applied-cryptography/appliedcrypto

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Try not to look at these answers, unless you really have too ..

Introduction

A.1

pub  2048R/1AD74F42 2015-03-01 Bill Buchanan (None) 
sub  2048R/6F6AA48C 2015-03-01

A.2

The code used is:

from Crypto.PublicKey import RSA
from Crypto.Util import asn1
from base64 import b64decode

msg="Pob7AQZZSml618nMwTpx3V74N45x/rTimUQeTl0yHq8F0dsekZgOT385Jls1HUzWCx6ZRFPFMJ1RNYR2Yh7AkQtFLVx9lYDfb/Q+SkinBIBX59ER3/fDhrVKxIN4S6h2QmMSRblh4KdVhyY6cOxu+g48Jh7TkQ2Ig93/nCpAnYQ="
privatekey = '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'

keyDER = b64decode(privatekey)
keys = RSA.importKey(keyDER)

dmsg = keys.decrypt(b64decode(msg))
print dmsg

The output is:

Congrats! The flag is nothing_is_impossible

A.3

napieraccount@ubuntu:~/.ssh$ cd ~/.ssh
napieraccount@ubuntu:~/.ssh$ ssh-keygen -t rsa -C "w.buchanan@napier.ac.uk"
Generating public/private rsa key pair.
Enter file in which to save the key (/home/napaccount/.ssh/id_rsa): 
/home/napaccount/.ssh/id_rsa already exists.
Overwrite (y/n)? 
napieraccount@ubuntu:~/.ssh$ cat id_rsa
-----BEGIN RSA PRIVATE KEY-----
Proc-Type: 4,ENCRYPTED
DEK-Info: AES-128-CBC,231906D9476629A1F38BF98A15E72E03
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-----END RSA PRIVATE KEY-----
napieraccount@ubuntu:~/.ssh$ ls
id_rsa  id_rsa.pub  known_hosts
napieraccount@ubuntu:~/.ssh$ cat id_rsa.pub
ssh-rsa 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 w.buchanan@napier.ac.uk

For the RSA private key, protecting it with 128-bit AES, CBC, and the salt used is "231906D9476629A1F38BF98A15E72E03":

AES-128-CBC,231906D9476629A1F38BF98A15E72E03

OpenSSL RSA

B.1

What is the type of public key method used? RSA

How long is the default key: 1024

A sample key:

B.2

Start and end are:

-----BEGIN RSA PRIVATE KEY-----
-----END RSA PRIVATE KEY-----

B.3

We get modulus (N), publicExponent (e), privateExponent (d), prime1 (p), prime2 (q). The other parameters are stored to speed up the RSA process, such as exponent1 (d mod p-1), exponent2 (d mod q-1) and coefficient (inv q mod p).

