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2022-09-16T03:22:44Z

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Pythagoras0: /* 메타데이터 */ 새 문단

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Pythagoras0: /* 메타데이터 */ 새 문단

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2022-09-16T02:27:08Z

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2022-09-15T09:53:50Z

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Pythagoras0: /* 노트 */ 새 문단

2022-09-15T09:53:47Z

노트: 새 문단

새 문서

== 노트 ==

===말뭉치===
# But Schnorr signatures are much more elegant and simple, and it has one more magical property; linearity.<ref name="ref_27782bb7">[https://medium.com/bitbees/what-the-heck-is-schnorr-52ef5dba289f What The Heck Is Schnorr]</ref>
# Schnorr signature was invented by Claus-Peter Schnorr back in the 1980s.<ref name="ref_27782bb7" />
# Because of his patent, the Schnorr signature algorithm did not see any widespread use for decades.<ref name="ref_27782bb7" />
# Six more years later, in 2014 the first talk of implementing Schnorr signature on Bitcoin protocol came up in the bitcoin-talk forum.<ref name="ref_27782bb7" />
# In the near future, Bitcoin will enable Schnorr signatures in addition to ECDSA signatures.<ref name="ref_db591c4c">[https://river.com/learn/what-are-schnorr-signatures/ What Do Schnorr Signatures Do for Bitcoin?]</ref>
# Schnorr signatures will be introduced to Bitcoin through Taproot upgrade, which will hopefully be activated around 2022.<ref name="ref_db591c4c" />
# Although developers have added all necessary code to Bitcoin Core, Bitcoin nodes must accept the upgrade in order to consider Schnorr signatures valid.<ref name="ref_db591c4c" />
# Schnorr signatures are quite simple compared to other schemes.<ref name="ref_dd62bb89">[https://academy.binance.com/en/articles/what-do-schnorr-signatures-mean-for-bitcoin What do Schnorr Signatures Mean for Bitcoin?]</ref>
# Schnorr signatures have been touted as a solution to these privacy and scalability issues.<ref name="ref_dd62bb89" />
# As with most upgrades to the Bitcoin protocol, it could take time for the broader community of Bitcoin users to agree on the Schnorr signature inclusion.<ref name="ref_dd62bb89" />
# Schnorr signatures could be merged into the code as a soft fork , meaning that a change would not split the network.<ref name="ref_dd62bb89" />
# In this post I will explain what Schnorr signatures are and how they intuitively work.<ref name="ref_3440f6d6">[https://suredbits.com/introduction-to-schnorr-signatures/ Introduction to Schnorr Signatures]</ref>
# And that is all there is to the actual computation surrounding “vanilla” Schnorr signatures!<ref name="ref_3440f6d6" />
# In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr.<ref name="ref_492c923b">[https://www.geeksforgeeks.org/schnorr-digital-signature/ Schnorr Digital Signature]</ref>
# Note: When you construct the signature like this, it’s known as a Schnorr signature, which is discussed in a following section.<ref name="ref_440c07d2">[https://tlu.tarilabs.com/cryptography/introduction-schnorr-signatures Introduction to Schnorr Signatures]</ref>
# The Schnorr signature is considered the simplest digital signature scheme to be provably secure in a random oracle model.<ref name="ref_440c07d2" />
# Historically, EdDSA is known as a variant of Schnorr signatures, which are well-studied and suitable for efficient thresholdization,...<ref name="ref_6a94b9af">[https://csrc.nist.gov/publications/detail/nistir/8214b/draft NISTIR 8214B (Draft), Notes on Threshold EdDSA/Schnorr Signatures]</ref>
# We aim at designing a leakage-resilient variant of the Schnorr signature scheme whose secret key’s storage space is constant, independently of the amount of leakage that it can tolerate.<ref name="ref_4e437487">[https://link.springer.com/chapter/10.1007/978-3-642-45239-0_11 A Leakage-Resilient Pairing-Based Variant of the Schnorr Signature Scheme]</ref>
# We proceed by first proposing a pairing analogue of the Schnorr signature scheme, that we next transform to include split signing key updates.<ref name="ref_4e437487" />
# As the increased uptake in connected devices revives the interest in resource-constrained signature algorithms, we introduce a variant of Schnorr signatures that mutualises exponentiation eorts.