# Digital Signature
Computational components for signing any objects
# hash[ ], ⌗[ ], ⌗@
A **hash code** is a fixed-size numerical value generated from input data of arbitrary size, used primarily for indexing data in hash tables. It allows for efficient data retrieval and storage by mapping variable-length data to a fixed-length representation.
Think of the hash code as a unique digital signature for any data that once even if one bit of that data altered the entire new hash code would be different.
**Example**: "dara is good lookin" has the hash code:
"0x05ee501e3232083ca0f16b02011944e735f78db170c568c2ea85e56380ddca05"
**Counterexample**: "dara is good lookin**.**" the ending red dot cause an entire change to the has code above:
"0x4700eceb9e5cbc887ad3dea1833081d51c3572c7886ea9c8a3f30b0c5ad4c614"
```kotlin
hash1 = ⌗["dara is good lookin"];
hash2 = ⌗@"dara is good lookin";
hash3 = hash["dara is good looking"];
show hash1 also hash2 also hash3;
save as myhash;
```
**Output**
hash1⟶("0x05ee501e3232083ca0f16b02011944e735f78db170c568c2ea85e56380ddca05")
hash2⟶("0x05ee501e3232083ca0f16b02011944e735f78db170c568c2ea85e56380ddca05")
hash3⟶("0x4700eceb9e5cbc887ad3dea1833081d51c3572c7886ea9c8a3f30b0c5ad4c614")
#####
# Digital Signature
- Your digital signature is the proof that you signed something
- Your digital signature attests to the fact that your data was not tampered with
- In asymmetric key system you ought to sign with the private key 🗝 or any symbol representing one
- message: any expression from symbols to numerals to expressions to images to audio and video and so on
- : Free Form language symbol for digital signature in binary operator form in this case. keymessage computes a signature for the message given this key. Operator form should be thought of a multiplication a ⨉ b where two left and right operands act on each other to compute a product. In a b, the key a acts on the message/data b to output a signature.
##### Sign
```
🔐["rsa"];
message = "hi";
signature = 🗝message;
save as signature1;
```
##### Cloud Object Browser: signature1
##### Verify Signature
- Signature, generally performed in another program in another system and in the past. To access that signature Free Form language follows the path paradigm e.g. "/certs/free/signature1"
- base = "/certs/free/signature1"; states that the symbol base represents the path on the rhs; base can by any other symbol/word
- s = "base/signature/value"; allows the access to the external signature value again in path form and s presents the accessed signature
> Paths starting with / are external paths e.g. "/certs/free/signature1" created by other programs and networks , while paths like "base/signature/value" are local to the current Free Form language script.
- key = "base/🔑"; in paired key cryptography systems, assumption is everyone has access to the public key 🔑. This public key is then used to verify if the computed signature was indeed performed by the secret private key 🗝 .
- q = (✍🏻 s ⚲ message)key; this time the rhs the public key acts on the lhs namely (✍🏻 s ⚲ message) and places returns the evaluation boolean result in q.
- (✍🏻 s ⚲ message) is a generalization of list in other programming languages. Symbols ✍🏻 and ⚲ "pin" contents into the list and depending the pin symbol the content is interpreted
- ⚲ message pins a message the subject matter of interest in this signature computations
- ✍🏻 s pins the signature from a previous program who allegedly signed the message namely ⚲ message
```
base = "/certs/free/signature1";
s = "base/signature/value";
key = "base/🔑";
message = "hi";
q = (✍🏻 s ⚲ message)key;
show q;
save as verify1;
```
Output:
"q" ⟶ True
##### Cloud Object Browser: verify1
##### FAIL: Verify Signature
```
base = "/certs/free/signature1";
s = "base/signature/value";
key = "base/🔑";
message = "hi!";
q = ( ✍🏻 s ⚲ message ) key;
show q;
save as verify1-2;
```
Output:
"q" ⟶ False
##### Cloud Object Browser: verify1-2