Private-Key: (1024 bit)
modulus:
    00:b7:a9:72:b8:90:2c:67:dc:13:64:f3:bb:c9:50:
    cc:08:ce:75:3c:a5:38:eb:d7:42:a6:6b:df:89:92:
    3e:33:13:2f:df:89:9b:58:c6:f7:66:9f:5a:ca:36:
    af:fc:7c:45:03:09:c4:55:0b:c8:50:06:97:af:ab:
    11:62:27:77:5b:03:b6:4c:e9:58:d4:02:6c:ed:39:
    f4:5f:c5:27:b3:82:f9:23:b3:05:52:17:5f:dc:80:
    13:37:d8:00:78:9f:1d:5d:90:25:7f:5a:07:9d:9f:
    72:85:20:55:3e:6f:c2:c7:d5:92:e8:c9:13:32:2e:
    7c:16:98:09:13:fe:60:42:fd
publicExponent: 65537 (0x10001)
privateExponent:
    13:c6:1a:a3:e4:61:e3:8c:be:49:d0:34:17:a8:ab:
    4f:07:6b:77:ec:12:04:d2:58:4a:b2:b2:8e:8d:40:
    45:1f:7b:b8:05:88:c4:36:27:cc:d4:bb:61:aa:21:
    a8:7d:78:b0:ab:0c:88:5b:8c:65:91:50:23:89:b7:
    85:69:da:5f:b3:85:8e:12:6f:c4:a8:cf:eb:e0:5d:
    5c:ab:27:c1:6c:69:c1:e7:3b:45:2e:a7:f6:9b:40:
    ee:a9:44:68:81:5f:54:04:72:89:68:c6:fa:af:bc:
    06:0f:02:4d:a1:e3:1a:0b:58:3e:77:cb:cc:93:34:
    55:e7:fa:80:a8:39:be:01
prime1:
    00:d9:48:a1:b1:b5:d6:e9:5f:05:f0:54:00:bb:f1:
    2c:9f:38:e6:26:58:a2:f5:1e:26:6c:d2:7c:93:3a:
    76:66:84:c4:a4:13:8f:92:df:cc:e1:0d:38:c8:4e:
    1d:1c:b8:a4:e4:b1:31:5e:52:4b:bf:b1:18:a3:e1:
    3e:18:f6:2c:f9
prime2:
    00:d8:63:29:79:e4:53:dc:84:27:b6:6c:d0:81:37:
    3b:46:07:b3:ef:76:3f:51:61:72:9e:e1:2b:83:ef:
    bd:83:32:3b:e7:c4:ce:dc:0a:15:94:5b:38:34:e5:
    00:aa:16:79:7d:dc:22:ce:ce:ac:6b:46:e3:62:6f:
    81:0b:59:9b:25
exponent1:
    00:c4:15:b6:ce:10:22:d5:52:4a:a2:ba:bc:3a:df:
    87:fc:5c:b5:de:2f:29:48:79:a0:05:9e:e2:8b:5f:
    3c:10:82:8a:8e:e3:94:32:e0:c3:1c:e9:f8:af:53:
    47:14:6f:51:67:8c:bc:d7:b8:fe:e1:0c:2a:07:62:
    b2:ce:86:02:c9
exponent2:
    00:9f:32:95:59:30:3a:e2:89:f8:0d:a6:90:e0:00:
    1a:83:b3:37:16:7e:10:a7:76:e2:35:31:c4:2a:15:
    3f:80:3e:7d:04:4f:2f:41:83:c9:cc:94:30:0d:fa:
    4d:3a:d5:be:1c:72:d0:c9:06:14:a3:f8:4b:62:28:
    56:f0:5a:c4:61
coefficient:
    27:10:f9:fe:ea:6d:dd:8d:3c:09:33:0f:36:0f:12:
    b5:ab:67:dc:22:34:d1:d2:78:3c:a7:2a:c5:da:22:
    11:3f:ba:01:3f:c2:38:84:68:b1:fc:53:ab:57:c3:
    3c:be:2a:ca:ea:20:ac:b2:51:1c:64:1a:37:f4:59:
    04:a9:cd:0d
writing RSA key
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

B.4

If someone gets your private key they could decrypt things sent to you with your public key, or sign things on your behalf.

B.5

We see a PUBLIC KEY string:

B.7

napieraccount@ubuntu:~/test$ openssl rsautl -decrypt -inkey private.pem -in file.bin -out decrypted.txt
napieraccount@ubuntu:~/test$ cat decrypted.txt 
Hello

B.8

We have a hex format for the -hexdump output:

napieraccount@ubuntu:~/test$ openssl rsautl -encrypt -inkey public.pem -pubin -in myfile.txt -out file.bin -hexdump
napieraccount@ubuntu:~/test$ cat file.bin
0000 - 88 a7 53 b6 da 09 6d 9f-c6 80 95 3b 23 2a bd 20   ..S...m....;#*. 
0010 - 46 fb 4b f0 51 ee 64 66-79 96 3a b4 5c 32 c4 2b   F.K.Q.dfy.:.\2.+
0020 - 62 b6 5b 1c da 99 1d 5f-1f 81 06 2e 2e 53 eb 7e   b.[...._.....S.~
0030 - c9 c4 4e 6c d4 60 86 e0-9f 52 8c aa d2 8f 65 c2   ..Nl.`...R....e.
0040 - 7c 08 83 13 d3 c0 3e ce-fc b6 be 01 75 ad ee bb   |.....>.....u...
0050 - 9a b6 56 b4 e5 22 7b ea-a5 85 2d 16 fa 7f 50 6f   ..V.."{...-...Po
0060 - d7 67 ff bd 97 c2 26 04-1f 8d 4d c7 52 ea 40 6e   .g....&...M.R.@n
0070 - 9a d9 03 10 67 52 a3 05-8f 0c fd 83 7b 1b 89 1b   ....gR......{...
napieraccount@ubuntu:~/test$ openssl rsautl -encrypt -inkey public.pem -pub

