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Public key cryptography

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R
rinnocente

The document discusses public key cryptography, digital certificates, and Transport Layer Security (TLS). It provides an overview of symmetric and asymmetric key cryptography, algorithms like RSA and ElGamal, the use of digital signatures and certificates, and how TLS uses public key encryption to securely transmit data over the internet, such as for email.

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2001/03/26 r.innocente 1 Public Key Cryptography, Digital Certificates, Transport Layer Security and Internet encrypted services Roberto Innocente inno@sissa.it
2001/03/26 r.innocente 2 Summary • PKC (Public Key Cryptography) Introduction • Digital Certificates • SSL/TLS • Use of SSL/TLS over Internet • Encrypted services: pop, imap, smtp
2001/03/26 r.innocente 3 Cryptographic systems taxonomy • Symmetric key cryptography • same key for encryption and decryption • relatively fast • RC2, RC4, DES, triple DES • Asymmetric key cryptography • different keys for encryption/decryption • slow • RSA, ElGamal, Elliptic curves
2001/03/26 r.innocente 4 Symmetric Key Cryptography Encryption Decryption Plain text Cipher text Plain text m c=K(m) m=K(c) m message c cipher text K key key K K.K=1
2001/03/26 r.innocente 5 Asymmetric Key Cryptography Encryption Decryption Plain text Cipher text Plain text Encryption key E Decryption key D m c=E(m) m=D(c) m message c cipher text E encryption key D decryption key D.E=1
2001/03/26 r.innocente 6 Another classification • Secret Key Cryptography • the key is kept secret • it requires a secure channel to be transmitted • Public Key Crytpography • one key (the deciphering key) is kept secret • the other key is made public
2001/03/26 r.innocente 7 Public-Key Cryptography Diffie – Hellmann (1976) • Each user generates a pair of inverse transformation E and D. • The deciphering key D must be kept secret but need never be communicated on a channel • The enciphering key E can be made public by placing it in a public directory (Public File) The original idea here is that keys can be produced in pairs and that it can be very hard to generate a key from the other
2001/03/26 r.innocente 8 PKC algorithms Since DH idea in 1976 many algorithms have been proposed, most were discovered insecure, of the remaining many are not feasible. Some of the algorithms are: • Knapsack algorithms (later shown insecure) • RSA (still considered secure) • El Gamal (still considered secure)
2001/03/26 r.innocente 9 Knapsack algorithms/1 (!!! insecure !!!) First PKC algorithm proposed by Merckle and Hellmann in 1978. • Given n integers M1,M2,M3,..., and a sum S, find a binary sequence b1,b2,b3... such that • S=b1*M1+ b2*M2+b3*M3+ .... • where: • M1,M2,M3,... is the public key • b1,b2,b3,... are the bits of the plain message • S is the ciphertext In general it is an hard problem, but ...
2001/03/26 r.innocente 10 Knapsack algorithms/2 (!!! insecure !!!) A subclass of the general problem can be easily solved and mapped onto a more general one. • A superincreasing knapsack is a knapsack in which every number in the ordered sequence is greater than the sum of the preceeding numbers e.g.{ 2,3,6,13,27} • Solving the problem for a superincreasing knapsack is quite easy. Starting from the greatest number, that will be an addend if it is less than the sum S, and so on ... • Now, choosing a number m (=55) greater than the sum of all numbers in the sequence, and a number n (=29) prime with m, and taking the remainder module m of the numbers in the sequence multiplied by n e.g. {2*29=58mod 55 =3, 3*29=87mod 55=32,...} we obtain a knapsack that is not superincreasing... if we take this sequence as the public key, and the underlaying superincreasing sequence as the private key ...
2001/03/26 r.innocente 11 RSA/1 (Rivest,Shamir,Adleman 1978) • Choose primes p,q n=p*q • Choose encryption key e prime with (p-1)*(q-1) • Compute the inverse d such that • now for each message m : • n,e is the public key • d is the private key e*d = 1 mod n c = me mod n m = cd mod n
2001/03/26 r.innocente 12 RSA/2 • Fermat’s little theorem (p prime,(p|a)=1): • Euler Totient function: • Euler’s generalization of Fermat’s theorem: ap-1 ≅ 1 (mod p) φ(n)= # of integers less than n primes with n For p,q primes : φ(p) = p-1 φ(p*q) = (p-1)*(q-1) aφ(n) ≅1 mod n aφ(n) –1 ≅ a-1 mod n therefore : e-1 ≅ e(p-1)(q-1)-1 mod n
2001/03/26 r.innocente 13 RSA/3 • Software speedups: • RSA goes faster if you choose e carefully • 3 (PEM), 65537 (X.509), 17 (PKCS#1) are good choices having only 2 bits set • in particular 65537 requires only 17 multiplications to exponentiate • Hardware chips: • it’s about 1000 times slower than DES • 1 Mb/s using a 512 bits modulus (GEC Marconi)
2001/03/26 r.innocente 14 RSA/4 The RSA patent was valid only for the US because it was requested after publication. In any case the patent expired on September,20 2000 and from then on RSA it’s now free everywhere
2001/03/26 r.innocente 15 El Gamal (T.ElGamal 1984) • Choose a prime p and two random numbers g(<p),x (<p)and compute y = g**x mod p • public key is y,g,p • private key is x • To encrypt a message M choose a random k, (p-1|k)=1 and compute • a= g**k mod p • b = (y**k)* M mod p • a,b is the ciphertext, to decrypt : • M = b/a**x mod p
2001/03/26 r.innocente 16 Message digests or Hash or fingerprints • One way function that maps a file on a fixed length key. As with real fingerprints one hopes that no 2 msgs have the same fingerprint. • collision free • un-reversible • e.g : • Unix sum is a bad example (16 bits) (Unix sum,cksum) • MD5(128 bits) invented by RSA (Unix md5sum) • SHA1(160 bits) Secure Hash Algorithm-1
2001/03/26 r.innocente 17 Uses of PKC Pics from M.Branchaud Pic from M.Branchaud
2001/03/26 r.innocente 18 Digital Signature Message Message Digest MD5 Signature RSA with private key
2001/03/26 r.innocente 19 Pitney-Bowes Veritas system • Uses digital signatures to authenticate info stored on physical documents (including the digital encoding of photographs) • It’s been used successfully at the Olympic World Games in New Haven in 1995 • On the back of a badge a high density bar code encoded a photograph, biographical data and medical data of the athletes • A Veritas reader can scan the bar code, verify the digital signature and then display a copy of the photograph
2001/03/26 r.innocente 20 Digital Certificates L.Kohnfelder (1978) In an effort to overcome performance problems related to the use of a single Public File, Kohnfelder proposed a digitally signed data record containing a name and a public key called a CERTIFICATE.
