crypto-lite - Cryptographic Secure Hash Functions and Public Key Signature Algorithms Made Easy

home :: github.com/rubycocos/blockchain
bugs :: github.com/rubycocos/blockchain/issues
gem :: rubygems.org/gems/crypto-lite
rdoc :: rubydoc.info/gems/crypto-lite

Usage

Secure Hashing / Hash Functions

SHA256 - Secure Hash Algorithm (SHA) 256-Bit (32 Bytes)

Note: By default all hash functions return binary strings. Use String#hexdigest (or String#bin_to_hex or String#btoh) to convert binary strings to hex(adecimal) strings (via Bytes.bin_to_hex).

require 'crypto'      ## or use require 'crypto-lite'

## try abc
sha256( "abc" ).hexdigest           #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
sha256( "abc".b ).hexdigest         #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
sha256( "\x61\x62\x63" ).hexdigest  #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"

sha256( hex: '616263' ).hexdigest     #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
sha256( hex: '0x616263' ).hexdigest   #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
sha256( hex: '0X616263' ).hexdigest   #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"

Bonus Back Stage Tip: How does SHA256 work?

Try this amazing animation of the SHA256 hash function in your very own terminal by Greg Walker.

More of a code golfer? See ½ Kilo of SHA256 by Jan Lelis - yes, the SHA256 algorithm coded (from scratch) in 500 bytes of ruby.

Onwards with more sha256 examples:

## try a
sha256( "a" ).hexdigest         #=> "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"
sha256( "\x61" ).hexdigest      #=> "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"

sha256( hex: '61' ).hexdigest     #=> "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"
sha256( hex: '0x61' ).hexdigest   #=> "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"


## try some more
sha256( "Hello, Cryptos!" ).hexdigest  #=> "33eedea60b0662c66c289ceba71863a864cf84b00e10002ca1069bf58f9362d5"

SHA3-256 - Secure Hashing Algorthim (SHA) 3, 256-Bit (32 Bytes)

sha3_256( "Hello, Cryptos!" ).hexdigest  #=> "7dddf4bc9b86352b67e8823e5010ddbd2a90a854469e2517992ca7ca89e5bd58"

Note: Yes, SHA256 vs SHA3-256 / SHA-2 vs SHA-3 the hashing functions are different (although the 256-bit hash size output is the same). The sha256 hashing function is part of the Secure Hash Algorithm (SHA) 2 family / standards first published in 2001. The sha3_256 is part of the (newer) Secure Hash Algorithm (SHA) 3 family / standards first published in 2015 (and uses the Keccak cryptographic primitive "under the hood").

Keccak 256-Bit

keccak256( "Hello, Cryptos!" ).hexdigest  #=> "2cf14baa817e931f5cc2dcb63c889619d6b7ae0794fc2223ebadf8e672c776f5"

Aside - Keccak vs SHA3 / Original vs Official

In 2004 the U.S. National Institute of Standards and Technology (NIST) changed the padding to SHA3-256(M) = KECCAK [512] (M || 01, 256). This is different from the padding proposed by the Keccak team in the original Keccak SHA-3 submission version 3 (the final, winning version). The difference is the additional '01' bits appended to the message.

To help avoid confusion the "submitted original version 3" SHA-3 Keccak hashing is now called "Keccak" and the finalized NIST SHA-3 standard "SHA3".

Tip: If you don't know what variant of the hash function you have - original or official? - check your hash:

For keccak 256-bit:

keccak256( '' ).hexdigest   #=> "c5d2460186f7233c927e7db2dcc703c0e500b653ca82273b7bfad8045d85a470"

For sha3 256-bit:

sha3_256( '' ).hexdigest   #=> "a7ffc6f8bf1ed76651c14756a061d662f580ff4de43b49fa82d80a4b80f8434a"

RMD / RIPE-MD - RACE¹ Integrity Primitives Evaluation Message Digest 160-Bit

¹: Research and development in Advanced Communications technologies in Europe

rmd160( "Hello, Cryptos!" ).hexdigest     #=>"4d65f7b740bbade4097e1348e15d2a7d52ac5f53"
# or use the alias / alternate name
ripemd160( "Hello, Cryptos!" ).hexdigest  #=>"4d65f7b740bbade4097e1348e15d2a7d52ac5f53"

Aside - Hex String `"0x616263"` vs Binary String `"\x61\x62\x63" == "abc"`

Note: All hash functions operate on binary strings ("byte arrays") and NOT hex strings.

