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appliedcrypto/unit04_public_key/lab/sample_ans.md
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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:

# https://asecuritysite.com/encryption/rsa_example
from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
import base64

binPrivKey = "-----BEGIN RSA PRIVATE KEY-----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\nNXCCvRjQhpNVhlor7y4FC2p3thje9xox6QiwNr/5siyccw==\n-----END RSA PRIVATE KEY-----"

ciphertext=base64.b64decode("uW6FQth0pKaWc3haoqxbjIA7q2rF+G0Kx3z9ZDPZGU3NmBfzpD9ByU1ZBtbgKC8ATVZzwj15AeteOnbjO3EHQC4A5Nu0xKTWpqpngYRGGmzMGtblW3wBlNQYovDsRUGt+cJK7RD0PKn6PMNqK5EQKCD6394K/gasQ9zA6fKn3f0=")

privKeyObj = RSA.importKey(binPrivKey)
cipher = PKCS1_OAEP.new(privKeyObj)
message = cipher.decrypt(ciphertext)


print
print ("====Decrypted===")
print ("Message:",message)

The output is:

Python is your friend

A sample is here

OpenSSL RSA

B.1

What is the type of public key method used? RSA

How long is the default key: 1024

A sample key:

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

-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQC3qXK4kCxn3BNk87vJUMwIznU8
pTjr10Kma9+Jkj4zEy/fiZtYxvdmn1rKNq/8fEUDCcRVC8hQBpevqxFiJ3dbA7ZM
6VjUAmztOfRfxSezgvkjswVSF1/cgBM32AB4nx1dkCV/Wgedn3KFIFU+b8LH1ZLo
yRMyLnwWmAkT/mBC/QIDAQAB
-----END PUBLIC KEY-----

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

C.4

The curves are:

% openssl ecparam -list_curves
  secp112r1 : SECG/WTLS curve over a 112 bit prime field
  secp112r2 : SECG curve over a 112 bit prime field
  secp128r1 : SECG curve over a 128 bit prime field
  secp128r2 : SECG curve over a 128 bit prime field
  secp160k1 : SECG curve over a 160 bit prime field
  secp160r1 : SECG curve over a 160 bit prime field
  secp160r2 : SECG/WTLS curve over a 160 bit prime field
  secp192k1 : SECG curve over a 192 bit prime field
  secp224k1 : SECG curve over a 224 bit prime field
  secp224r1 : NIST/SECG curve over a 224 bit prime field
  secp256k1 : SECG curve over a 256 bit prime field
  secp384r1 : NIST/SECG curve over a 384 bit prime field
  secp521r1 : NIST/SECG curve over a 521 bit prime field
  prime192v1: NIST/X9.62/SECG curve over a 192 bit prime field
  prime192v2: X9.62 curve over a 192 bit prime field
  prime192v3: X9.62 curve over a 192 bit prime field
  prime239v1: X9.62 curve over a 239 bit prime field
  prime239v2: X9.62 curve over a 239 bit prime field
  prime239v3: X9.62 curve over a 239 bit prime field
  prime256v1: X9.62/SECG curve over a 256 bit prime field
  sect113r1 : SECG curve over a 113 bit binary field
  sect113r2 : SECG curve over a 113 bit binary field
  sect131r1 : SECG/WTLS curve over a 131 bit binary field
  sect131r2 : SECG curve over a 131 bit binary field
  sect163k1 : NIST/SECG/WTLS curve over a 163 bit binary field
  sect163r1 : SECG curve over a 163 bit binary field
  sect163r2 : NIST/SECG curve over a 163 bit binary field
  sect193r1 : SECG curve over a 193 bit binary field
  sect193r2 : SECG curve over a 193 bit binary field
  sect233k1 : NIST/SECG/WTLS curve over a 233 bit binary field
  sect233r1 : NIST/SECG/WTLS curve over a 233 bit binary field
  sect239k1 : SECG curve over a 239 bit binary field
  sect283k1 : NIST/SECG curve over a 283 bit binary field
  sect283r1 : NIST/SECG curve over a 283 bit binary field
  sect409k1 : NIST/SECG curve over a 409 bit binary field
  sect409r1 : NIST/SECG curve over a 409 bit binary field
  sect571k1 : NIST/SECG curve over a 571 bit binary field
  sect571r1 : NIST/SECG curve over a 571 bit binary field
  c2pnb163v1: X9.62 curve over a 163 bit binary field
  c2pnb163v2: X9.62 curve over a 163 bit binary field
  c2pnb163v3: X9.62 curve over a 163 bit binary field
  c2pnb176v1: X9.62 curve over a 176 bit binary field
  c2tnb191v1: X9.62 curve over a 191 bit binary field
  c2tnb191v2: X9.62 curve over a 191 bit binary field
  c2tnb191v3: X9.62 curve over a 191 bit binary field
  c2pnb208w1: X9.62 curve over a 208 bit binary field
  c2tnb239v1: X9.62 curve over a 239 bit binary field
  c2tnb239v2: X9.62 curve over a 239 bit binary field
  c2tnb239v3: X9.62 curve over a 239 bit binary field
  c2pnb272w1: X9.62 curve over a 272 bit binary field
  c2pnb304w1: X9.62 curve over a 304 bit binary field
  c2tnb359v1: X9.62 curve over a 359 bit binary field
  c2pnb368w1: X9.62 curve over a 368 bit binary field
  c2tnb431r1: X9.62 curve over a 431 bit binary field
  wap-wsg-idm-ecid-wtls1: WTLS curve over a 113 bit binary field
  wap-wsg-idm-ecid-wtls3: NIST/SECG/WTLS curve over a 163 bit binary field
  wap-wsg-idm-ecid-wtls4: SECG curve over a 113 bit binary field
  wap-wsg-idm-ecid-wtls5: X9.62 curve over a 163 bit binary field
  wap-wsg-idm-ecid-wtls6: SECG/WTLS curve over a 112 bit prime field
  wap-wsg-idm-ecid-wtls7: SECG/WTLS curve over a 160 bit prime field
  wap-wsg-idm-ecid-wtls8: WTLS curve over a 112 bit prime field
  wap-wsg-idm-ecid-wtls9: WTLS curve over a 160 bit prime field
  wap-wsg-idm-ecid-wtls10: NIST/SECG/WTLS curve over a 233 bit binary field
  wap-wsg-idm-ecid-wtls11: NIST/SECG/WTLS curve over a 233 bit binary field
  wap-wsg-idm-ecid-wtls12: WTLS curve over a 224 bit prime field
  Oakley-EC2N-3: 
	IPSec/IKE/Oakley curve #3 over a 155 bit binary field.
	Not suitable for ECDSA.
	Questionable extension field!
  Oakley-EC2N-4: 
	IPSec/IKE/Oakley curve #4 over a 185 bit binary field.
	Not suitable for ECDSA.
	Questionable extension field!
  brainpoolP160r1: RFC 5639 curve over a 160 bit prime field
  brainpoolP160t1: RFC 5639 curve over a 160 bit prime field
  brainpoolP192r1: RFC 5639 curve over a 192 bit prime field
  brainpoolP192t1: RFC 5639 curve over a 192 bit prime field
  brainpoolP224r1: RFC 5639 curve over a 224 bit prime field
  brainpoolP224t1: RFC 5639 curve over a 224 bit prime field
  brainpoolP256r1: RFC 5639 curve over a 256 bit prime field
  brainpoolP256t1: RFC 5639 curve over a 256 bit prime field
  brainpoolP320r1: RFC 5639 curve over a 320 bit prime field
  brainpoolP320t1: RFC 5639 curve over a 320 bit prime field
  brainpoolP384r1: RFC 5639 curve over a 384 bit prime field
  brainpoolP384t1: RFC 5639 curve over a 384 bit prime field
  brainpoolP512r1: RFC 5639 curve over a 512 bit prime field
  brainpoolP512t1: RFC 5639 curve over a 512 bit prime field
  SM2       : SM2 curve over a 256 bit prime field

C.5

The commands are:

% openssl ecparam -name secp128r1 -genkey -out priv.pem
% openssl ecparam -in priv.pem -text -param_enc explicit -noout
Field Type: prime-field
Prime:
    00:ff:ff:ff:fd:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:ff
A:   
    00:ff:ff:ff:fd:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:fc
B:   
    00:e8:75:79:c1:10:79:f4:3d:d8:24:99:3c:2c:ee:
    5e:d3
Generator (uncompressed):
    04:16:1f:f7:52:8b:89:9b:2d:0c:28:60:7c:a5:2c:
    5b:86:cf:5a:c8:39:5b:af:eb:13:c0:2d:a2:92:dd:
    ed:7a:83
Order: 
    00:ff:ff:ff:fe:00:00:00:00:75:a3:0d:1b:90:38:
    a1:15
Cofactor:  1 (0x1)
Seed:
    00:0e:0d:4d:69:6e:67:68:75:61:51:75:0c:c0:3a:
    44:73:d0:36:79

For the prime number we have 16 bytes (128 bits).