<ref name="ref_d70872a7">[https://eprint.iacr.org/2018/069.pdf Reusing nonces in schnorr signatures]</ref>
# Sharing a nonce is a deadly blow to Schnorr signatures, but is not a security concern for our variant.<ref name="ref_d70872a7" />
# We start by reminding how the original Schnorr signature scheme works and explain how we extend it assuming that k is randomly drawn from Zp1.<ref name="ref_d70872a7" />
# 3.1 Our Signature Scheme Similar to the Schnorr signature scheme, our scheme is a tuple of algorithms (Setup, KeyGen, Sign, and Verify), which we dene as follows: Setup(1): Generate primes q1, . .<ref name="ref_d70872a7" />
# This has lead to a long line of research investigating the existence of tighter security proofs for Schnorr signatures.<ref name="ref_1b944f9d">[https://eprint.iacr.org/2013/418.pdf On tight security proofs for schnorr signatures]</ref>
# We begin with the hypothesis that there exists a tight generic re- duction R from some hard non-interactive problem to the UUF-NMA-security of Schnorr signatures.<ref name="ref_1b944f9d" />
# I'm trying to understand the security of the short schnorr signature a little bit better.<ref name="ref_d5ffc39f">[https://crypto.stackexchange.com/questions/95345/security-proof-of-short-schnorr-signature Security Proof of Short Schnorr Signature]</ref>
# The Schnorr signatures (Schnorr, n.d.) have been known before ECDSA signatures, yet they were not so widely used due to the patent which expired in the year 2008.<ref name="ref_a00e3450">[https://mareknarozniak.com/2021/05/25/schnorr-signature/ Schnorr Signature]</ref>
# One of the advantages is the existence of proof that breaking the Schnorr signature is equivalent to breaking the discrete logarithm problem.<ref name="ref_a00e3450" />
# If you like to know more, I based this tutorial on what the heck is Schnorr medium article and cryptography fandom Schnorr signature page.<ref name="ref_a00e3450" />
# So Schnorr signature solves these 2 problems, it is non-malleable, which means #Bitcoin network becomes more secure.<ref name="ref_3c9b8920">[https://www.linkedin.com/pulse/cryptography-digital-signatures-schnorr-taproot-upgrade-nitesh-balusu Cryptography: Digital Signatures and Schnorr Signatures Explained-#Bitcoin Taproot Upgrade]</ref>
# A Schnorr signature is a digital signature produced by the Schnorr signature algorithm.<ref name="ref_02d5a128">[https://www.bitstamp.net/learn/blockchain/what-are-schnorr-signatures/ What are Schnorr Signatures?]</ref>
# Another advantage of Schnorr signatures is increased privacy in terms of securing your bitcoins.<ref name="ref_02d5a128" />
# By reducing the amount of signature data stored on the blockchain, Schnorr signatures free up block storage space.<ref name="ref_02d5a128" />
# But scaling is not the only way Schnorr signatures can improve the Bitcoin protocol.<ref name="ref_02d5a128" />
# FROST is a threshold Schnorr signature protocol that contains two important components.<ref name="ref_adf8fce0">[https://blog.coinbase.com/frost-flexible-round-optimized-schnorr-threshold-signatures-b2e950164ee1 FROST: Flexible Round-Optimized Schnorr Threshold Signatures]</ref>
# Afterwards, any t-out-of-n participants can run a threshold signing protocol to collaboratively generate a valid Schnorr signature.<ref name="ref_adf8fce0" />
# In addition, FROST also requires each participant to demonstrate knowledge of their own secret by sending to other participants a zero-knowledge proof, which itself is a Schnorr signature.<ref name="ref_adf8fce0" />
# To create a valid Schnorr signature, any t participants work together to execute this round.<ref name="ref_adf8fce0" />
# We have implemented Schnorr signatures on Bitcoin.<ref name="ref_2b5e61bd">[https://coingeek.com/schnorr-signatures-on-bitcoin/ Schnorr signatures on Bitcoin]</ref>
# In this blog post we will explain one of the main advantages of Schnorr signatures’: its native support for Multi-Signatures (MultiSig).<ref name="ref_d65743ce">[https://hackernoon.com/a-brief-intro-to-bitcoin-schnorr-multi-signatures-b9ef052374c5 A brief intro to Bitcoin Schnorr Multi-signatures]</ref>
# But Schnorr signatures can add a new advantage to CoinJoin.<ref name="ref_626bfe1f">[https://bitcoinmagazine.com/culture/the-power-of-schnorr-the-signature-algorithm-to-increase-bitcoin-s-scale-and-privacy-1460642496 The Power of Schnorr: The Signature Algorithm to Increase Bitcoin's Scale and Privacy]</ref>
# Note: The process of implementing Schnorr signatures in Bitcoin is still in the concept phase.