We get a binary format with:

napieraccount@ubuntu:~/test$ openssl rsautl -encrypt -inkey public.pem -pubin -in myfile.txt -out file.bin 
napieraccount@ubuntu:~/test$ cat file.bin
:<3A>H<EFBFBD>n<EFBFBD>D.Y<><59>?rѐ<72><D190>XRfZ'<27><><EFBFBD><EFBFBD>Rs<52><04>5|o<><6F>{<7B>W<EFBFBD><57>I<EFBFBD>f<EFBFBD><66>^9<06><>LP.<2E>z<EFBFBD><7A><EFBFBD>bunn_<02>RX<1B>N<EFBFBD><06>%<25>9<EFBFBD><39><EFBFBD>w_<77><5F><<3C>x<EFBFBD><78>ɯ<EFBFBD><C9AF>G1<>={|"<22>p<EFBFBD><1E>F<EFBFBD><46>94.P[_

ECC

C.1

napieraccount@ubuntu:~/test$ openssl ecparam -name secp256k1 -genkey -out priv.pem
napieraccount@ubuntu:~/test$ cat priv.pem 
-----BEGIN EC PARAMETERS-----
BgUrgQQACg==
-----END EC PARAMETERS-----
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIIjZk1BI+xwWQZ6XetT17JrQgGLdQzvDnTB6iqLEFsGCoAcGBSuBBAAK
oUQDQgAE4VZg4yjli491gWC+f7mNAtI8pdRyHYXhUVjVTFlVXKvflEd3BxRiMUWC
KJPzklyIgOZFAOMYzSv5YvMA/YovWQ==
-----END EC PRIVATE KEY-----

C.2

Values are A, B, Generator (G) and Prime (p), and where G is the generator point. The curve is:

y²=x³+a x + b (mod p)

napieraccount@ubuntu:~/test$ openssl ecparam -in priv.pem -text -param_enc explicit -noout
Field Type: prime-field
Prime:
    00:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:fe:ff:
    ff:fc:2f
A:    0
B:    7 (0x7)
Generator (uncompressed):
    04:79:be:66:7e:f9:dc:bb:ac:55:a0:62:95:ce:87:
    0b:07:02:9b:fc:db:2d:ce:28:d9:59:f2:81:5b:16:
    f8:17:98:48:3a:da:77:26:a3:c4:65:5d:a4:fb:fc:
    0e:11:08:a8:fd:17:b4:48:a6:85:54:19:9c:47:d0:
    8f:fb:10:d4:b8
Order: 
    00:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:fe:ba:ae:dc:e6:af:48:a0:3b:bf:d2:5e:8c:d0:
    36:41:41
Cofactor:  1 (0x1)

C.3

We generate the public key from the private key. If we have a private key (priv) and a generator point (G). The public key is priv G. In this case we are using a curve of secp256k1.

napieraccount@ubuntu:~/test$ openssl ec -in priv.pem -text -noout
read EC key
Private-Key: (256 bit)
priv:
    00:88:d9:93:50:48:fb:1c:16:41:9e:97:7a:d4:f5:
    ec:9a:d0:80:62:dd:43:3b:c3:9d:30:7a:8a:a2:c4:
    16:c1:82
pub: 
    04:e1:56:60:e3:28:e5:8b:8f:75:81:60:be:7f:b9:
    8d:02:d2:3c:a5:d4:72:1d:85:e1:51:58:d5:4c:59:
    55:5c:ab:df:94:47:77:07:14:62:31:45:82:28:93:
    f3:92:5c:88:80:e6:45:00:e3:18:cd:2b:f9:62:f3:
    00:fd:8a:2f:59
ASN1 OID: secp256k1

How many bits and bytes does your private key have: 256 bits (32 bytes)

How many bit and bytes does your public key have (Note the 04 is not part of the elliptic curve point): 512 bits (64 bytes)