2001/03/26 r.innocente 21 Digital Certificates/2 Name Public key Digital signature
2001/03/26 r.innocente 22 Certificates/3 • Binary format of certificates is defined using ASN.1 (x.208) • Binary encoding is defined using DER(Distinguished Encoding Rules) which is based on BER (Basic Encoding Rules) • Binary format can be translated into ASCII using Base64 encoding, this form is called PEM encoding
2001/03/26 r.innocente 23 ASN.1 (X.208 1988) Certificate ::=SEQUENCE { tbsCertificate TBSCertificate, signatureAlgorithm AlgorithmIdentifier, signature BIT STRING } TBSCertificate ::=SEQUENCE { version [0] EXPLICIT Version DEFAULT v1, serialNumber CertificateSerialNumber, signatureAlgorithmIdentifier, issuer Name, validity Validity, subject Name, subjectPucliKeyInfo, issuerUniqueID [1] IMPLICIT UniqueIdentifier OPTIONAL, subjectUniqueID [1] IMPLICIT UniqueIdentifier OPTIONAL, extensions [3] EXPLICIT Extensions OPTIONAL } UniqueIdentifier::= BITSTRING Extensions::=SEQUENCE OF Extension
2001/03/26 r.innocente 24 ASN.1/2Private-Key: (1024 bit) modulus: 00:a0:11:a6:01:c6:d6:55:23:06:12:af:76:04:94: 5d:6a:94:67:f7:02:6e:4c:1b:90:39:b8:6d:a6:02: 01:57:87:0b:57:ed:c9:ad:89:28:bf:71:62:7d:26: 9a:de:2d:d8:15:ed:82:07:cf:07:a5:4d:9c:83:b3: 11:19:1a:f4:c9:68:ac:39:c9:98:be:69:5c:dd:da: f1:44:7e:80:9e:53:c9:7c:ca:3c:60:20:99:ce:b3: 53:be:67:7f:31:06:91:b2:c5:76:04:53:0d:5a:42: b9:26:b1:fe:93:15:f0:04:75:03:1c:e7:a9:3a:cf: 9d:5e:01:01:93:81:23:09:45 publicExponent: 65537 (0x10001) privateExponent: 5a:db:a9:af:38:7e:50:b5:20:ad:5a:8b:52:ee:24: 58:6b:04:d8:60:b8:da:da:8a:73:39:0c:84:3e:7f: 24:7f:b3:20:a6:08:e4:48:06:a9:24:63:13:46:e6: 81:56:e4:61:0d:ff:d1:0e:e2:f8:21:a5:c5:db:ce: c8:c1:54:50:58:f4:d5:4c:53:ba:f7:dd:25:9d:a4: 55:25:a1:4b:07:25:38:14:20:0c:a6:c2:07:1d:a6: cd:b0:f0:5b:cc:58:f6:fd:1d:0a:93:01:58:83:79: 46:e4:fc:67:91:f9:36:9c:07:c5:9c:26:12:bd:ab: 1e:86:4c:63:a4:0b:31:c1 prime1: 00:d1:d7:69:c9:c5:b0:50:37:9f:2e:2d:21:b5:9f: 96:7e:e8:c1:05:29:b1:62:da:e4:b5:cd:04:03:b1: 27:c7:3e:ca:27:a1:bd:69:4f:33:e2:97:5a:03:d0: 33:6f:41:c8:e0:f9:94:e2:0d:c1:a6:85:e1:09:ac: 31:f5:97:7f:77 prime2: 00:c3:47:72:4a:31:ea:e4:e6:0f:79:7f:68:da:c8: 40:7a:96:86:be:69:1c:94:e7:ab:1f:03:66:e0:05: 00:92:4f:e9:ac:ff:0e:51:45:9c:ed:9b:9e:01:ba: e5:00:a2:0f:d4:59:e6:06:d9:24:21:ba:b1:96:79: 51:5b:37:44:23 exponent1: 64:1e:98:6d:d9:f1:be:c4:5b:21:a8:0c:ee:60:5f: 68:db:da:c4:80:d9:0e:e6:8b:bb:26:3f:65:17:90: 78:23:40:46:da:87:ca:08:2d:24:4e:bc:77:17:4e: 83:25:eb:17:54:5d:b1:e1:88:64:d0:79:c7:a8:ae: 09:94:a8:0f exponent2: 65:64:77:67:26:bb:fb:d5:a8:3b:41:78:44:00:ad: d9:f8:c6:45:9f:76:03:aa:b6:23:08:35:26:23:f2: c4:05:52:23:4c:db:36:3f:9a:d7:94:71:5a:1c:9c: 42:d3:e2:bc:33:61:48:34:fe:99:b4:c1:f8:8b:4d: 3e:bb:57:59 coefficient: 24:c5:7d:c3:22:1b:cf:ae:15:20:97:9c:73:78:4a: d5:98:39:da:be:12:7e:94:1d:81:fa:0e:08:2a:dc: 3d:18:9e:b3:f8:cf:29:66:76:16:22:11:8f:d1:c1: a3:ec:6f:50:d5:e1:0f:66:ba:6a:43:ec:86:20:08: 39:0c:20:9e -----BEGIN RSA PRIVATE KEY----- MIICWwIBAAKBgQCgEaYBxtZVIwYSr3YElF1qlGf3Am5MG5A5uG2mAgFXhwtX7cmt iSi/cWJ9JpreLdgV7YIHzwelTZyDsxEZGvTJaKw5yZi+aVzd2vFEfoCeU8l8yjxg IJnOs1O+Z38xBpGyxXYEUw1aQrkmsf6TFfAEdQMc56k6z51eAQGTgSMJRQIDAQAB AoGAWtuprzh+ULUgrVqLUu4kWGsE2GC42tqKczkMhD5/JH+zIKYI5EgGqSRjE0bm gVbkYQ3/0Q7i+CGlxdvOyMFUUFj01UxTuvfdJZ2kVSWhSwclOBQgDKbCBx2mzbDw W8xY9v0dCpMBWIN5RuT8Z5H5NpwHxZwmEr2rHoZMY6QLMcECQQDR12nJxbBQN58u LSG1n5Z+6MEFKbFi2uS1zQQDsSfHPsonob1pTzPil1oD0DNvQcjg+ZTiDcGmheEJ rDH1l393AkEAw0dySjHq5OYPeX9o2shAepaGvmkclOerHwNm4AUAkk/prP8OUUWc 7ZueAbrlAKIP1FnmBtkkIbqxlnlRWzdEIwJAZB6YbdnxvsRbIagM7mBfaNvaxIDZ DuaLuyY/ZReQeCNARtqHyggtJE68dxdOgyXrF1RdseGIZNB5x6iuCZSoDwJAZWR3
2001/03/26 r.innocente 25 ASN.1/3 0:d=0 hl=4 l= 603 cons: SEQUENCE 4:d=1 hl=2 l= 1 prim: INTEGER :00 7:d=1 hl=3 l= 129 prim: INTEGER :A011A601C6D655230612AF7604945D6A9467F7026E4C1B9039B86DA6020157870B57EDC9AD8928B F71627D269ADE2DD815ED8207CF07A54D9C83B311191AF4C968AC39C998BE695CDDDAF1447E809E5 3C97CCA3C602099CEB353BE677F310691B2C57604530D5A42B926B1FE9315F00475031CE7A93ACF9 D5E01019381230945 139:d=1 hl=2 l= 3 prim: INTEGER :010001 144:d=1 hl=3 l= 128 prim: INTEGER : 5ADBA9AF387E50B520AD5A8B52EE24586B04D860B8DADA8A73390C843E7F247FB320A608E44806A9 24631346E68156E4610DFFD10EE2F821A5C5DBCEC8C1545058F4D54C53BAF7DD259DA45525A14B07 