<ref name="ref_626bfe1f" />
# Schnorr signatures can be proved secure in the random oracle model (ROM) under the discrete logarithm assumption (DL) by rewinding the adversary; but this security proof is loose.<ref name="ref_d7c091b0">[https://www.semanticscholar.org/paper/Blind-Schnorr-Signatures-in-the-Algebraic-Group-Fuchsbauer-Plouviez/abfbac3d8b2de10803b9df6fe6625090feddb991 PDF Blind Schnorr Signatures in the Algebraic Group Model]</ref>
# The written specication for Schnorr signatures should fully describe the algorithm.<ref name="ref_b8368f56">[https://courses.csail.mit.edu/6.857/2020/projects/4-Elbahrawy-Lovejoy-Ouyang-Perez.pdf Analysis of bitcoin improvement proposal 340]</ref>
# In the Bitcoin specication of Schnorr signatures, the public key Q is 32 bytes, and it can be converted from existing generated public keys by dropping the rst byte (the prex).<ref name="ref_b8368f56" />
# The Schnorr signature scheme is constructed by applying the Fiat-Shamir heuristic to Schnorrs identication protocol.<ref name="ref_b8368f56" />
# Schnorr signature is an alternative algorithm to Bitcoin’s original ECDSA.<ref name="ref_ee937991">[https://www.telemediaonline.co.uk/schnorr-signatures-role-in-bitcoin-transactions/ Schnorr Signatures Role in Bitcoin Transactions]</ref>
# Schnorr signatures are the second type of signatures scheme introduced with the Taproot upgrade to address some of the flaws of the ECDSA protocol.<ref name="ref_ee937991" />
# Schnorr signatures offer that advantage, allowing the Bitcoin network to optimize payment processing and data storage.<ref name="ref_ee937991" />
# That makes it impossible for chain analysis to distinguish between multi-sig and single-sign Bitcoin transactions with Schnorr signatures, ensuring enhanced privacy.<ref name="ref_ee937991" />
# In 2005, when elliptic curve cryptography was being standardized people built on top of DSA rather than Schnorr signatures that had advantages.<ref name="ref_3fd754e6">[https://diyhpl.us/wiki/transcripts/scalingbitcoin/milan/schnorr-signatures/ schnorr-signatures]</ref>
# What I want you to take away from this is Schnorr signatures are not an established standard.<ref name="ref_3fd754e6" />
# The security proof of Schnorr signatures says that they are existentially unforgeable under the assumptions I mentioned before.<ref name="ref_3fd754e6" />
# It turns out if you take Schnorr signatures naively and apply it to an elliptic curve group it has a really annoying interaction with BIP 32 when used with public derivation.<ref name="ref_3fd754e6" />
# Package schnorr implements the vanilla Schnorr signature scheme.<ref name="ref_a63ab04b">[https://pkg.go.dev/go.dedis.ch/kyber/sign/schnorr go.dedis.ch/kyber/sign/schnorr]</ref>
# To analyze the security of Schnorr signatures, we model the hash function as a random oracle.<ref name="ref_565a2e8d">[https://web.stanford.edu/class/cs259c/lectures/schnorr.pdf Schnorr identiﬁcation and signatures]</ref>
# We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group rep- resentations such as those which occur in elliptic curve groups.<ref name="ref_6d25ea82">[http://www.neven.org/papers/schnorr.pdf Hash function requirements]</ref>
# First, since security does not rely on the hash function being collision resistant, Schnorr signatures can still be securely instantiated with SHA-1/SHA- 256, unlike DSA signatures.<ref name="ref_6d25ea82" />
# Apart from instantiation candidates for the hash function, our results have a number of other important implications for the eciency and security of Schnorr signatures.<ref name="ref_6d25ea82" />
# ii Abstract This thesis investigates implicit multi-party protocols based on Schnorr signature scheme and their benefits to the Bitcoin ecosystem.<ref name="ref_6be9281a">[https://is.muni.cz/th/oaxta/thesis.pdf Masaryk university]</ref>
# To demonstrate the practicality of Schnorr signatures, a solution for Bitcoin transaction cosigning is designed and implemented.<ref name="ref_6be9281a" />
# signature, Schnorr signature scheme, Bitcoin, JavaCard iv Contents 1 Introduction 2 Schnorr Signature Scheme 2.1 Alternative Formulation . .<ref name="ref_6be9281a" />
# The most prominent alternative signature scheme with the desired properties is the Schnorr signature scheme.<ref name="ref_6be9281a" />
===소스===
<references />