% openssl ecparam -name secp521r1 -genkey -out priv.pem
% openssl ecparam -in priv.pem -text -param_enc explicit -noout

Field Type: prime-field
Prime:
    01: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: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:ff:ff:ff:ff:ff:
    ff:ff:ff:ff:ff:ff
A:   
    01: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: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:ff:ff:ff:ff:ff:
    ff:ff:ff:ff:ff:fc
B:   
    51:95:3e:b9:61:8e:1c:9a:1f:92:9a:21:a0:b6:85:
    40:ee:a2:da:72:5b:99:b3:15:f3:b8:b4:89:91:8e:
    f1:09:e1:56:19:39:51:ec:7e:93:7b:16:52:c0:bd:
    3b:b1:bf:07:35:73:df:88:3d:2c:34:f1:ef:45:1f:
    d4:6b:50:3f:00
Generator (uncompressed):
    04:00:c6:85:8e:06:b7:04:04:e9:cd:9e:3e:cb:66:
    23:95:b4:42:9c:64:81:39:05:3f:b5:21:f8:28:af:
    60:6b:4d:3d:ba:a1:4b:5e:77:ef:e7:59:28:fe:1d:
    c1:27:a2:ff:a8:de:33:48:b3:c1:85:6a:42:9b:f9:
    7e:7e:31:c2:e5:bd:66:01:18:39:29:6a:78:9a:3b:
    c0:04:5c:8a:5f:b4:2c:7d:1b:d9:98:f5:44:49:57:
    9b:44:68:17:af:bd:17:27:3e:66:2c:97:ee:72:99:
    5e:f4:26:40:c5:50:b9:01:3f:ad:07:61:35:3c:70:
    86:a2:72:c2:40:88:be:94:76:9f:d1:66:50
Order: 
    01: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:ff:ff:
    ff:ff:ff:fa:51:86:87:83:bf:2f:96:6b:7f:cc:01:
    48:f7:09:a5:d0:3b:b5:c9:b8:89:9c:47:ae:bb:6f:
    b7:1e:91:38:64:09
Cofactor:  1 (0x1)
Seed:
    d0:9e:88:00:29:1c:b8:53:96:cc:67:17:39:32:84:
    aa:a0:da:64:ba

For the prime number we have 65 bytes + 1 bit (521 bits).

ECC Encryption

D.1

Python 3.8:

from cryptography.hazmat.primitives.asymmetric import ec
from cryptography.hazmat.primitives import serialization
import binascii
import sys

private_key = ec.generate_private_key(ec.SECP256K1())


vals = private_key.private_numbers()
no_bits=vals.private_value.bit_length()
print (f"Private key value: {vals.private_value}. Number of bits {no_bits}")

public_key = private_key.public_key()
vals=public_key.public_numbers()

enc_point=binascii.b2a_hex(vals.encode_point()).decode()

print (f"\nPublic key encoded point: {enc_point} \nx={enc_point[2:(len(enc_point)-2)//2+2]} \ny={enc_point[(len(enc_point)-2)//2+2:]}")


pem = private_key.private_bytes(encoding=serialization.Encoding.PEM,format=serialization.PrivateFormat.PKCS8,encryption_algorithm=serialization.NoEncryption())

der = private_key.private_bytes(encoding=serialization.Encoding.DER,format=serialization.PrivateFormat.PKCS8,encryption_algorithm=serialization.NoEncryption())



print ("\nPrivate key (PEM):\n",pem.decode())
print ("Private key (DER):\n",binascii.b2a_hex(der))

pem = public_key.public_bytes(encoding=serialization.Encoding.PEM,format=serialization.PublicFormat.SubjectPublicKeyInfo)

der = public_key.public_bytes(encoding=serialization.Encoding.DER,format=serialization.PublicFormat.SubjectPublicKeyInfo)

print ("\nPublic key (PEM):\n",pem.decode())
print ("Public key (DER):\n",binascii.b2a_hex(der))	

 
	
Private key value: 100412371531109186445752967835007606723422767215817529341655177594081088564056.  Number of bits 256

Public key encoded point: 048987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b 
x=8987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910 
y=babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b

Private key (PEM):
 -----BEGIN PRIVATE KEY-----
MIGEAgEAMBAGByqGSM49AgEGBSuBBAAKBG0wawIBAQQg3f9jZOIMwueRirpNJc9/
WefKlG5mLuIZNEPDFuJ661ihRANCAASJh+x4ZqXR4xFvCKOouNU7fITsJzlWUZy+
My4KZsTJELq+VR06IIGzJ0b7n1dsErJaahvGrch7Thw5GAXPu9Ab
-----END PRIVATE KEY-----

Private key (DER):
 b'308184020100301006072a8648ce3d020106052b8104000a046d306b0201010420ddff6364e20cc2e7918aba4d25cf7f59e7ca946e662ee2193443c316e27aeb58a144034200048987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b'