253814200CA6C2071DA6CDB0F05BCC58F6FD1D0A930158837946E4FC6791F9369C07C59C2612BDAB 1E864C63A40B31C1 275:d=1 hl=2 l= 65 prim: INTEGER :D1D769C9C5B050379F2E2D21B59F967EE8C10529B162DAE4B5CD0403B127C73ECA27A1BD694F33E 2975A03D0336F41C8E0F994E20DC1A685E109AC31F5977F77 342:d=1 hl=2 l= 65 prim: INTEGER :C347724A31EAE4E60F797F68DAC8407A9686BE691C94E7AB1F0366E00500924FE9ACFF0E51459CE D9B9E01BAE500A20FD459E606D92421BAB19679515B374423 409:d=1 hl=2 l= 64 prim: INTEGER : 641E986DD9F1BEC45B21A80CEE605F68DBDAC480D90EE68BBB263F65179078234046DA87CA082D24 4EBC77174E8325EB17545DB1E18864D079C7A8AE0994A80F 475:d=1 hl=2 l= 64 prim: INTEGER : 6564776726BBFBD5A83B41784400ADD9F8C6459F7603AAB62308352623F2C40552234CDB363F9AD7 94715A1C9C42D3E2BC33614834FE99B4C1F88B4D3EBB5759 541:d=1 hl=2 l= 64 prim: INTEGER : 24C57DC3221BCFAE1520979C73784AD59839DABE127E941D81FA0E082ADC3D189EB3F8CF29667616 22118FD1C1A3EC6F50D5E10F66BA6A43EC862008390C209E
2001/03/26 r.innocente 26 OID (object identifiers) • Object identifiers are unique numbers assigned to objects. They identify a node in a global tree. • e.g. 1.2.840.113549.1.7.2 is an OID, it means SignedData which is defined by RSADSI 0 ITU-T 1 ISO 2 joint ISO/ITU
2001/03/26 r.innocente 27 OID global tree Pic from M.Branchaud
2001/03/26 r.innocente 28 RSA keys according to PKCS#.. Private-Key: (1024 bit) modulus: 00:a0:11:a6:01:c6:d6:55:23:06:12:af:76:04:94: 5d:6a:94:67:f7:02:6e:4c:1b:90:39:b8:6d:a6:02: 01:57:87:0b:57:ed:c9:ad:89:28:bf:71:62:7d:26: 9a:de:2d:d8:15:ed:82:07:cf:07:a5:4d:9c:83:b3: 11:19:1a:f4:c9:68:ac:39:c9:98:be:69:5c:dd:da: f1:44:7e:80:9e:53:c9:7c:ca:3c:60:20:99:ce:b3: 53:be:67:7f:31:06:91:b2:c5:76:04:53:0d:5a:42: b9:26:b1:fe:93:15:f0:04:75:03:1c:e7:a9:3a:cf: 9d:5e:01:01:93:81:23:09:45 publicExponent: 65537 (0x10001) privateExponent: 5a:db:a9:af:38:7e:50:b5:20:ad:5a:8b:52:ee:24: 58:6b:04:d8:60:b8:da:da:8a:73:39:0c:84:3e:7f: 24:7f:b3:20:a6:08:e4:48:06:a9:24:63:13:46:e6: 81:56:e4:61:0d:ff:d1:0e:e2:f8:21:a5:c5:db:ce: c8:c1:54:50:58:f4:d5:4c:53:ba:f7:dd:25:9d:a4: 55:25:a1:4b:07:25:38:14:20:0c:a6:c2:07:1d:a6: cd:b0:f0:5b:cc:58:f6:fd:1d:0a:93:01:58:83:79: 46:e4:fc:67:91:f9:36:9c:07:c5:9c:26:12:bd:ab:
2001/03/26 r.innocente 29 X.500 Directory Services
2001/03/26 r.innocente 30 X.500 Pic from M.Branchaud
2001/03/26 r.innocente 31 Distinguished Names (DN) fields • Common name CN e.g. CN=Joe Wells • Organizational unit OU e.g OU=Sales • Organization O e.g. O=Heaven,Inc. • City/Locality L e.g. L=Tampa • State/Province ST e.g. ST=Florida • Country C e.g. C=US • / C=US/ST=Florida/L=Tampa/O=Heaven,Inc./OU=Sale s/CN=Joe Wells
2001/03/26 r.innocente 32 Digital Certificates/3
2001/03/26 r.innocente 33 X.509 cert v1-2 Pic from M.Branchaud
2001/03/26 r.innocente 34 CRL(CertificateRevocationList)
2001/03/26 r.innocente 35 CRLv2 Pic from M.Branchaud
2001/03/26 r.innocente 36 SSL/1 The SSL (Secure Socket Layer) protocol was designed by Netscape to be used with its browser. • SSL v.1 was used only internally. • SSL v.2 was incorporated in Navigator v1 and v2. • Microsoft created a similar protocol called PCT which overcame some problems of SSL • SSL v.3 incorporated PCT enhancements
2001/03/26 r.innocente 37 SSL/2 • The first implementation of SSL was available only in Netscape browsers and servers • SSLRef is a reference implementation in C that Netscape made available in source code (does’nt include RC2 or RC4 encryption algorithms) • SSLeay is an indipendent implementation of SSLv.3 made by Eric A. Young a programmer in Australia • OpenSSL is based on SSLeay
2001/03/26 r.innocente 38 TLS/SSL Layers e.g. TCP TLS Record protocol TLS Handshake prot TLS layers Transport protocol
2001/03/26 r.innocente 39 SSL record protocol • Each SSL record contains: • content type • proto version • length • payload • Message auhentication ( Changed in TLS to HMAC), it contains a sequence number to be hashed together with data
2001/03/26 r.innocente 40 SSL/TLS handshake • ClientHello (version,random,session,ciperhs) – Server hello(version,random,session,cipher) – [server may send its certificate] – [server may send a KeyExchange] – [server may send a CertReq] • [Client sends its certificate] • client sends a KeyExchange • [client sends a cert verify] • both send a Change CIpher
2001/03/26 r.innocente 41 SSL cert accept Pic From netscape