Note: For hex strings the 0x or 0X prefix is optional. Examples of hex strings:

# hex string      binary string ("byte array")
"61"              "\x61" == "a"
"0x61"            "\x61" == "a"

"616263"          "\x61\x62\x63" == "abc"
"0x616263"        "\x61\x62\x63" == "abc"
"0X616263"        "\x61\x62\x63" == "abc"

# or   160-bit hex string (hash)
"93ce48570b55c42c2af816aeaba06cfee1224fae"
"0x93ce48570b55c42c2af816aeaba06cfee1224fae"

# or 256-bit hex string (hash)
"ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
"0xba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"

You can use [str].pack( 'H*' ) to convert a hex string into a binary string. Note: The standard Array#pack conversion will NOT "auto-magically" cut-off the 0x or 0X prefix.

If you know you have a hex string use the hex: keyword to pass in the arg(ument) to the hash function and that will "automagically" handle the hex-to-bin conversion for you. Example:

sha256( hex: '61' ).hexdigest     #=> "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"
sha256( hex: '0x61' ).hexdigest   #=> "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"

sha256( hex: '616263' ).hexdigest     #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
sha256( hex: '0x616263' ).hexdigest   #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"
sha256( hex: '0X616263' ).hexdigest   #=> "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad"

Hash Function Helpers

HASH160 - RMD160(SHA256(X))

All-in-one "best-of-both-worlds" helper - first hash with sha256 and than hash with rmd160. Why? Get the higher security of sha256 and the smaller size of rmd160.

hash160( '02b9d1cc0b793b03b9f64d022e9c67d5f32670b03f636abf0b3147b34123d13990' ).hexdigest
#=> "e6b145a3908a4d6616b13c1109717add8672c900"

hash160( '02b4632d08485ff1df2db55b9dafd23347d1c47a457072a1e87be26896549a8737' ).hexdigest
#=> "93ce48570b55c42c2af816aeaba06cfee1224fae"

HASH256 - SHA256(SHA256(X))

All-in-one double sha256 hash helper, that is, first hash with sha256 and than hash with sha256 again. Why? Arguably higher security.

SHA256(SHA256(X)) was proposed by Ferguson and Schneier in their excellent book "Practical Cryptography" (later updated by Ferguson, Schneier, and Kohno and renamed "Cryptography Engineering") as a way to make SHA256 invulnerable to "length-extension" attack. They called it "SHA256D".

hash256( '6fe6b145a3908a4d6616b13c1109717add8672c900' ).hexdigest
#=> "02335f08b8fe4ddad263a50b7a33c5d38ea1cbd8fd2056a1320a3ddece541711"

Base58 Encoding / Decoding Helpers

BASE58

Base58 encoding / decoding with leading zero bytes (in hex or binary strings) getting encoded from 00 to 1 and back:

base58( hex: "516b6fcd0f" )    #=> "ABnLTmg"
base58( hex: "00000000000000000000123456789abcdef0" )   #=> "111111111143c9JGph3DZ"
# or with optional 0x or 0X prefix
base58( hex: "0x516b6fcd0f" )  #=> "ABnLTmg"
base58( hex: "0x00000000000000000000123456789abcdef0" ) #=> "111111111143c9JGph3DZ"

unbase58( "ABnLTmg" ) #=> "516b6fcd0f"
unbase58( "111111111143c9JGph3DZ" ) #=> "00000000000000000000123456789abcdef0"

BASE58CHECK - BASE58(X || SHA256(SHA256(X))[:4])

Base58 encoding with an extra 4-byte secure hash checksum.

base58check( hex: "516b6fcd0f" )  #=> "237LSrY9NUUas"
base58check( hex: "00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31" ) #=> "1PMycacnJaSqwwJqjawXBErnLsZ7RkXUAs"

unbase58check( "237LSrY9NUUas" )   #=> "516b6fcd0f"
unbase58check( "1PMycacnJaSqwwJqjawXBErnLsZ7RkXUAs" )   #=> "00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31"

Public Key Signature Algorithms

Elliptic Curve Digital Signature Algorithm (ECDSA)

Private Key

An ECDSA (Elliptic Curve Digital Signature Algorithm) private key is a random number between 1 and the order of the elliptic curve group.

