IBE) Smart card solutions for IDbased encryption! DesmedtQuisquater IBE! BonehFranklin IBE (Smart IBE) Future research! More efficient implementations of pairings on constrained devices! Share the master key s amongst several TTPs! Design an IBE based on standard assumptions Comments/Questions? More info:
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