← 이전 판		2022년 9월 16일 (금) 03:19 판
221번째 줄:		221번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1465057 Q1465057]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'schnorr'}, {'LEMMA': 'signature'}]
		+	* [{'LOWER': 'schnorr'}, {'LOWER': 'digital'}, {'LOWER': 'signature'}, {'LEMMA': 'scheme'}]
		+	* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]
		+	* [{'LOWER': 'sdsa'}]

← 이전 판		2022년 9월 16일 (금) 02:27 판
141번째 줄:		141번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1465057 Q1465057]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'schnorr'}, {'LEMMA': 'signature'}]
		+	* [{'LOWER': 'schnorr'}, {'LOWER': 'digital'}, {'LOWER': 'signature'}, {'LEMMA': 'scheme'}]
		+	* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]
		+	* [{'LOWER': 'sdsa'}]

← 이전 판		2022년 9월 15일 (목) 09:53 판
67번째 줄:		67번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1465057 Q1465057]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'schnorr'}, {'LEMMA': 'signature'}]
		+	* [{'LOWER': 'schnorr'}, {'LOWER': 'digital'}, {'LOWER': 'signature'}, {'LEMMA': 'scheme'}]
		+	* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]
		+	* [{'LOWER': 'sdsa'}]

← 이전 판		2022년 9월 16일 (금) 03:19 판
151번째 줄:		151번째 줄:
	* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]		* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]
	* [{'LOWER': 'sdsa'}]		* [{'LOWER': 'sdsa'}]
		+
		+	== 노트 ==
		+
		+	===말뭉치===
		+	# In the near future, Bitcoin will enable Schnorr signatures in addition to ECDSA signatures.<ref name="ref_db591c4c">[https://river.com/learn/what-are-schnorr-signatures/ What Do Schnorr Signatures Do for Bitcoin?]</ref>
		+	# Schnorr signatures will be introduced to Bitcoin through Taproot upgrade, which will hopefully be activated around 2022.<ref name="ref_db591c4c" />
		+	# Although developers have added all necessary code to Bitcoin Core, Bitcoin nodes must accept the upgrade in order to consider Schnorr signatures valid.<ref name="ref_db591c4c" />
		+	# Schnorr signatures are quite simple compared to other schemes.<ref name="ref_dd62bb89">[https://academy.binance.com/en/articles/what-do-schnorr-signatures-mean-for-bitcoin What do Schnorr Signatures Mean for Bitcoin?]</ref>
		+	# Schnorr signatures have been touted as a solution to these privacy and scalability issues.<ref name="ref_dd62bb89" />
		+	# As with most upgrades to the Bitcoin protocol, it could take time for the broader community of Bitcoin users to agree on the Schnorr signature inclusion.<ref name="ref_dd62bb89" />
		+	# Schnorr signatures could be merged into the code as a soft fork , meaning that a change would not split the network.<ref name="ref_dd62bb89" />
		+	# In this post I will explain what Schnorr signatures are and how they intuitively work.<ref name="ref_3440f6d6">[https://suredbits.com/introduction-to-schnorr-signatures/ Introduction to Schnorr Signatures]</ref>
		+	# And that is all there is to the actual computation surrounding “vanilla” Schnorr signatures!<ref name="ref_3440f6d6" />
		+	# But Schnorr signatures are much more elegant and simple, and it has one more magical property; linearity.<ref name="ref_27782bb7">[https://medium.com/bitbees/what-the-heck-is-schnorr-52ef5dba289f What The Heck Is Schnorr]</ref>
		+	# Schnorr signature was invented by Claus-Peter Schnorr back in the 1980s.<ref name="ref_27782bb7" />
		+	# Because of his patent, the Schnorr signature algorithm did not see any widespread use for decades.<ref name="ref_27782bb7" />
		+	# Six more years later, in 2014 the first talk of implementing Schnorr signature on Bitcoin protocol came up in the bitcoin-talk forum.<ref name="ref_27782bb7" />