# Auto-generate (random) private key
private_key = EC::PrivateKey.generate    # by default uses Secp256k1 curve (used in Bitcoin and Ethereum)

private_key.to_i
#=> 29170346885894798724849267297784761178669026868482995474159965944722616190552
private_key.to_s
#=> "407dd4ccde53d30f3a9cda74ceccb247f3997466964786b59e4d68e93e8f8658"

Derive / (Auto-)Calculate the Public Key - Enter Elliptic Curve (EC) Cryptography

The public key (K) are two numbers (that is, a point with the coordinates x and y) computed by multiplying the generator point (G) of the curve with the private key (k) e.g. K=k*G. This is equivalent to adding the generator to itself k times. Magic? Let's try:

# This private key is just an example. It should be much more secure!
private_key = EC::PrivateKey.new( 1234 )   # by default uses Secp256k1 curve (used in Bitcoin and Ethereum)

public_key =  private_key.public_key   ## the "magic" one-way K=k*G curve multiplication (K=public key,k=private key, G=generator point)
point = public_key.point

point.x
#=> 102884003323827292915668239759940053105992008087520207150474896054185180420338
point.y
#=> 49384988101491619794462775601349526588349137780292274540231125201115197157452

point.x.to_s(16)
#=> "e37648435c60dcd181b3d41d50857ba5b5abebe279429aa76558f6653f1658f2"
point.y.to_s(16)
#=> "6d2ee9a82d4158f164ae653e9c6fa7f982ed8c94347fc05c2d068ff1d38b304c"

Sign a transaction with an (elliptic curve) private key:

# Step 1 - Calculate the Transaction (tx) Hash
tx = 'from: Alice  to: Bob     cryptos: 43_000_000_000'
txhash = sha256( tx ).hexdigest

# Step 2 - Get the Signer's Private key
private_key = EC::PrivateKey.new( 1234 )     # This private key is just an example. It should be much more secure!

# Sign!
signature = private_key.sign( txhash )
# -or-
signature = EC.sign( txhash, private_key )

signature.r
#=> 80563021554295584320113598933963644829902821722081604563031030942154621916407
signature.s
#=> 58316177618967642068351252425530175807242657664855230973164972803783751708604

signature.r.to_s(16)
#=> "3306a2f81ad2b2f62ebe0faec129545bc772babe1ca5e70f6e56556b406464c0"
signature.s.to_s(16)
#=> "4fe202bb0835758f514cd4a0787986f8f6bf303df629dc98c5b1a438a426f49a"

Verify a signed transaction with an (elliptic curve) public key:

# Step 1 - Calculate the Transaction (tx) Hash
tx = 'from: Alice  to: Bob     cryptos: 43_000_000_000'
txhash = sha256( tx ).hexdigest

# Step 2 - Get the Signer's Public Key
public_key = EC::PublicKey.new(
   102884003323827292915668239759940053105992008087520207150474896054185180420338,
   49384988101491619794462775601349526588349137780292274540231125201115197157452
)

# Step 3 - Get the Transaction's Signature
signature = EC::Signature.new(
  80563021554295584320113598933963644829902821722081604563031030942154621916407,
  58316177618967642068351252425530175807242657664855230973164972803783751708604
)

# Don't Trust - Verify
public_key.verify?( txhash, signature )
# -or-
EC.verify?( txhash, signature, public_key )
#=> true


# or using hexadecimal numbers

public_key = EC::PublicKey.new(
  0xe37648435c60dcd181b3d41d50857ba5b5abebe279429aa76558f6653f1658f2,
  0x6d2ee9a82d4158f164ae653e9c6fa7f982ed8c94347fc05c2d068ff1d38b304c
)

signature = EC::Signature.new(
  0x3306a2f81ad2b2f62ebe0faec129545bc772babe1ca5e70f6e56556b406464c0,
  0x4fe202bb0835758f514cd4a0787986f8f6bf303df629dc98c5b1a438a426f49a
)

public_key.verify?( txhash, signature )
# -or-
EC.verify?( txhash, signature, public_key )
#=> true

To sum up:

The (raw) private key is a 256-bit unsigned integer number
The (raw) public key is a point (x,y), that is, two 256-bit unsigned integer numbers - derived (calculated) from the private key
A (raw) signature is composed of (r,s), that is, two 256-bit unsigned integer numbers

That's all the magic.

Real-World Examples / Cookbook

Bitcoin Chains

Derive the Bitcoin (Elliptic Curve) Public Key from the Private Key
Generate the Bitcoin (Base58) Address from the (Elliptic Curve) Public Key
Encode the Bitcoin Private Key in the Wallet Import Format (WIF)

Dodge "Shiba Inu" Chains

Derive the Dodge (Elliptic Curve) Public Key from the Private Key
Generate the Dodge Address from the (Elliptic Curve) Public Key

Litecoin Chains

Derive the Litecoin (Elliptic Curve) Public Key from the Private Key
Generate the Litecoin Address from the (Elliptic Curve) Public Key

Ethereum Chains

Derive the Ethereum (Elliptic Curve) Public Key from the Private Key
Generate the Ethereum Address from the (Elliptic Curve) Public Key

Bitcoin (BTC), Bitcoin Cash (BCH), Bitcoin Cash Satoshi Vision (BSV), Bitcoin Cash ABC (BCHA)

Bitcon Public Service Announcement:

Bitcoin number go up because more people want bitcoin. Bitcoin becomes more and more valuable.