2001/03/26 r.innocente 42 Key Exchange • SSL v.2 uses RSA key exchange only • SSL v.3 supports: • RSA key exchange when certificates are used • DH (Diffie-Hellmann) for exchanging keys w/o certificates or prior communication
2001/03/26 r.innocente 43 Diffie-Hellmann Key Exchange • Given a large prime n and a primitive g • A chooses a random x and sends to B • X = g^x mod n • B choses a random y and sends to A • Y = g^y mod n • A and B can compute • k = Y^x mod n = g^(y*x) mod n = X^y mod n • The patent held by PKP expired in 1997
2001/03/26 r.innocente 44 PKI (Public Key Infrastructure) • It is a practical and viable way of publishing public keys on the Internet • PGP,PEM,PKIX ,SPKI and SDSI are different proposals
2001/03/26 r.innocente 45 PEM CA model Pic from M.Branchaud
2001/03/26 r.innocente 46 PKI Pic from M.Branchaud
2001/03/26 r.innocente 47 STARTTLS (RFC 2487) • a server announce its support of TLS • ehlo heaven.org • 250 inferno.org • 250 starttls • the client then can switch to TLS • starttls • 220 ready to start tls • STARTTLS is supported in sendmail 8.11
2001/03/26 r.innocente 48 Microsoft Authenticode • Announced in 1996 by Microsoft as part of IE3.0 and ActiveX (A system for downloading programs from web pages) • It describes some file formats to sign Microsoft 32bit EXEs, DLLs and OCXs • The signed file contains: • original file • digital signature • an X.509 certificate for the public key needed to verify the authenticode signature • The tools needed are in the ActiveX software developer’s Kit (CSW Code Signing Wizard)
2001/03/26 r.innocente 49 Java signed applets • Java too can use X.509 certificates to sign the code in a jar file (keytool and jarsign utilities) • The idea is similar to that of Microsoft, the code signed can obtain better trust according to user chosen confidence in signing publishers
2001/03/26 r.innocente 50 Encrypted services Note that recently the name of crypted services has changed from an initial s to a final s (simap to imaps) • https 443/tcp #http over ssl • telnets 992/tcp #telnet over ssl • pop3s 995/tcp • imaps 993/tcp • smtps 465/tcp • sshell 614/tcp #SSLshell • nsiiops 261/tcp #IIOP name service over ssl

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Public key cryptography

  • 1. 2001/03/26 r.innocente 1 Public Key Cryptography, Digital Certificates, Transport Layer Security and Internet encrypted services Roberto Innocente [email protected]
  • 2. 2001/03/26 r.innocente 2 Summary • PKC (Public Key Cryptography) Introduction • Digital Certificates • SSL/TLS • Use of SSL/TLS over Internet • Encrypted services: pop, imap, smtp
  • 3. 2001/03/26 r.innocente 3 Cryptographic systems taxonomy • Symmetric key cryptography • same key for encryption and decryption • relatively fast • RC2, RC4, DES, triple DES • Asymmetric key cryptography • different keys for encryption/decryption • slow • RSA, ElGamal, Elliptic curves
  • 4. 2001/03/26 r.innocente 4 Symmetric Key Cryptography Encryption Decryption Plain text Cipher text Plain text m c=K(m) m=K(c) m message c cipher text K key key K K.K=1
  • 5. 2001/03/26 r.innocente 5 Asymmetric Key Cryptography Encryption Decryption Plain text Cipher text Plain text Encryption key E Decryption key D m c=E(m) m=D(c) m message c cipher text E encryption key D decryption key D.E=1
  • 6. 2001/03/26 r.innocente 6 Another classification • Secret Key Cryptography • the key is kept secret • it requires a secure channel to be transmitted • Public Key Crytpography • one key (the deciphering key) is kept secret • the other key is made public
  • 7. 2001/03/26 r.innocente 7 Public-Key Cryptography Diffie – Hellmann (1976) • Each user generates a pair of inverse transformation E and D. • The deciphering key D must be kept secret but need never be communicated on a channel • The enciphering key E can be made public by placing it in a public directory (Public File) The original idea here is that keys can be produced in pairs and that it can be very hard to generate a key from the other
  • 8. 2001/03/26 r.innocente 8 PKC algorithms Since DH idea in 1976 many algorithms have been proposed, most were discovered insecure, of the remaining many are not feasible. Some of the algorithms are: • Knapsack algorithms (later shown insecure) • RSA (still considered secure) • El Gamal (still considered secure)
