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BBSE

Properties Cryptographic hash functions:

1. Hash functions:

a) **Compression** (hash maps input x of arbitrary length to h(x) fixed bit length

b) **Ease of computation: given x and h --> h(x) **

2. Cryptographic hash functions:

a) Preimage resistance: for all outputs y it is unfeasible to find solution to h(x)=y (hard and sufficient (no better than random and long enough to be unsolvable (currently))

b) 2nd preimage resistance: given x it is unfeasible to find any second input x´with x!=x´ such that h(x)=h(x´)

c) collision resistance: infeasible to find two different values with sam ehash function

BBSE

Examples use cases hash functions

2nd preimage resistance:

want to make shure other party does not tamper with data - want to delete from own storage: -_> save hash of data. after time compare download data with hash, if change --> different

hiding:

secret value r chosen, then given h(r//x) infeasible to find x

- Combine
**random number and x -> hash and give to other.**Later reveal random number --> x clear **Commitments- commit to value w/ revealing it:**- Concatinate random and x h(r//x) com: commit(msg, nonce)
- vErification: verify(com. Msg, nonce)

--> everyone can verify after, if random number and x compute the hash

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Application search puzzle

- hash function computes pzzle results, id makes solutions unique, target set y

--> puzzle set must lie withn range = difficulty

computation id is cocatinated with value x and hashed. X changes until puzzle result lies within y (id//x - id//x+1

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Hash pointers and data structures

Hash pointer contains data to a location data enriched with cg hasg.

Hsh pointers allow to verify data is not changes. (head of hash pointers ensures integrity of blockchain

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Bloom filters

Probabilistic data structure, alows to test if element is in set.

Example newspapaper:

- Inputs are calculated with cg hash --> basket in filter filled
- Validation: if filled filter basket returns. Probability depends on number of buckets

**--> true /false positives!!! (example apple/lime(grapefruit) false positives, as bucket might be filled by chance already. Ocurence depends on number hash functions**

Example new paper: fp not a problem, because irrelevant if misses article he has not read and get another one he has not read.

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Unforgeable (signing)

attacker knows pblic key

sees signature on arbitrary amount of messages

--> Undforgeable means, that attacker is not able to create a signature on a message that he has not seen

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Concerns signatures:

1) based on entropy: must be truely random or else not safe e.g. nuclear zerfall

2) signatures can only sin small amount of data - sign hash of the message is sufficient, as hash is collision resistant

3) private keys are not recoverable. If lost, no way act under this entity

Appropriate key length. if too short computed in future

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Quantum resistance:

Signature Schemes based on the integer factorization problem, **the discrete logarithm problem or the elliptic curve discrete logarithm problem**

**Can be solved with Shors algorithm with an enough powerful quantum computer [SHOR1999]**

**Hash functions relatively secure against QC **

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Concept of World Computer in ETH

- All computers use same CPU

- Users issue actions

- everyone shares same ressources

- no explicit owner/Compuer

**- Using ressources costs money**

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EVM

Ethereum virtual machine:

EV specifies execution model for chain

- Tuple for specification: (block_state, transaction, message, code, memory, stack, pc, gas)

--> Block_state = global state of blockchain

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EVM Block state

All ethereum accounts controlled by a private key, all smart contracts including their storage

All Blocks

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Messages

Mesages similar to transaction (BUT ONLY SENT BY SC)

AND exist only virtually i.e. are not mined into a block) (Übung: they are result of calculation in block)

-Sender

-Recipient

-Amount of ether to transfer alongside the message

-Optional data field

-STARTGAS value

Contract calls method on another contract VIRTUAL message is sent

Wallet to SC- transaction sent

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