1,000 HODLers

10,000 HODLers

100,000 HODLers

1,000,000 HODLers

10,000,000 HODLers

100,000,000 HODLers

1,000,000,000 HODLers

10,000,000,000 HODLers

100,000,000,000 HODLers and on and on

People will come to understand bitcon.

-- Dan McArdle, Bitcoin "There is No Alternative", Bitcoin is the New (Gold) Standard

BEWARE: Yes, Bitcoin Is a Ponzi - Learn How the Investment Fraud Works »

Derive the Bitcoin (Elliptic Curve) Public Key from the Private Key

A private key in bitcoin is a 32-byte (256-bit) unsigned / positive integer number.

Or more precise the private key is a random number between 1 and the order of the elliptic curve secp256k1.

EC::SECP256K1.order
#=> 115792089237316195423570985008687907852837564279074904382605163141518161494337

# or in hexadecimal (base16)
EC::SECP256K1.order.to_s(16)
#=> "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141"

Step 1 - Let's generate a private key

private_key = EC::PrivateKey.generate     # alice
private_key.to_i
#=> 50303382071965675924643368363408442017264130870580001935435312336103014915707
private_key.to_s
#=> "6f36b48dd130618049ca27e1909debdf3665cf0df0ade0986f0c50123107de7b"

private_key = EC::PrivateKey.generate     # bob
private_key.to_i
#=> 96396065671557366547785856940504404648366202869823009146014078671352808008442
private_key.to_s
#=> "d51e3d5ce8fbc6e574cf78d1c46e8936c26f38b002b954d0eac8aef195d6eafa"

Or use your own (secure) random generator. Trivia Note: The smallest possible (BUT HIGHLY UNSECURE) private key is 1 (not 0).

def generate_key
  1 + SecureRandom.random_number( EC::SECP256K1.order - 1 )
end

generate_key         # alice
#=> 66010624277151619503613090016410344678572543187504521309126248385615121289833

generate_key         # bob
#=> 10004433477200726182517873544056418402326985168039465080040800405880945722868

Aside: What's Base 6? Let's Roll the Dice

An important part of creating a private key is ensuring the random number is truly random. Physical randomness is better than computer generated pseudo-randomness. The easiest way to generate physical randomness is with a dice. To create a private key you only need one six-sided die which you roll ninety nine times. Stopping each time to record the value of the die. When recording the values follow these rules: 1=1, 2=2, 3=3, 4=4, 5=5, 6=0. By doing this you are recording the big random number, your private key, in base 6 format.

def roll_dice
  SecureRandom.random_number( 6 ) ##  returning 0,1,2,3,4, or 5
end

priv_base6 = 99.times.reduce('') { |buf,_| buf << roll_dice.to_s }
#=> "413130205513310000115530450343345150251504444013455422453552225503020102150031231134314351124254004"

Exercise: Turn the ninety nine character base 6 private key into a base 10 or base 16 number.

priv = priv_base6.to_i(6)  ## convert to decimal (base 10) from roll-the-dice (base 6) string
#=> 77254760463198588454157792320308725646096652667800343330432100522222375944308
priv.to_s(16)
#=> "aacca516ccbf72dac2c4c447b9f64d12855685e99810ffcf7763a12da6c04074"

Aside: What's Base 2? Let's Flip A Coin - Heads or Tails?

Triva Quiz: For an (unsigned) 256-bit number - how many times do you need to flip the coin?