What is the ECC method that you have used? secp256k1

ECC Encryption

D.1

import OpenSSL
import pyelliptic

secretkey="password"
test="Test123"

alice = pyelliptic.ECC() 
bob = pyelliptic.ECC()

print "++++Keys++++"
print "Bob's private key: "+bob.get_privkey().encode('hex')
print "Bob's public key: "+bob.get_pubkey().encode('hex')

print
print "Alice's private key: "+alice.get_privkey().encode('hex')
print "Alice's public key: "+alice.get_pubkey().encode('hex')


ciphertext = alice.encrypt(test, bob.get_pubkey())

print "\n++++Encryption++++"

print "Cipher: "+ciphertext.encode('hex')

print "Decrypt: "+bob.decrypt(ciphertext)

signature = bob.sign("Alice")

print 
print "Bob verified: "+ str(pyelliptic.ECC(pubkey=bob.get_pubkey()).verify
(signature, "Alice"))

++++Keys++++
Bob's private key: 02f9f16a09b1e7dbb7b6697f94407616d9cd57965146f9fa93e6167c8d59239e09ec68da
Bob's public key: 040634cbbfe036049706a41449a8528bf0f72cb4ada794f57bcaffa7edf77106ac74ce86e605c488184302331d4586638a879b717e66d53ee65363330bfc9f0e780ffed18dab5ff6bf

Alice's private key: 037cfc7ee3bc58f54f213877003b0d3bf8e6d760cc4474ccf9d6fed2ae1b241c0bb9b733
Alice's public key: 04063eefc97bf6cf4b21f9cdad6899c77826f54c03db6c3b08b417bcaac605b53d9e1852f20369db917baa69e30b1a7eafaca8264028bee780701a957f81f8202c86c1f93515227a88

++++Encryption++++
Cipher: ad8e883133fcaf6d14bd7a8d66a610310406d6a7dfb1ea892d5a518ce9155abca28212ed103c4c194aef62462d62eb409e33e5203604291d73d25d0aa63228e1b91fca6339eb384c956b8df64bad1ec4b19883d6531c950ef9e53f4e4686cd8889bdef3edc6625263dd94360585bc3774273402f93d87211767ebd3bde961be86a121c52881873078a
Decrypt: Test123

Bob verified: True

D.2

y² = x^{3 + 7 (mod 89)}

A:  0
B:  7
Prime number:		89
Elliptic curve is:		y^2=x^3+ 7
Finding the first 20 points

(14, 9) (15, 0) (16, 3) (17, 5) (22, 8) (24, 6) (40, 4) (60, 2) (70, 1) (71, 7)

D.3

napier@napier-virtual-machine:~$ python ecc1.py 
Message:	Hello
Type:		NIST192p
=========================
Signature:	ntghRZKzExfLcoR2TJOw9J+ZJ+Pwq1+n/5UPUQqM5qoM9BKu/hUV/KMFvVIgDmU1
=========================
Signatures match:	True

RSA

E.1

import rsa
(bob_pub, bob_priv) = rsa.newkeys(512)
print bob_pub
print bob_priv
ciphertext = rsa.encrypt('Here is my message', bob_pub)
message = rsa.decrypt(ciphertext, bob_priv)
print(message.decode('utf8'))

A sample run gives:

PublicKey(7044152640361902500168576401792350494310726185372977704588682647070501920385795486653093710793158373161949147824992313215786223524754692116109993477603703, 
65537)
PrivateKey(7044152640361902500168576401792350494310726185372977704588682647070501920385795486653093710793158373161949147824992313215786223524754692116109993477603703, 
65537, 1031520101462581111343482730793310461173078401529280666355457029829494893917496934907266419334856470211959662572029962392609614789178286814805200163248601, 
7009636621105341733056641551350073875772161289792261672243040042003271353299512989, 1004924081107519375914073833480034561474534624800691686376057520755477027)
Here is my message

The keys are (e,N) for the public key, and (d,N) for the private key. In this case the value of N is:

7044152640361902500168576401792350494310726185372977704588682647070501920385795486653093710793158373161949147824992313215786223524754692116109993477603703

And e is:

For the decryption key, N is the same value as the encryption key, and d is:

1031520101462581111343482730793310461173078401529280666355457029829494893917496934907266419334856470211959662572029962392609614789178286814805200163248601

The two prime numbers used (p and q) are then:

7009636621105341733056641551350073875772161289792261672243040042003271353299512989 1004924081107519375914073833480034561474534624800691686376057520755477027

Sample:

>>> 7009636621105341733056641551350073875772161289792261672243040042003271353299512989*1004924081107519375914073833480034561474534624800691686376057520755477027 
7044152640361902500168576401792350494310726185372977704588682647070501920385795486653093710793158373161949147824992313215786223524754692116109993477603703L

GPG

F.1

napieraccount@ubuntu:~/test$ gpg key01.key 
pub   512R/362DD998 2019-01-19 bill 
sub   512R/4AA5846A 2019-01-19

F.3

napieraccount@ubuntu:~/test$ gpg --gen-key
gpg (GnuPG) 1.4.20; Copyright (C) 2015 Free Software Foundation, Inc.
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.