  • 9. 2001/03/26 r.innocente 9 Knapsack algorithms/1 (!!! insecure !!!) First PKC algorithm proposed by Merckle and Hellmann in 1978. • Given n integers M1,M2,M3,..., and a sum S, find a binary sequence b1,b2,b3... such that • S=b1*M1+ b2*M2+b3*M3+ .... • where: • M1,M2,M3,... is the public key • b1,b2,b3,... are the bits of the plain message • S is the ciphertext In general it is an hard problem, but ...
  • 10. 2001/03/26 r.innocente 10 Knapsack algorithms/2 (!!! insecure !!!) A subclass of the general problem can be easily solved and mapped onto a more general one. • A superincreasing knapsack is a knapsack in which every number in the ordered sequence is greater than the sum of the preceeding numbers e.g.{ 2,3,6,13,27} • Solving the problem for a superincreasing knapsack is quite easy. Starting from the greatest number, that will be an addend if it is less than the sum S, and so on ... • Now, choosing a number m (=55) greater than the sum of all numbers in the sequence, and a number n (=29) prime with m, and taking the remainder module m of the numbers in the sequence multiplied by n e.g. {2*29=58mod 55 =3, 3*29=87mod 55=32,...} we obtain a knapsack that is not superincreasing... if we take this sequence as the public key, and the underlaying superincreasing sequence as the private key ...
  • 11. 2001/03/26 r.innocente 11 RSA/1 (Rivest,Shamir,Adleman 1978) • Choose primes p,q n=p*q • Choose encryption key e prime with (p-1)*(q-1) • Compute the inverse d such that • now for each message m : • n,e is the public key • d is the private key e*d = 1 mod n c = me mod n m = cd mod n
  • 12. 2001/03/26 r.innocente 12 RSA/2 • Fermat’s little theorem (p prime,(p|a)=1): • Euler Totient function: • Euler’s generalization of Fermat’s theorem: ap-1 ≅ 1 (mod p) φ(n)= # of integers less than n primes with n For p,q primes : φ(p) = p-1 φ(p*q) = (p-1)*(q-1) aφ(n) ≅1 mod n aφ(n) –1 ≅ a-1 mod n therefore : e-1 ≅ e(p-1)(q-1)-1 mod n
  • 13. 2001/03/26 r.innocente 13 RSA/3 • Software speedups: • RSA goes faster if you choose e carefully • 3 (PEM), 65537 (X.509), 17 (PKCS#1) are good choices having only 2 bits set • in particular 65537 requires only 17 multiplications to exponentiate • Hardware chips: • it’s about 1000 times slower than DES • 1 Mb/s using a 512 bits modulus (GEC Marconi)
  • 14. 2001/03/26 r.innocente 14 RSA/4 The RSA patent was valid only for the US because it was requested after publication. In any case the patent expired on September,20 2000 and from then on RSA it’s now free everywhere
  • 15. 2001/03/26 r.innocente 15 El Gamal (T.ElGamal 1984) • Choose a prime p and two random numbers g(<p),x (<p)and compute y = g**x mod p • public key is y,g,p • private key is x • To encrypt a message M choose a random k, (p-1|k)=1 and compute • a= g**k mod p • b = (y**k)* M mod p • a,b is the ciphertext, to decrypt : • M = b/a**x mod p
  • 16. 2001/03/26 r.innocente 16 Message digests or Hash or fingerprints • One way function that maps a file on a fixed length key. As with real fingerprints one hopes that no 2 msgs have the same fingerprint. • collision free • un-reversible • e.g : • Unix sum is a bad example (16 bits) (Unix sum,cksum) • MD5(128 bits) invented by RSA (Unix md5sum) • SHA1(160 bits) Secure Hash Algorithm-1
  • 17. 2001/03/26 r.innocente 17 Uses of PKC Pics from M.Branchaud Pic from M.Branchaud
  • 18. 2001/03/26 r.innocente 18 Digital Signature Message Message Digest MD5 Signature RSA with private key
  • 19. 2001/03/26 r.innocente 19 Pitney-Bowes Veritas system • Uses digital signatures to authenticate info stored on physical documents (including the digital encoding of photographs) • It’s been used successfully at the Olympic World Games in New Haven in 1995 • On the back of a badge a high density bar code encoded a photograph, biographical data and medical data of the athletes • A Veritas reader can scan the bar code, verify the digital signature and then display a copy of the photograph
  • 20. 2001/03/26 r.innocente 20 Digital Certificates L.Kohnfelder (1978) In an effort to overcome performance problems related to the use of a single Public File, Kohnfelder proposed a digitally signed data record containing a name and a public key called a CERTIFICATE.