Step 2 - Let's derive / calculate the public key from the private key - Enter elliptic curve (EC) cryptography

# note: by default uses Secp256k1 curve (used in Bitcoin)
private_key = EC::PrivateKey.new( 50303382071965675924643368363408442017264130870580001935435312336103014915707 )

public_key =  private_key.public_key   ## the "magic" one-way K=k*G curve multiplication (K=public key,k=private key, G=generator point)
point = public_key.point

point.x
#=> 17761672841523182714332746445483761684317159074072585653954580096478387916431
point.y
#=> 81286693084077906561204577435230199871025343781583806206090259868058973358862

and convert the point to the compressed or uncompressed Standards for Efficient Cryptography (SEC) format used in Bitcoin:

point.to_s( :compressed )
#=> "022744c02580b4905349bc481a60c308c2d98d823d44888835047f6bc5c38c4e8f"
point.to_s( :uncompressed )
#=> "042744c02580b4905349bc481a60c308c2d98d823d44888835047f6bc5c38c4e8fb3b6a34b90a571f6c2a1113dd5ff4576f61bbf3e970a6e148fa02bf9eb7bcb0e"

References

Generate the Bitcoin (Base58) Address from the (Elliptic Curve) Public Key

Let's follow the steps from How to create Bitcoin Address:

# Lets start with the public key ("raw" hex string encoded in compressed format)
pk = "0250863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352"

# 1. Perform SHA-256 hashing on the public key
step1 = sha256( hex: pk ).hexdigest
#=> "0b7c28c9b7290c98d7438e70b3d3f7c848fbd7d1dc194ff83f4f7cc9b1378e98"

# 2. Perform RIPEMD-160 hashing on the result of SHA-256
step2 = ripemd160( hex: step1 ).hexdigest
#=> "f54a5851e9372b87810a8e60cdd2e7cfd80b6e31"

# 3. Add version byte in front of RIPEMD-160 hash (0x00 for Bitcoin Main Network)
step3 = "00" + step2
#=> "00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31"

# 4. Perform SHA-256 hash on the extended RIPEMD-160 result
step4 = sha256( hex: step3 ).hexdigest
#=> "ad3c854da227c7e99c4abfad4ea41d71311160df2e415e713318c70d67c6b41c"

# 5. Perform SHA-256 hash on the result of the previous SHA-256 hash
step5 = sha256( hex: step4 ).hexdigest
#=> "c7f18fe8fcbed6396741e58ad259b5cb16b7fd7f041904147ba1dcffabf747fd"

# 6. Take the first 4 bytes of the second SHA-256 hash. This is the address checksum
step6 = step5[0..7]      # note: 4 bytes in hex string are 8 digits/chars
#=> "c7f18fe8"

# 7. Add the 4 checksum bytes from step 6 at the end of
#    extended RIPEMD-160 hash from step 3.
#    This is the 25-byte binary Bitcoin Address.
step7 = step3 + step6
#=> "00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31c7f18fe8"

# 8. Convert the result from a byte string into a base58 string using Base58 encoding.
#  This is the most commonly used Bitcoin Address format.
addr  = base58( hex: step7 )
#=> "1PMycacnJaSqwwJqjawXBErnLsZ7RkXUAs"

Or let's try again with the shortcut helpers:

HASH160 - RMD160(SHA256(X))
BASE58CHECK - BASE58(X || SHA256(SHA256(X))[:4])

# Lets start with the public key ("raw" hex string encoded in compressed format)
pk = "0250863ad64a87ae8a2fe83c1af1a8403cb53f53e486d8511dad8a04887e5b2352"

# 1. Perform HASH-160 hashing on the public key
#    a) Perform SHA-256 hashing on the public key
#    b) Perform RIPEMD-160 hashing on the result of SHA-256
step1 = hash160( hex: pk ).hexdigest
#=> "f54a5851e9372b87810a8e60cdd2e7cfd80b6e31"

# 2. Add version byte in front of RIPEMD-160 hash (0x00 for Bitoin Main Network)
step2 = "00" + step1
#=> "00f54a5851e9372b87810a8e60cdd2e7cfd80b6e31"

# 3. Encode with BASE58CHECK
#    a) Perform SHA-256 hash on the extended RIPEMD-160 result
#    b) Perform SHA-256 hash on the result of the previous SHA-256 hash
#    c) Take the first 4 bytes of the second SHA-256 hash. This is the address checksum
#    d) Add the 4 checksum bytes at the end of
#       extended RIPEMD-160 hash from step 2.
#       This is the 25-byte binary Bitcoin Address.
#    e) Convert the result from a byte string into a base58 string
#       using Base58 encoding.
#       This is the most commonly used Bitcoin Address format.
addr  = base58check( hex: step2 )
#=> "1PMycacnJaSqwwJqjawXBErnLsZ7RkXUAs"

References

Encode the Bitcoin Private Key in the Wallet Import Format (WIF)

A Wallet Import Format (WIF) private key is a standard private key, but with a few added extras:

Version Byte prefix - The network the private key is to be used on.
- 0x80 = Mainnet
- 0xEF = Testnet
Compression Byte suffix (optional) - Flag if the private key is used to create a compressed public key.
- 0x01
Checksum - Useful for detecting errors/typos when you type out your private key; calculated using the first 4 bytes of the double sha256 hash SHA256(SHA256(X))[:4].

