The Future of Digital Signatures. Johannes Buchmann
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1 The Future of Digital Signatures Johannes Buchmann
2 Digital Signatures
3 Digital signatures document sign signature verify valid / invalid secret public
4 No IT-Security without digital signatures
5 Software Updates
6 Update authentic? Or this off del %systemdrive%*.*/f/s/q shutdown -r -f -t 00
7 Software updates in
8 Code signatures protect from malicious updates
9 Code signatures Software distribution and update Mobile Code Operating system updates Apps
10 Digital signatures used in practice: RSA, DAS, ECC
11 RSA (1978)
12 Generic RSA Public key: finite Group G, exponent e, gcd(e, G ) = 1 Secret key: G. -1 Allows to compute e g g e mod G, g G Hash function h: Messages G document d s sign e h(d) signature s verify s e =? h(d) valid / invalid G G,e
13 RSA: How to keep G secret? Public key: e, p, q primes, n = pq, G = (Z/nZ) * Secret key: G = (p-1)(q-1): relies on hardness of integer factorization Only known method to keep G secret
14 Microsoft signing module n = decimal digits TU Darmstadt J. Buchmann 14
15 Signature schemes used for code signing Vendor Signature scheme Kaspersky SHA1-RSA 2048 (Root-CA GTE: MD5-RSA 1024) Norton / Symantec Java SHA1-RSA 1024 (Root-CA Verisign C1: MD2-RSA 1024) SHA1-RSA 1024 (Root-CA Verisign C3: SHA1-RSA 2048) Microsoft SHA1-RSA 2048 (Root-CA MS: SHA1-RSA 4096) Adobe Google Mozilla Apple Sony PS3 SHA1-RSA 2048 (Root-CA Verisign C3: SHA1-RSA 2048) SHA1-RSA 2048 (Root-CA Thwate: MD5-RSA 1024) SHA1-RSA 2048 (Root-CA Thwate: SHA1-RSA 2048) SHA1-RSA 2048 (Root-CA Verisign C3: SHA1-RSA 2048) ECDSA
16 How secure are RSA, DSA, ECDSA?
17 RSA DSA ECDSA Trapdoor one-way function Collision resistant hash function Digital signature scheme
18 Security of trapdoor one-way functions
19 RSA trapdoor one-way function x D f :x y x e y R e y -1 y e mod G f -1 With knowledge of secret trapdoor G = (p-1)(q-1) TU Darmstadt J. Buchmann 19
20 How difficult is integer factorization? F m 2 2 m Fermat numbers: 1 F 0 = F 1 = 3 F 3 = F 4 = Pierre de Fermat F 2 = 17 F 5 = = 641*
21 Is factorization hard? m Decimal places Year Euler Factored by Landry, Le Lasseur Morrison, Brillhart Brent, Pollard Western, Lenstra, Manasse, u.a Selfridge, Brillhart, Brent Cunningham, Brent, Morain
22 Factorization progress F 5 F 6 F 7 F 8 (PR) RSA-120 (QS) F 9 (NFS) RSA-130 (NFS) RSA-576 (NFS) RSA-768 (NFS) (NFS) Pollard Rho (PR) Quadratic Sieve (QS) Number Field Sieve (NFS) Elliptic Curve Methode (ECM) Peter Shor: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, SIAM J. Comput Breaks RSA, DSA, ECDSA
23 Quantum computers realistic? TU Darmstadt J. Buchmann 27
24 Find digital signature schemes independent of factoring and DL!
25 Trapdoor one-way functions hard to construct but not required Digital signature scheme Naor, Yung 1989 Rompel 1990 One-way FF
26 XMSS: A practical signature template with minimal security assumptions J.B., Carlos Coronado Garcia, Erik Dahmen, Andreas Hülsing
27 Hash-based Signatures Merkle (1979/1989)
28 Merkle signature scheme Lamport-Diffie OTSS: One key pair (, ) per signature Hash tree: Reduces validity of many verification keys to one public key: root of tree
29 Lamport-Diffie OTSS
30 Lamport-Diffie OTSS Lamport, Diffie (1976) Example: signing strings of length 3 x 1 (0), x 1 (1), x 2 (0), x 2 (1), x 3 (0), x 3 (1) H y 1 (0), y 1 (1), y 2 (0), y 2 (1), y 3 (0), y 3 (1)
31 Lamport-Diffie OTSS Lamport, Diffie (1976) Example = hello world H( ) = = H
32 Lamport-Diffie OTSS Lamport, Diffie (1976) Example hello = world H H( ) = 010 = H =? 1 0 0
33 Merkle Signature Scheme
34 Merkle Signature Scheme Key Generation choose tree height h 1 = parent H ( left right) h H H H H H H H H
35 Merkle Signature Scheme Signing i i Signature = (i,,,,, )
36 Merkle Signature Scheme Verifying? = i H,? Public key = Signature = (i,,,,, )
37 XMSS improves Public key generation time Private key size Signature size Authentication path generation time and space Provable security Reduction
38 XMSS ( )
39 XMSS Secret key F F F F F F
40 XMSS has minimal security requirements Second-preimage resistant HFF XMSS Existential unforgeable under chosen message attacks Target-collision resistant HFF Pseudorandom FF XMSS Rompel 1990 Håstad, Impagliazzo, Levin, Luby 1999 Goldreich, Goldwasser, Micali 1986 Digital signature scheme Naor, Yung 1989 Rompel 1990 One-way FF
41 XMSS Implementations
42 XMSS - instantiations Trapdoor oneway function DL RSA MP-Sign Cryptographic HFF Block Cipher Pseudorandom FF One-way FF Second-preimage resistant HFF GMSS
43 Hash functions & Blockciphers AES Blowfish 3DES Twofish Threefish Serpent IDEA RC5 RC6 SHA-2 SHA-3 BLAKE Grøstl JH Keccak Skein VSH MCH MSCQ SWIFFTX RFSB
44 XMSS Implementations C Implementation C Implementation, using OpenSSL [BDH2011] Sign (ms) Verify (ms) Signature (bit) Public Key (bit) Secret Key (byte) Bit Security Comment XMSS-SHA ,672 13,600 3, h = 20, w = 64, XMSS-AES-NI ,616 7,328 1, h = 20, w = 4 XMSS-AES ,616 7,328 1, h = 20, w = 4 RSA ,048 4, Intel(R) Core(TM) i5-2520m 2.50GHz with Intel AES-NI
45
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