Using Cryptography CMSC 414. October 16, 2017
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1 Using Cryptography CMSC 414 October 16, 2017
2 Digital Certificates Recall: K pub = (n, e) This is an RSA public key How do we know who this is for? Need to bind identity to a public key We can do this using a Digital Certificate This is a binding that has been signed by some third party Often a trusted third party Sometimes self-signed
3 What s in a Digital Certificate? $ openssl x509 -in mmarsh.req.cert -noout -text Certificate: Data: Version: 3 (0x2) Serial Number: (0x552a34c5) Signature Algorithm: sha256withrsaencryption Issuer: CN=CA, OU=CA, O=soucis Validity Not Before: May 5 20:29: GMT Not After : Jan 30 20:29: GMT Subject: O=soucis, OU=user, CN=Michael Marsh Subject Public Key Info: Public Key Algorithm: rsaencryption RSA Public Key: (4096 bit) Modulus (4096 bit): 00:fe:e2:a3:4c:1c:63:1a:f2:aa:d3:70:bd:d2:8c:... 4f:a6:0c:ef:b3:f6:9c:46:65:94:9f:03:45:73:64: e0:ff:f7 Exponent: (0x10001) X509v3 extensions: X509v3 Authority Key Identifier: keyid:ce:6a:a6:71:63:cf:58:0b:f1:25:e2:b6:5c:0e:ad:73:51:3e:d6:e7 X509v3 Subject Key Identifier: DF:69:B6:41:CF:FC:21:25:C8:5D:CC:A7:89:A2:C8:3F:92:00:66:3D Signature Algorithm: sha256withrsaencryption 6b:10:11:19:fc:e7:d4:0a:b8:67:58:c4:f8:97:99:51:76:60:... 45:a0:b0:64:ff:f8:3f:97:ec:22:23:74:bc:61:0a:a3:b3:cf: 08:ab:ee:29
4 How Do We Know if This is Valid? Certificates have an Issuer The issuer signs the certificate, with an validity period We then need the certificate for the issuer How do we know that certificate is valid...? [Note: Slides marked with an asterisk contain cynicism]
5 Certification Authorities (*) A Root Certification Authority (root CA) is a Root of Trust That means we trust it implicitly CAs issue certificates to users, servers, or intermediate CAs Usually, a root CA only certifies intermediate CAs What we end up with is a Certificate Chain Your browser is pre-loaded with a lot of root CAs, and you trust them, whether you really do or should
6 What Does a CA Do? (*) A CA should check that the name in a certificate request matches the principal sending the request If the certificate is for a service, the CA should check that this is, in fact, the public key for that service, and the requester actually represents the service This usually works, but... Rogue CAs might sign bogus certificates Some CAs only provide this level of verification for higher-paying customers, and issue less-secure certificates for others
7 What Does a Certificate Request Look Like? $ openssl req -in /Downloads/XXXX.req -noout -text Certificate Request: Data: Version: 0 (0x0) Subject: O=soucis, OU=user, CN=XXXX Subject Public Key Info: Public Key Algorithm: rsaencryption RSA Public Key: (4096 bit) Modulus (4096 bit): 00:a8:fe:4a:3e:d0:4e:d1:ad:93:b3:76:fe:c1:78:... 65:17:36:d9:49:22:9a:c9:45:79:e5:14:9f:bd:ed: a1:0d:8d Exponent: (0x10001) Attributes: a0:00 Signature Algorithm: sha1withrsaencryption 48:cb:42:38:f7:d0:2a:d7:8d:95:96:20:60:ae:19:9d:82:ac:... 91:0c:66:b5:4a:92:4b:ec:f1:41:59:ee:47:0e:9f:c7:b7:05: 08:e9:1e:1d:83:1c:2b:32 Unlike the certificate, this is signed with the subject s private key, not the issuer s
8 PGP, GPG, and the Web of Trust Pretty Good Privacy, GNU Privacy Guard Similar idea, but without a root of trust Instead of relying on a third party we don t know Alice and Bob meet (possibly at a key-signing party) 2. They exchange public keys 3. They sign those keys and hand each other the certs Anyone with a cert for Alice can validate Bob s cert from Alice If Bob has a cert signed by Alice, we sometimes refer to him as Alice s Bob when he uses this cert Forms a Web of Trust that can connect users Requires ability to form a trusted path from verifier to subject