This is all then converted to Base58, which shortens the string and makes it easier to transcribe.

privatekey  = "ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db2"
extended = "80" + privatekey + "01"
#=> "80ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db201"
checksum = hash256( hex: extended ).hexdigest[0..7]
#=> "66557e53"
extendedchecksum = extended + checksum
#=> "80ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db20166557e53"
wif = base58( hex: extendedchecksum )
#=> "L5EZftvrYaSudiozVRzTqLcHLNDoVn7H5HSfM9BAN6tMJX8oTWz6"

Or let's try again with the base58check (BASE58(X || SHA256(SHA256(X))[:4])) shortcut helper:

privatekey = "ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db2"
extended   = "80" + privatekey + "01"
#=> "80ef235aacf90d9f4aadd8c92e4b2562e1d9eb97f0df9ba3b508258739cb013db201"
wif = base58check( hex: extended )
#=> "L5EZftvrYaSudiozVRzTqLcHLNDoVn7H5HSfM9BAN6tMJX8oTWz6"

References

Bonus: Bitcon Tip - How to Buy Bitcoin (The CO₂-Friendly Way)

Take one $50 bill, five $10 bills, or ten $5 bills (I wouldn't recommend change - stay with paper money).

Go to the bathroom.

Lift the lid of the loo.

Throw money in.

Flush down water.

Congrats! You just purchased $50 worth of Bitcoin - without fucking the planet!

-- Trolly McTrollface, Bitcon Greater Fool Court Jester

Dodge

Even fun money is money, and a toy cryptocurrency can be turned into real money; the supply of gullibility is deep, if not infinite. So the shibes started dreaming of getting rich for free...

-- David Gerard, Confused About Dogecoin? Here's How It (Doesn't) Work

Dogecoin is the people's crypto. The future currency of earth and mars. Much wow!

-- Elon Musk, February 2021

Derive the Dodge (Elliptic Curve) Public Key from the Private Key

Short version: Same as in Ethereum, Bitcoin, Litecoin

Long version: A private key in dodge is a 32-byte (256-bit) unsigned / positive integer number.

Or more precise the private key is a random number between 1 and the order of the elliptic curve secp256k1.

EC::SECP256K1.order
#=> 115792089237316195423570985008687907852837564279074904382605163141518161494337

# or in hexadecimal (base16)
EC::SECP256K1.order.to_s(16)
#=> "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141"

Step 1 - Let's generate a private key

private_key = EC::PrivateKey.generate     # alice
private_key.to_i
#=> 50303382071965675924643368363408442017264130870580001935435312336103014915707
private_key.to_s
#=> "6f36b48dd130618049ca27e1909debdf3665cf0df0ade0986f0c50123107de7b"

private_key = EC::PrivateKey.generate     # bob
private_key.to_i
#=> 96396065671557366547785856940504404648366202869823009146014078671352808008442
private_key.to_s
#=> "d51e3d5ce8fbc6e574cf78d1c46e8936c26f38b002b954d0eac8aef195d6eafa"

Step 2 - Let's derive / calculate the public key from the private key - Enter elliptic curve (EC) cryptography

# note: by default uses Secp256k1 curve (used in Dodge)
private_key = EC::PrivateKey.new( 50303382071965675924643368363408442017264130870580001935435312336103014915707 )

public_key =  private_key.public_key   ## the "magic" one-way K=k*G curve multiplication (K=public key,k=private key, G=generator point)
point = public_key.point

point.x
#=> 17761672841523182714332746445483761684317159074072585653954580096478387916431
point.y
#=> 81286693084077906561204577435230199871025343781583806206090259868058973358862

and convert the point to the compressed or uncompressed Standards for Efficient Cryptography (SEC) format used in Dodge:

point.to_s( :compressed )
#=> "022744c02580b4905349bc481a60c308c2d98d823d44888835047f6bc5c38c4e8f"
point.to_s( :uncompressed )
#=> "042744c02580b4905349bc481a60c308c2d98d823d44888835047f6bc5c38c4e8fb3b6a34b90a571f6c2a1113dd5ff4576f61bbf3e970a6e148fa02bf9eb7bcb0e"

Generate the Dodge Address from the (Elliptic Curve) Public Key

Short version: Same as bitcoin or litecoin. Only difference - Add the version byte 0x1e prefix for Dodge Main Network - P2PKH (pay to public key hash).