Public key (PEM):
 -----BEGIN PUBLIC KEY-----
MFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAEiYfseGal0eMRbwijqLjVO3yE7Cc5VlGc
vjMuCmbEyRC6vlUdOiCBsydG+59XbBKyWmobxq3Ie04cORgFz7vQGw==
-----END PUBLIC KEY-----

Public key (DER):
 b'3056301006072a8648ce3d020106052b8104000a034200048987ec7866a5d1e3116f08a3a8b8d53b7c84ec273956519cbe332e0a66c4c910babe551d3a2081b32746fb9f576c12b25a6a1bc6adc87b4e1c391805cfbbd01b'

D.2

y2 = x3 + 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)
msg='Here is my message'
ciphertext = rsa.encrypt(msg.encode(), 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:

65537

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

E.3

b'-----BEGIN RSA PRIVATE KEY-----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\n5KhZKXGaM/GKRR3Z4fayjRPBNoUC17YqxhZx2GviWoVoLBP6n7Fi\n-----END RSA PRIVATE KEY-----'
b'-----BEGIN PUBLIC KEY-----\nMIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEA0GOWzvm7NnW27wAHzmfs\nJA4pC6vJT5Cgjt5qoIfCZHPvoz7z8cdoYPY3N9Z7rCB8a2ev3SBePTs8kBjw32Bp\nvXgNNKtlYHnNi4A5Nuo+kdNqq15V+Mz0pX4otPz7Gl+lFHSZSQuDYp0GlCrLP9xz\nYbtFPwvCZcYBVDQSSjT3LOJx5JQZp9HlzLFR7Q8t7mXt7/wn8ynnlvU9UrBHFPhk\nAfX1UQmcIghbKVNErfTNTwc6blk/mVUvDITh2LOwel5ML+tAjRBfvz+OlyYoY45d\nlvgzeRAzeLJRtW4d2qXEGj27mlOFFd45H5z0CqaVf4GtA+0MBwrlSSFxJKDZi0Og\n2QIDAQAB\n-----END PUBLIC KEY-----'

The code is here.

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
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B8wk8IYFC750Z48Zs1GKWvkf4rBiaaLptCVRqTHmZzesOUdJg8lF+kY43aMrksrk
f4lt
=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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dPLovHzLR9RSpCVsybk/LXR3FRbkXLetz1fYauSyzL9u9wwBCD/MSEYwu4sjyplW
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86me8QHuw92oJLiwDVBrgSYcwG6QdhsRLhve9Ik/Szb3/ti6+c3WiQEfBBgBAgAJ
BQJeOzeSAhsMAAoJEEyg9hSzOWclPbEIAMxcp0rIZU2d3MfynvBglEiTcWUI0fgF
1zxY5sk6jPdDk8F5Nbsfbi4/Y3wLQfEosG6VS6XBFM/awI4zZohkYtVn3Ar5GQXL
hbkSFs+kfsaBwAvw7LM9g8Xu3vm/xFQN3VvpgBUlGnfHgoKKubCk6iSbNor2XmGW
Yv1RRLsIKk/EddIkFbd8gNZxKn9GKgBxymaPDFjDB3Dm0Hmkriaei9EG8HFeso8o
jdZRufTH7FLzanmWOcqtvrtLK4mt3Jia4z0RZayxMQMziuyojpIHzCTwhgULvnRn
jxmzUYpa+R/isGJpoum0JVGpMeZnN6w5R0mDyUX6RjjdoyuSyuR/iW0=
=Ul23
-----END PGP PRIVATE KEY BLOCK-----
```


## I.1

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

H.1

Password: napier tc

Additional

from Crypto.PublicKey import RSA
from base64 import b64decode
from Crypto.Cipher import PKCS1_OAEP


binPrivKey = "-----BEGIN RSA PRIVATE KEY-----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\HMTjSeRDEU0Qm5UXhXkCQQCPlZJqlgksBN/TULHC4RgsXIx+oFylBrkiFamYsuEt\nKn52h41pX7FI5TXcqIDPw+uqAu50JnwDR0dLYY6fvIce\n-----END RSA PRIVATE KEY-----"

privKeyObj = RSA.importKey(binPrivKey)

pubKeyObj="fIVuuWFLVANs9MjatXbIbtH7/n0dBpDirXKi82jZovXS/krxy43cP0J9jlNz4dqxLgdiqtRe1AcymX06JUo1SrcqDEh3lQxoU1KUvV7jG9GE3pSxHq4dQlcWdHz95b9go6QYbe/5S/uJgolR+S9qaDE8tXYysP8FeXIPd0dXxHo="

ciphertext=b64decode(pubKeyObj)

cipher = PKCS1_OAEP.new(privKeyObj)
message = cipher.decrypt(ciphertext)

print
print ("====Decrypted===")
print ("Message:",message)

Sample test run here.

To give:

Message: b'help me...'
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