9 How Do We Use Certificates? (*) CA-based certificates are commonly used on the web for encrypted connections (HTTPS) PGP-based certificates are commonly used in for signing messages Requires the mail client to have a PGP/GPG-capable extension
10 Public Key Infrastructure (*) Certificates are only one component We also need (this is not the precise technical specification) Distribution mechanism for CA certificates Revocation Lists A Revocation is a CA-issued statement that a certificate is no longer valid (other than due to expiry) This can be due to issues like private key disclosure Your browser almost certainly never checks for these With these, we have a Public Key Infrastructure (PKI)
11 Group Exercise 1 In your crypto-exercises repository run git pull upstream master to merge changes to the upstream repository that you initially forked. Using Crypto Exercise 1 contains instructions for setting up and using your own OpenSSL-based Certification Authority.
12 Symmetric and Asymmetric Crypto Notation To keep things sane, let s define k AB a secret key shared by A and B K A the public key of A k A the private key of A {P} kab symmetric-key encryption of plaintext P with k AB E A (P) asymmetric-key encryption of plaintext P with K A D A (C) asymmetric-key decryption of ciphertext C with k A S A (M) message M signed with k A The short version: {P} k is symmetric-key encryption E(), D(), and S() are asymmetric-key operations
13 Symmetric and Asymmetric Crypto Key Sizes and Security From NIST publication SP Part 1 Rev. 4 (January 2016), by Elaine Barker Security Symmetric RSA Key ECC Key Hash Strength Cryptosystem Length Length Functions 80 2-key 3DES SHA key 3DES SHA AES SHA AES SHA AES SHA-512
14 Symmetric and Asymmetric Crypto Performance 3DES and AES can be implemented in hardware very fast software implementations slower, but still fairly fast using lookup tables RSA, ElGamal, ECC must be implemented in software, and private key operations are fairly slow
15 Symmetric and Asymmetric Crypto Getting the Best of Both A B: M 1, s 1. select random nonce n A 2. M 1 = E B (n A ) 3. s 1 = S A (M 1 ) 1. V A (M 1, s 1 ) 2. compute n A = D B (M 1 ) A simple example: 3. select symmetric key k AB 4. compute n B = n A k AB 5. M 2 = E A (n B ) 6. s 2 = S B (M 2 ) B A: M 2, s 1. V B (M 2, s 2 ) 2. compute n B = D A (M 2 ) 3. compute k AB = n B n A
16 Group Encryption Sometimes we want to send encrypted data to a large number of principals Videoconferencing Premium cable channels Subscription services Public keys too many, takes too long to compute them all Secret keys too many, expensive key exchange (though doesn t have to be done often)
17 Group Encryption Both result in one of lots of individual messages (can t take advantage of efficient delivery mechanisms) extremely long messages that contain lots of copies of encryption extremely long messages that contain one encrypted message and lots of encryptions of the message key Must be a better way...
18 Group Keys We would like to have a single symmetric key for a stream, that can be shared with everyone This could be distributed by a central authority individually to every user, or agreed upon/determined by the set of users A common way to do either of these is with Key Trees There are many ways to do this, all of which share common issues: Key distribution/agreement needs to be fairly efficient Only legitimate group members should be able to learn the key Keys must be changed when members join or leave the group distribution k k 01 k 23 agreement k 0 k 1 k 2 k 3
19 Group Exercise 2 Now you re going to combine public-key and secret-key cryptography for yourself. See Using Crypto Exercise 2 in the README. The instructions assume that you re using python, but you may use any language you like.
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