Please select what kind of key you want:
   (1) RSA and RSA (default)
   (2) DSA and Elgamal
   (3) DSA (sign only)
   (4) RSA (sign only)
Your selection? 1
RSA keys may be between 1024 and 4096 bits long.
What keysize do you want? (2048) 
Requested keysize is 2048 bits
Please specify how long the key should be valid.
         0 = key does not expire
        = key expires in n days
      w = key expires in n weeks
      m = key expires in n months
      y = key expires in n years
Key is valid for? (0) 
Key does not expire at all
Is this correct? (y/N) y

You need a user ID to identify your key; the software constructs the user ID
from the Real Name, Comment and Email Address in this form:
    "Heinrich Heine (Der Dichter) "

Real name: Bill Buchanan
Email address: w.buchanan@napier.ac.uk
Comment: Test
You selected this USER-ID:
    "Bill Buchanan (Test) "

Change (N)ame, (C)omment, (E)mail or (O)kay/(Q)uit? O
You need a Passphrase to protect your secret key.

We need to generate a lot of random bytes. It is a good idea to perform
some other action (type on the keyboard, move the mouse, utilize the
disks) during the prime generation; this gives the random number
generator a better chance to gain enough entropy.
..+++++
......+++++
We need to generate a lot of random bytes. It is a good idea to perform
some other action (type on the keyboard, move the mouse, utilize the
disks) during the prime generation; this gives the random number
generator a better chance to gain enough entropy.
....+++++
+++++
gpg: key B3396725 marked as ultimately trusted
public and secret key created and signed.

gpg: checking the trustdb
gpg: 3 marginal(s) needed, 1 complete(s) needed, PGP trust model
gpg: depth: 0  valid:   3  signed:   0  trust: 0-, 0q, 0n, 0m, 0f, 3u
pub   2048R/B3396725 2020-02-05
      Key fingerprint = C6AA 3C69 9BB9 B49F 1E19  55B7 4CA0 F614 B339 6725
uid                  Bill Buchanan (Test) 
sub   2048R/F06888D7 2020-02-05

Next we export to the public key:

napieraccount@ubuntu:~/test$ gpg --export -a "Bill Buchanan" > mypub.key
napieraccount@ubuntu:~/test$ cat mypub.key 
-----BEGIN PGP PUBLIC KEY BLOCK-----
Version: GnuPG v1