  • 21. 2001/03/26 r.innocente 21 Digital Certificates/2 Name Public key Digital signature
  • 22. 2001/03/26 r.innocente 22 Certificates/3 • Binary format of certificates is defined using ASN.1 (x.208) • Binary encoding is defined using DER(Distinguished Encoding Rules) which is based on BER (Basic Encoding Rules) • Binary format can be translated into ASCII using Base64 encoding, this form is called PEM encoding
  • 23. 2001/03/26 r.innocente 23 ASN.1 (X.208 1988) Certificate ::=SEQUENCE { tbsCertificate TBSCertificate, signatureAlgorithm AlgorithmIdentifier, signature BIT STRING } TBSCertificate ::=SEQUENCE { version [0] EXPLICIT Version DEFAULT v1, serialNumber CertificateSerialNumber, signatureAlgorithmIdentifier, issuer Name, validity Validity, subject Name, subjectPucliKeyInfo, issuerUniqueID [1] IMPLICIT UniqueIdentifier OPTIONAL, subjectUniqueID [1] IMPLICIT UniqueIdentifier OPTIONAL, extensions [3] EXPLICIT Extensions OPTIONAL } UniqueIdentifier::= BITSTRING Extensions::=SEQUENCE OF Extension
  • 24. 2001/03/26 r.innocente 24 ASN.1/2Private-Key: (1024 bit) modulus: 00:a0:11:a6:01:c6:d6:55:23:06:12:af:76:04:94: 5d:6a:94:67:f7:02:6e:4c:1b:90:39:b8:6d:a6:02: 01:57:87:0b:57:ed:c9:ad:89:28:bf:71:62:7d:26: 9a:de:2d:d8:15:ed:82:07:cf:07:a5:4d:9c:83:b3: 11:19:1a:f4:c9:68:ac:39:c9:98:be:69:5c:dd:da: f1:44:7e:80:9e:53:c9:7c:ca:3c:60:20:99:ce:b3: 53:be:67:7f:31:06:91:b2:c5:76:04:53:0d:5a:42: b9:26:b1:fe:93:15:f0:04:75:03:1c:e7:a9:3a:cf: 9d:5e:01:01:93:81:23:09:45 publicExponent: 65537 (0x10001) privateExponent: 5a:db:a9:af:38:7e:50:b5:20:ad:5a:8b:52:ee:24: 58:6b:04:d8:60:b8:da:da:8a:73:39:0c:84:3e:7f: 24:7f:b3:20:a6:08:e4:48:06:a9:24:63:13:46:e6: 81:56:e4:61:0d:ff:d1:0e:e2:f8:21:a5:c5:db:ce: c8:c1:54:50:58:f4:d5:4c:53:ba:f7:dd:25:9d:a4: 55:25:a1:4b:07:25:38:14:20:0c:a6:c2:07:1d:a6: cd:b0:f0:5b:cc:58:f6:fd:1d:0a:93:01:58:83:79: 46:e4:fc:67:91:f9:36:9c:07:c5:9c:26:12:bd:ab: 1e:86:4c:63:a4:0b:31:c1 prime1: 00:d1:d7:69:c9:c5:b0:50:37:9f:2e:2d:21:b5:9f: 96:7e:e8:c1:05:29:b1:62:da:e4:b5:cd:04:03:b1: 27:c7:3e:ca:27:a1:bd:69:4f:33:e2:97:5a:03:d0: 33:6f:41:c8:e0:f9:94:e2:0d:c1:a6:85:e1:09:ac: 31:f5:97:7f:77 prime2: 00:c3:47:72:4a:31:ea:e4:e6:0f:79:7f:68:da:c8: 40:7a:96:86:be:69:1c:94:e7:ab:1f:03:66:e0:05: 00:92:4f:e9:ac:ff:0e:51:45:9c:ed:9b:9e:01:ba: e5:00:a2:0f:d4:59:e6:06:d9:24:21:ba:b1:96:79: 51:5b:37:44:23 exponent1: 64:1e:98:6d:d9:f1:be:c4:5b:21:a8:0c:ee:60:5f: 68:db:da:c4:80:d9:0e:e6:8b:bb:26:3f:65:17:90: 78:23:40:46:da:87:ca:08:2d:24:4e:bc:77:17:4e: 83:25:eb:17:54:5d:b1:e1:88:64:d0:79:c7:a8:ae: 09:94:a8:0f exponent2: 65:64:77:67:26:bb:fb:d5:a8:3b:41:78:44:00:ad: d9:f8:c6:45:9f:76:03:aa:b6:23:08:35:26:23:f2: c4:05:52:23:4c:db:36:3f:9a:d7:94:71:5a:1c:9c: 42:d3:e2:bc:33:61:48:34:fe:99:b4:c1:f8:8b:4d: 3e:bb:57:59 coefficient: 24:c5:7d:c3:22:1b:cf:ae:15:20:97:9c:73:78:4a: d5:98:39:da:be:12:7e:94:1d:81:fa:0e:08:2a:dc: 3d:18:9e:b3:f8:cf:29:66:76:16:22:11:8f:d1:c1: a3:ec:6f:50:d5:e1:0f:66:ba:6a:43:ec:86:20:08: 39:0c:20:9e -----BEGIN RSA PRIVATE KEY----- MIICWwIBAAKBgQCgEaYBxtZVIwYSr3YElF1qlGf3Am5MG5A5uG2mAgFXhwtX7cmt iSi/cWJ9JpreLdgV7YIHzwelTZyDsxEZGvTJaKw5yZi+aVzd2vFEfoCeU8l8yjxg IJnOs1O+Z38xBpGyxXYEUw1aQrkmsf6TFfAEdQMc56k6z51eAQGTgSMJRQIDAQAB AoGAWtuprzh+ULUgrVqLUu4kWGsE2GC42tqKczkMhD5/JH+zIKYI5EgGqSRjE0bm gVbkYQ3/0Q7i+CGlxdvOyMFUUFj01UxTuvfdJZ2kVSWhSwclOBQgDKbCBx2mzbDw W8xY9v0dCpMBWIN5RuT8Z5H5NpwHxZwmEr2rHoZMY6QLMcECQQDR12nJxbBQN58u LSG1n5Z+6MEFKbFi2uS1zQQDsSfHPsonob1pTzPil1oD0DNvQcjg+ZTiDcGmheEJ rDH1l393AkEAw0dySjHq5OYPeX9o2shAepaGvmkclOerHwNm4AUAkk/prP8OUUWc 7ZueAbrlAKIP1FnmBtkkIbqxlnlRWzdEIwJAZB6YbdnxvsRbIagM7mBfaNvaxIDZ DuaLuyY/ZReQeCNARtqHyggtJE68dxdOgyXrF1RdseGIZNB5x6iuCZSoDwJAZWR3