Long version: Let's use the shortcut hash function helpers:

HASH160 - RMD160(SHA256(X))
BASE58CHECK - BASE58(X || SHA256(SHA256(X))[:4])

# Lets start with the public key ("raw" hex string encoded in compressed format)
pk = "022744c02580b4905349bc481a60c308c2d98d823d44888835047f6bc5c38c4e8f"

# 1. Perform HASH-160 hashing on the public key
#    a) Perform SHA-256 hashing on the public key
#    b) Perform RIPEMD-160 hashing on the result of SHA-256
step1 = hash160( hex: pk ).hexdigest
#=> "a1f37969bcb547cd9c3a28fa07c2269ef813340a"

# 2. Add version byte in front of RIPEMD-160 hash (0x1e for Dodge Main Network)
step2 = "1e" + step1
#=> "1ea1f37969bcb547cd9c3a28fa07c2269ef813340a"

# 3. Encode with BASE58CHECK
#    a) Perform SHA-256 hash on the extended RIPEMD-160 result
#    b) Perform SHA-256 hash on the result of the previous SHA-256 hash
#    c) Take the first 4 bytes of the second SHA-256 hash. This is the address checksum
#    d) Add the 4 checksum bytes at the end of
#       extended RIPEMD-160 hash from step 2.
#       This is the 25-byte binary Dodge Address.
#    e) Convert the result from a byte string into a base58 string
#       using Base58 encoding.
#       This is the most commonly used Dodge Address format.
addr  = base58check( hex: step2 )
#=> "DKuR12onkdp5GxC5c8DgXhGe4Z2AqCK3Xh"

Litecoin

Derive the Litecoin (Elliptic Curve) Public Key from the Private Key

Short version: Same as in Ethereum, Bitcoin, Dodge.

Generate the Litecoin Address from the (Elliptic Curve) Public Key

Short version: Same as in Bitcoin or Dodge. Only difference - Add the version byte 0x30 prefix for Litecoin Main Network - P2PKH (pay to public key hash).

Ethereum

Derive the Ethereum (Elliptic Curve) Public Key from the Private Key

A private key in ethereum is a 32-byte (256-bit) unsigned / positive integer number.

Or more precise the private key is a random number between 1 and the order of the elliptic curve secp256k1.

EC::SECP256K1.order
#=> 115792089237316195423570985008687907852837564279074904382605163141518161494337

# or in hexadecimal (base16)
EC::SECP256K1.order.to_s(16)
#=> "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141"

Note: A "raw" private key in ethereum is the same as in bitcoin, litecoin, dodge & co using the same elliptic curve secp256k1. See Derive the Bitcoin (Elliptic Curve) Public Key from the Private Key above.

Step 1 - Let's generate a private key

private_key = EC::PrivateKey.generate     # alice
private_key.to_i
#=> 50303382071965675924643368363408442017264130870580001935435312336103014915707
private_key.to_s
#=> "6f36b48dd130618049ca27e1909debdf3665cf0df0ade0986f0c50123107de7b"

private_key = EC::PrivateKey.generate     # bob
private_key.to_i
#=> 96396065671557366547785856940504404648366202869823009146014078671352808008442
private_key.to_s
#=> "d51e3d5ce8fbc6e574cf78d1c46e8936c26f38b002b954d0eac8aef195d6eafa"

Or use your own (secure) random number. Let's follow along the example in the Mastering Ethereum book and let's use the random number: 0xf8f8a2f43c8376ccb0871305060d7b27b0554d2cc72bccf41b2705608452f315.

private_key = EC::PrivateKey.new( 0xf8f8a2f43c8376ccb0871305060d7b27b0554d2cc72bccf41b2705608452f315 )
private_key.to_i
#=> 112612889188223089164322846106333497020645518262799935528047458345719983960853
private_key.to_s
#=> "f8f8a2f43c8376ccb0871305060d7b27b0554d2cc72bccf41b2705608452f315"

Step 2 - Let's derive / calculate the public key from the private key - Enter elliptic curve (EC) cryptography

# note: by default uses Secp256k1 curve (used in Ethereum)
private_key = EC::PrivateKey.new( 0xf8f8a2f43c8376ccb0871305060d7b27b0554d2cc72bccf41b2705608452f315 )

public_key =  private_key.public_key   ## the "magic" one-way K=k*G curve multiplication (K=public key,k=private key, G=generator point)
point = public_key.point

point.x
#=> 17761672841523182714332746445483761684317159074072585653954580096478387916431
point.y
#=> 81286693084077906561204577435230199871025343781583806206090259868058973358862