mI0EXjs2VQEEALlDB1D/z+7Ydqjus2JPcT53RrRjRSQtwlDlZ9omiisTlEvqw6rx
6OkXF9lqjM4q5mEN1BwKBaZfmYYwtsJUzV6GWz2p9lEtHWWtn8pv66ve8tGrBpGj
+Bbx3p5DnAq9rKuOKFXoNj35cda/xpYv4R7WyBeTgisRK4yEb9tbZeBpABEBAAG0
LkJpbGwgQnVjaGFuYW4gKFRlc3QpIDx3LmJ1Y2hhbmFuQG5hcGllci5hYy51az6I
uAQTAQIAIgUCXjs2VQIbAwYLCQgHAwIGFQgCCQoLBBYCAwECHgECF4AACgkQQGhL
ZyBWhFp+/AP/YiEtJTahVgmczHtVkfOTdGiQraJZLB9ZiRBOT+Qby6f5gNtPM1SB
DHARFORQ2d9pXDj4x8I7esx+7WfZyR7Yv6XQznpAGxaALLNy4fkCJV2vew/Err2Q
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AQQA5HIN6FoHZYNagQ45k/uFMtvE4h+QdCvdvNZthj/RmFwuRZpmS9DlebdmM5v2
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WqvB9W0bEl6r9qGv+jHqjk4uDq88TWAniHp5Y4oOYm8ro0MAEQEAAYifBBgBAgAJ
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BD7oNhW7b1xGFqW4VmSTuu3wzAmti+6YD8lyaMEAHuFvHkSehg5PJACYd3Ymbpgr
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a/4d01wsxKF52A4nWYvWyvtPk1iOqv6Qk0hCtw8H1LNTCO+geRhRncF9baqWFqAN
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MQcH/2NBQGIyjKJjykyYZOwxI2nIOjQTwcD34eCsHkvZRu6Bir4bSCaBE1T6FrKv
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oixvpNMcgLxr+Vzj5mHs9wIBuKvQvk4/1gj9NSEXOjjyjRCkHfakTgqW1oIFF2d4
ArjtxFz7iHHJoYgGBdnx3XCJN7/Gl/VyDoLE+Abdj1IJRPKA0RQV9MTyDyxbFu9/
mkId5R6mss2dgfolfbhe270W3YXdIf4+Q8ZfNYvGB4xJPwAqkaZFHzcH4DDLzTrJ
HbEGDO0EQNXT8omOWRYMCM6+VlK5AQ0EXjs3PQEIAOV3lLRCu6TPkUl81aGB0/NV
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QGDCZ/eC//MdP/eXHT+PSYwBZXZzoeF6sgoYyw6f607+6TNb8WU9xNGuZR/L1FYM
Me7/GnhDwhyM5CoCELwtTJ9T9/t2QHgCLvl07eMYK8pCadrxt0S93sBZB86rHfvb
FmQsSY7zmwdraW7tUfFC/cp2pbAHwXqIiNv+0/SIzHwgp4Cb9VDsnktsy/wwlASB
YK+mRkcr1CyEc+Sec1BmQJ3fzf/CPgqAlMMKO2ZDrA/1ABEBAAG0LkJpbGwgQnVj
aGFuYW4gKFRlc3QpIDx3LmJ1Y2hhbmFuQG5hcGllci5hYy51az6JATgEEwECACIF
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/0BWUAv4SVMqSHJE9N93UodCnDLunagVFxJypkTNQ4bZmC7kmwH2wdOISB/gMpm+
N/xSMRx1+ZzXeAO3///AGnB2eReq05VlRkDdqkRtWDSXiZBUEfe3p5qjLK7FurL3
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jwLDUVMHcy2Yv7SzRClLb5E8YS9g9hVyaAQLznUkFXtgakR6Me4h5jFf3WPHAd+a
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x1Mr0j4ByAN2Fcw3zyIAXOK5AQ0EXjs3kgEIAMAi60tB5VuiX+22wYgHujlhrQFR
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seESxttSypZN9Bt/5gAXLSCVVxcgNvMF7I7pBs9GYA180+6MgiUvOUCrORT/0avB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=3RvZ
-----END PGP PUBLIC KEY BLOCK-----

And the private key:

napieraccount@ubuntu:~/test$ gpg --export-secret-key -a "Bill Buchanan" > mypriv.key
napieraccount@ubuntu:~/test$ cat mypriv.key 
-----BEGIN PGP PRIVATE KEY BLOCK-----
Version: GnuPG v1
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IgUCXjs2VQIbAwYLCQgHAwIGFQgCCQoLBBYCAwECHgECF4AACgkQQGhLZyBWhFp+
/AP/YiEtJTahVgmczHtVkfOTdGiQraJZLB9ZiRBOT+Qby6f5gNtPM1SBDHARFORQ
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DehaB2WDWoEOOZP7hTLbxOIfkHQr3bzWbYY/0ZhcLkWaZkvQ5Xm3ZjOb9voS1Xgt
wmbhtw3+xC3qctAje5mkMWbM6amWIVV/19V3ZLvDyhmSHZ8VyobMNF2y+VqrwfVt
GxJeq/ahr/ox6o5OLg6vPE1gJ4h6eWOKDmJvK6NDABEBAAH+BwMCmiXKCB/32Hpg
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dvQLCJZT34EX10smiDJblBckLm2aEI3Em2dw1Cpum4/j462qvU+/CiQLac/njKdQ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=Ul23
-----END PGP PRIVATE KEY BLOCK-----

H.1

Password: napier

34 KiB Raw Blame History Unescape Escape

Introduction

A.1

A.2

A.3

OpenSSL RSA

B.1

B.2

B.3

B.4

B.5

B.7

B.8

ECC

C.1

C.2

C.3

ECC Encryption

D.1

D.2

D.3

RSA

E.1

GPG

F.1

F.3

H.1

34 KiB

Raw Blame History