  • 25. 2001/03/26 r.innocente 25 ASN.1/3 0:d=0 hl=4 l= 603 cons: SEQUENCE 4:d=1 hl=2 l= 1 prim: INTEGER :00 7:d=1 hl=3 l= 129 prim: INTEGER :A011A601C6D655230612AF7604945D6A9467F7026E4C1B9039B86DA6020157870B57EDC9AD8928B F71627D269ADE2DD815ED8207CF07A54D9C83B311191AF4C968AC39C998BE695CDDDAF1447E809E5 3C97CCA3C602099CEB353BE677F310691B2C57604530D5A42B926B1FE9315F00475031CE7A93ACF9 D5E01019381230945 139:d=1 hl=2 l= 3 prim: INTEGER :010001 144:d=1 hl=3 l= 128 prim: INTEGER : 5ADBA9AF387E50B520AD5A8B52EE24586B04D860B8DADA8A73390C843E7F247FB320A608E44806A9 24631346E68156E4610DFFD10EE2F821A5C5DBCEC8C1545058F4D54C53BAF7DD259DA45525A14B07 253814200CA6C2071DA6CDB0F05BCC58F6FD1D0A930158837946E4FC6791F9369C07C59C2612BDAB 1E864C63A40B31C1 275:d=1 hl=2 l= 65 prim: INTEGER :D1D769C9C5B050379F2E2D21B59F967EE8C10529B162DAE4B5CD0403B127C73ECA27A1BD694F33E 2975A03D0336F41C8E0F994E20DC1A685E109AC31F5977F77 342:d=1 hl=2 l= 65 prim: INTEGER :C347724A31EAE4E60F797F68DAC8407A9686BE691C94E7AB1F0366E00500924FE9ACFF0E51459CE D9B9E01BAE500A20FD459E606D92421BAB19679515B374423 409:d=1 hl=2 l= 64 prim: INTEGER : 641E986DD9F1BEC45B21A80CEE605F68DBDAC480D90EE68BBB263F65179078234046DA87CA082D24 4EBC77174E8325EB17545DB1E18864D079C7A8AE0994A80F 475:d=1 hl=2 l= 64 prim: INTEGER : 6564776726BBFBD5A83B41784400ADD9F8C6459F7603AAB62308352623F2C40552234CDB363F9AD7 94715A1C9C42D3E2BC33614834FE99B4C1F88B4D3EBB5759 541:d=1 hl=2 l= 64 prim: INTEGER : 24C57DC3221BCFAE1520979C73784AD59839DABE127E941D81FA0E082ADC3D189EB3F8CF29667616 22118FD1C1A3EC6F50D5E10F66BA6A43EC862008390C209E
  • 26. 2001/03/26 r.innocente 26 OID (object identifiers) • Object identifiers are unique numbers assigned to objects. They identify a node in a global tree. • e.g. 1.2.840.113549.1.7.2 is an OID, it means SignedData which is defined by RSADSI 0 ITU-T 1 ISO 2 joint ISO/ITU
  • 27. 2001/03/26 r.innocente 27 OID global tree Pic from M.Branchaud
  • 28. 2001/03/26 r.innocente 28 RSA keys according to PKCS#.. Private-Key: (1024 bit) modulus: 00:a0:11:a6:01:c6:d6:55:23:06:12:af:76:04:94: 5d:6a:94:67:f7:02:6e:4c:1b:90:39:b8:6d:a6:02: 01:57:87:0b:57:ed:c9:ad:89:28:bf:71:62:7d:26: 9a:de:2d:d8:15:ed:82:07:cf:07:a5:4d:9c:83:b3: 11:19:1a:f4:c9:68:ac:39:c9:98:be:69:5c:dd:da: f1:44:7e:80:9e:53:c9:7c:ca:3c:60:20:99:ce:b3: 53:be:67:7f:31:06:91:b2:c5:76:04:53:0d:5a:42: b9:26:b1:fe:93:15:f0:04:75:03:1c:e7:a9:3a:cf: 9d:5e:01:01:93:81:23:09:45 publicExponent: 65537 (0x10001) privateExponent: 5a:db:a9:af:38:7e:50:b5:20:ad:5a:8b:52:ee:24: 58:6b:04:d8:60:b8:da:da:8a:73:39:0c:84:3e:7f: 24:7f:b3:20:a6:08:e4:48:06:a9:24:63:13:46:e6: 81:56:e4:61:0d:ff:d1:0e:e2:f8:21:a5:c5:db:ce: c8:c1:54:50:58:f4:d5:4c:53:ba:f7:dd:25:9d:a4: 55:25:a1:4b:07:25:38:14:20:0c:a6:c2:07:1d:a6: cd:b0:f0:5b:cc:58:f6:fd:1d:0a:93:01:58:83:79: 46:e4:fc:67:91:f9:36:9c:07:c5:9c:26:12:bd:ab:
  • 29. 2001/03/26 r.innocente 29 X.500 Directory Services
  • 31. 2001/03/26 r.innocente 31 Distinguished Names (DN) fields • Common name CN e.g. CN=Joe Wells • Organizational unit OU e.g OU=Sales • Organization O e.g. O=Heaven,Inc. • City/Locality L e.g. L=Tampa • State/Province ST e.g. ST=Florida • Country C e.g. C=US • / C=US/ST=Florida/L=Tampa/O=Heaven,Inc./OU=Sale s/CN=Joe Wells
  • 33. 2001/03/26 r.innocente 33 X.509 cert v1-2 Pic from M.Branchaud
  • 36. 2001/03/26 r.innocente 36 SSL/1 The SSL (Secure Socket Layer) protocol was designed by Netscape to be used with its browser. • SSL v.1 was used only internally. • SSL v.2 was incorporated in Navigator v1 and v2. • Microsoft created a similar protocol called PCT which overcame some problems of SSL • SSL v.3 incorporated PCT enhancements
