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Lecture 09 - Encryption. Hashing. APIs
- Keywords: encryption, symmetric encryption, public key encryption, digital signatures, hash, fingerprinting, certificate, RSA, MAC,
openssl,gnutls,crypt,libgcrypt,botan, side channel attack, Heartbleed
Demos
For demos, we will use the demo archive. We will a Linux system to run the demos. We download the archive using the command
wget http://elf.cs.pub.ro/cns/res/lectures/lecture-09-demo.zip
and then we unpack the archive
unzip lecture-09-demo.zip
and then access the demo folder that resulted after the unpack operation
cd lecture-09-demo/
We will now pass through the demos below.
The demos show various ways of using the RSA algorithm: generating keys, encrypting a message and decrypting the message.
RSA in the Shell
We will first start using RSA inside the shell. We will do key generation, key inspection, encryption and decryptions using shell commands embedded in a shell script.
We will go to the shell/ subfolder in the lab archive folder:
student@mjolnir:~/lecture-09-demo$ cd shell/ student@mjolnir:~/lecture-09-demo/shell$ ls -F rsa-ctl*
The rsa-ctl file is an executable shell script that allows us to do common RSA operations. We run it with no arguments to check what arguments we can pass to it:
student@mjolnir:~/lecture-09-demo/shell$ ./rsa-ctl Provide one argument. Usage: ./rsa-ctl genkey | encrypt | decrypt | inspect
The arguments are quite clear: we can generate the RSA keys, we can encrypt messages, we can decrypt messages and we can inspect the keys.
First, use an editor or pager (such as vim or less) to explore the script. Check the four functions implementing the required functionality: rsa_genkey, rsa_encrypt, rsa_decrypt and rsa_inspect. All fuctions use the openssl command, the front-end command for the OpenSSL library.
First, let's generate the private and public keys:
student@mjolnir:~/lecture-09-demo/shell$ ./rsa-ctl genkey Generate private key in rsa.private ... Generate public key in rsa.public ... student@mjolnir:~/lecture-09-demo/shell$ ls rsa-ctl rsa.private rsa.public
The keys are generated in the rsa.private and rsa.public files. Two openssl commands are used in the rsa_genkey funciton in the rsa-ctl script. The first command generates all required parameters and saves them in the private key file (rsa.private). The second command extract the public key information (the modulus n and the public exponent e) and places the public key in the rsa.public file. Both keys are stored in PEM format:
student@mjolnir:~/lecture-09-demo/shell$ cat rsa.private -----BEGIN RSA PRIVATE KEY----- MIICXAIBAAKBgQDfa9+gSRjtsHLNYo6fk4OHwp/ZkM2p7UQM9zMbQ3T8Ql+ST0li /GWx02zGD085eqIzzofZYEEn8/qm2l3iH94QofrbArTrERre4QGrNwUxBehYJKwo malJ0mvPJqY+rVt2lNYPXCgcnC4aDSMgFKsgf2UzGif9pI7sE9Xzlgo8WQIDAQAB AoGAaQG4Xws8DirKKkHSKqoYPax5mLX4E4+SVk2w1XWE/DLt3EQrh7x8x3FJRGVZ pPhAV/0P2FjnBrIi8lzblzXHFkUQyFGOH+oyizIwDhFznb/XBt6VpEJZXDe278PP 2Mtr0pGzmUMTYdzDXLxg267C4zPRJyqI3z1my9Vdljj03KkCQQD7vFTOdjkN+HZK hJN90leDuGE9HhyFR0nErfPJFbMtXUXHXn7/MsB0N3R61FD0zSR0RcHRouYkAUwk JEUx7S6vAkEA4zTBZK24V7iyHmpXMQPILQ7hVP3oggsT14bXZzVzHwNo/WvFTK4K 43Pqo6o27xNxMQkLSp0t7GG7S5ZCAllHdwJBALWyVqf6zu2Vg5P/oxFy6/XH9G+P t1g/fzA1ujtOrVg19XKUcyexsxVvHWS2sIQxOXmvC9lLMb+VLCb+Au+pWUMCQDAN x11o1JVRDfMa4KgQObU18XiNXzCp8R9jeIlup5OGoB0BPzBxmwHyUU0eQhIclZMe a5HzXnQhU4CwHfPrOA8CQD9TTziWkpYAvcFQNhyvjeJIBVODkBKZx9d3qoSzq9bn ei0hbY6VL+gCkIHLuv4oBWqCl4EuN319amxzv+bJCAk= -----END RSA PRIVATE KEY----- student@mjolnir:~/lecture-09-demo/shell$ cat rsa.public -----BEGIN PUBLIC KEY----- MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDfa9+gSRjtsHLNYo6fk4OHwp/Z kM2p7UQM9zMbQ3T8Ql+ST0li/GWx02zGD085eqIzzofZYEEn8/qm2l3iH94Qofrb ArTrERre4QGrNwUxBehYJKwomalJ0mvPJqY+rVt2lNYPXCgcnC4aDSMgFKsgf2Uz Gif9pI7sE9Xzlgo8WQIDAQAB -----END PUBLIC KEY-----
As the private key stores extensive information it is considerable larger than the public key.