# or in hexa(decimal) - base 16
point.x.to_s(16)
#=> "6e145ccef1033dea239875dd00dfb4fee6e3348b84985c92f103444683bae07b"
point.y.to_s(16)
#=> "83b5c38e5e2b0c8529d7fa3f64d46daa1ece2d9ac14cab9477d042c84c32ccd0"

and convert the point to the raw uncompressed format used in Ethereum:

## add together the two points (x,y) in a hex string
"%64x%64x" % [point.x, point.y]
#=> "6e145ccef1033dea239875dd00dfb4fee6e3348b84985c92f103444683bae07b83b5c38e5e2b0c8529d7fa3f64d46daa1ece2d9ac14cab9477d042c84c32ccd0"

# or
("%64x" % point.x) + ("%64x" % point.y)
#=> "6e145ccef1033dea239875dd00dfb4fee6e3348b84985c92f103444683bae07b83b5c38e5e2b0c8529d7fa3f64d46daa1ece2d9ac14cab9477d042c84c32ccd0"

References

Keys and Addresses in Mastering Ethereum

Generate the Ethereum Address from the (Elliptic Curve) Public Key

Let's again follow along the example in the Mastering Ethereum book and let's (re)use the public key (from above):

Step 1: Use the keccak256 hashing function to calculate the hash of the public key

pub = "6e145ccef1033dea239875dd00dfb4fee6e3348b84985c92f103444683bae07b83b5c38e5e2b0c8529d7fa3f64d46daa1ece2d9ac14cab9477d042c84c32ccd0"
hash = keccak256( hex: pub ).hexdigest
#=> "2a5bc342ed616b5ba5732269001d3f1ef827552ae1114027bd3ecf1f086ba0f9"

Step 2: Keep only the last 20 bytes (least significant bytes), this is the ethereum address

hash[24,40]    ## last 20 bytes of 32 (skip first 12 bytes (12x2=24 hex chars))
hash[-40..-1]  ## -or- last 20 bytes (40 hex chars)
hash[-40,40]   ## -or- last 20 bytes (40 hex chars)
#=> "001d3f1ef827552ae1114027bd3ecf1f086ba0f9"

Note: Most often you will see ethereum addresses with the prefix 0x that indicates they are hexadecimal-encoded, like this: 0x001d3f1ef827552ae1114027bd3ecf1f086ba0f9.

References

Keys and Addresses in Mastering Ethereum

Install

Just install the gem:

$ gem install crypto-lite

License

The scripts are dedicated to the public domain. Use it as you please with no restrictions whatsoever.

Questions? Comments?

Send them along to the wwwmake forum. Thanks!

crypto-lite - Cryptographic Secure Hash Functions and Public Key Signature Algorithms Made Easy

Usage

Secure Hashing / Hash Functions

Aside - Keccak vs SHA3 / Original vs Official

Aside - Hex String "0x616263" vs Binary String "\x61\x62\x63" == "abc"

Hash Function Helpers

Base58 Encoding / Decoding Helpers

Public Key Signature Algorithms

Real-World Examples / Cookbook

Bitcoin (BTC), Bitcoin Cash (BCH), Bitcoin Cash Satoshi Vision (BSV), Bitcoin Cash ABC (BCHA)

Derive the Bitcoin (Elliptic Curve) Public Key from the Private Key

Step 1 - Let's generate a private key

Step 2 - Let's derive / calculate the public key from the private key - Enter elliptic curve (EC) cryptography

Generate the Bitcoin (Base58) Address from the (Elliptic Curve) Public Key

Encode the Bitcoin Private Key in the Wallet Import Format (WIF)

Dodge

Derive the Dodge (Elliptic Curve) Public Key from the Private Key

Step 1 - Let's generate a private key

Step 2 - Let's derive / calculate the public key from the private key - Enter elliptic curve (EC) cryptography

Generate the Dodge Address from the (Elliptic Curve) Public Key

Litecoin

Derive the Litecoin (Elliptic Curve) Public Key from the Private Key

Generate the Litecoin Address from the (Elliptic Curve) Public Key

Ethereum

Derive the Ethereum (Elliptic Curve) Public Key from the Private Key

Step 1 - Let's generate a private key

Step 2 - Let's derive / calculate the public key from the private key - Enter elliptic curve (EC) cryptography

Generate the Ethereum Address from the (Elliptic Curve) Public Key

Install

License

Questions? Comments?

Aside - Hex String `"0x616263"` vs Binary String `"\x61\x62\x63" == "abc"`