  • 37. 2001/03/26 r.innocente 37 SSL/2 • The first implementation of SSL was available only in Netscape browsers and servers • SSLRef is a reference implementation in C that Netscape made available in source code (does’nt include RC2 or RC4 encryption algorithms) • SSLeay is an indipendent implementation of SSLv.3 made by Eric A. Young a programmer in Australia • OpenSSL is based on SSLeay
  • 38. 2001/03/26 r.innocente 38 TLS/SSL Layers e.g. TCP TLS Record protocol TLS Handshake prot TLS layers Transport protocol
  • 39. 2001/03/26 r.innocente 39 SSL record protocol • Each SSL record contains: • content type • proto version • length • payload • Message auhentication ( Changed in TLS to HMAC), it contains a sequence number to be hashed together with data
  • 40. 2001/03/26 r.innocente 40 SSL/TLS handshake • ClientHello (version,random,session,ciperhs) – Server hello(version,random,session,cipher) – [server may send its certificate] – [server may send a KeyExchange] – [server may send a CertReq] • [Client sends its certificate] • client sends a KeyExchange • [client sends a cert verify] • both send a Change CIpher
  • 41. 2001/03/26 r.innocente 41 SSL cert accept Pic From netscape
  • 42. 2001/03/26 r.innocente 42 Key Exchange • SSL v.2 uses RSA key exchange only • SSL v.3 supports: • RSA key exchange when certificates are used • DH (Diffie-Hellmann) for exchanging keys w/o certificates or prior communication
  • 43. 2001/03/26 r.innocente 43 Diffie-Hellmann Key Exchange • Given a large prime n and a primitive g • A chooses a random x and sends to B • X = g^x mod n • B choses a random y and sends to A • Y = g^y mod n • A and B can compute • k = Y^x mod n = g^(y*x) mod n = X^y mod n • The patent held by PKP expired in 1997
  • 44. 2001/03/26 r.innocente 44 PKI (Public Key Infrastructure) • It is a practical and viable way of publishing public keys on the Internet • PGP,PEM,PKIX ,SPKI and SDSI are different proposals
  • 45. 2001/03/26 r.innocente 45 PEM CA model Pic from M.Branchaud
  • 47. 2001/03/26 r.innocente 47 STARTTLS (RFC 2487) • a server announce its support of TLS • ehlo heaven.org • 250 inferno.org • 250 starttls • the client then can switch to TLS • starttls • 220 ready to start tls • STARTTLS is supported in sendmail 8.11
  • 48. 2001/03/26 r.innocente 48 Microsoft Authenticode • Announced in 1996 by Microsoft as part of IE3.0 and ActiveX (A system for downloading programs from web pages) • It describes some file formats to sign Microsoft 32bit EXEs, DLLs and OCXs • The signed file contains: • original file • digital signature • an X.509 certificate for the public key needed to verify the authenticode signature • The tools needed are in the ActiveX software developer’s Kit (CSW Code Signing Wizard)
  • 49. 2001/03/26 r.innocente 49 Java signed applets • Java too can use X.509 certificates to sign the code in a jar file (keytool and jarsign utilities) • The idea is similar to that of Microsoft, the code signed can obtain better trust according to user chosen confidence in signing publishers
  • 50. 2001/03/26 r.innocente 50 Encrypted services Note that recently the name of crypted services has changed from an initial s to a final s (simap to imaps) • https 443/tcp #http over ssl • telnets 992/tcp #telnet over ssl • pop3s 995/tcp • imaps 993/tcp • smtps 465/tcp • sshell 614/tcp #SSLshell • nsiiops 261/tcp #IIOP name service over ssl