Let's also inspect the keys using the inspect argument to the rsa-ctl script. We will be able to see the modulus (n), the prime numbers (p and q), the public exponent (e) and the private exponent (d)).
You can see the large modulus and prime numbers. We generated the key for 1024 bits, so the modulus uses 256 hexadecimal digits (each digit ocuppies 4 bits, for a total or 256 * 4 = 1024 bits). We know we have a valid key pair since both the private and public key are using the same modulus.
A quick way of checking a match of a private and public key pair is to compute and compare the MD5 sum of the modulus. We can use the commands below to check the match for our private and public keys:
student@mjolnir:~/lecture-09-demo/shell$ openssl rsa -noout -modulus -in rsa.private | openssl md5 (stdin)= ea86ebad07960a02f630b9eb557ea0b3 student@mjolnir:~/lecture-09-demo/shell$ openssl rsa -noout -modulus -pubin -in rsa.public | openssl md5 (stdin)= ea86ebad07960a02f630b9eb557ea0b3
The MD5 sum is the same, so the modulus is the same, so the public and private keys are a pair.
We can use the keys to encrypt and decrypt a message, by passing the encrypt and decrypt arguments to the rsa-ctl script. The input message is passed from standard input, while the output message is written to standard output.
We will encrypt the all-for-the-empire string and store it in the encrypted.msg file:
student@mjolnir:~/lecture-09-demo/shell$ echo "all-for-the-empire" | ./rsa-ctl encrypt > encrypted.msg
The encrypted.msg file is a binary file that may only be decrypted by use of the private key. We use xxd to check its inside and see that it's useless without a private key:
student@mjolnir:~/lecture-09-demo/shell$ xxd encrypted.msg 0000000: 9f7c f947 9232 bf49 788c 81d2 ea21 5dc1 .|.G.2.Ix....!]. 0000010: b589 c712 a7f2 cd28 93f4 06a8 d18a fe5d .......(.......] 0000020: 25eb 1c8c ee2d 594a 0344 38a6 cef0 aa98 %....-YJ.D8..... 0000030: f29a 47b6 c8c3 fe73 4ce3 c7d4 1808 e4dd ..G....sL....... 0000040: b797 24eb 2a6a fc68 1230 583f 2e4a 4d2d ..$.*j.h.0X?.JM- 0000050: aed6 ae90 19ee 757f 8865 c373 ad59 1369 ......u..e.s.Y.i 0000060: ee32 a976 f010 8498 ac6b fbb9 1589 45e7 .2.v.....k....E. 0000070: 4e29 5e5a 68e6 78e0 5bcf 889c 5580 4f7c N)^Zh.x.[...U.O|
Now we can retrieve the original message by decrypting the encrypted.msg file. We will pass the decrypt argument to the rsa-ctl script:
student@mjolnir:~/lecture-09-demo/shell$ ./rsa-ctl decrypt < encrypted.msg all-for-the-empire
The output message is the initial string all-for-the-empire so everything works as expected.
Manual Running of the openssl Command
All the above steps can be undertaken directly in the command line, without necessarily using the rsa-ctl script.
In order to generate a private and public key pair, we will first generate a private key on 1024 bits using the openssl genrsa command:
student@mjolnir:~/lecture-09-demo/shell$ openssl genrsa 1024 > rsa.private Generating RSA private key, 1024 bit long modulus .......++++++ ......................................................................++++++ e is 65537 (0x10001)
Then we extract the public key using the openssl rsa command:
student@mjolnir:~/lecture-09-demo/shell$ openssl rsa -in rsa.private -pubout > rsa.public writing RSA key
We can inspect the two keys using the openssl rsa command:
RSA in C
TODO
RSA in Python
TODO