		+	# In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr.<ref name="ref_492c923b">[https://www.geeksforgeeks.org/schnorr-digital-signature/ Schnorr Digital Signature]</ref>
		+	# Note: When you construct the signature like this, it’s known as a Schnorr signature, which is discussed in a following section.<ref name="ref_440c07d2">[https://tlu.tarilabs.com/cryptography/introduction-schnorr-signatures Introduction to Schnorr Signatures]</ref>
		+	# The Schnorr signature is considered the simplest digital signature scheme to be provably secure in a random oracle model.<ref name="ref_440c07d2" />
		+	# The main function of Schnorr signatures is to allow multiple users to create a single signature for all parties involved.<ref name="ref_3bdb1e89">[https://academy.bit2me.com/en/que-son-las-firmas-schnorr/ What are Schnorr signatures?]</ref>
		+	# So the implementation of Schnorr signatures represents a real solution to this problem.<ref name="ref_3bdb1e89" />
		+	# Historically, EdDSA is known as a variant of Schnorr signatures, which are well-studied and suitable for efficient thresholdization,...<ref name="ref_6a94b9af">[https://csrc.nist.gov/publications/detail/nistir/8214b/draft NISTIR 8214B (Draft), Notes on Threshold EdDSA/Schnorr Signatures]</ref>
		+	# We aim at designing a leakage-resilient variant of the Schnorr signature scheme whose secret key’s storage space is constant, independently of the amount of leakage that it can tolerate.<ref name="ref_4e437487">[https://link.springer.com/chapter/10.1007/978-3-642-45239-0_11 A Leakage-Resilient Pairing-Based Variant of the Schnorr Signature Scheme]</ref>
		+	# We proceed by first proposing a pairing analogue of the Schnorr signature scheme, that we next transform to include split signing key updates.<ref name="ref_4e437487" />
		+	# As the increased uptake in connected devices revives the interest in resource-constrained signature algorithms, we introduce a variant of Schnorr signatures that mutualises exponentiation eorts.<ref name="ref_d70872a7">[https://eprint.iacr.org/2018/069.pdf Reusing nonces in schnorr signatures]</ref>
		+	# Sharing a nonce is a deadly blow to Schnorr signatures, but is not a security concern for our variant.<ref name="ref_d70872a7" />
		+	# We start by reminding how the original Schnorr signature scheme works and explain how we extend it assuming that k is randomly drawn from Zp1.<ref name="ref_d70872a7" />
		+	# 3.1 Our Signature Scheme Similar to the Schnorr signature scheme, our scheme is a tuple of algorithms (Setup, KeyGen, Sign, and Verify), which we dene as follows: Setup(1): Generate primes q1, . .<ref name="ref_d70872a7" />
		+	# This has lead to a long line of research investigating the existence of tighter security proofs for Schnorr signatures.<ref name="ref_1b944f9d">[https://eprint.iacr.org/2013/418.pdf On tight security proofs for schnorr signatures]</ref>
		+	# We begin with the hypothesis that there exists a tight generic re- duction R from some hard non-interactive problem to the UUF-NMA-security of Schnorr signatures.<ref name="ref_1b944f9d" />
		+	# So Schnorr signature solves these 2 problems, it is non-malleable, which means #Bitcoin network becomes more secure.<ref name="ref_3c9b8920">[https://www.linkedin.com/pulse/cryptography-digital-signatures-schnorr-taproot-upgrade-nitesh-balusu Cryptography: Digital Signatures and Schnorr Signatures Explained-#Bitcoin Taproot Upgrade]</ref>
		+	# I'm trying to understand the security of the short schnorr signature a little bit better.<ref name="ref_d5ffc39f">[https://crypto.stackexchange.com/questions/95345/security-proof-of-short-schnorr-signature Security Proof of Short Schnorr Signature]</ref>
		+	# A Schnorr signature is a digital signature produced by the Schnorr signature algorithm.<ref name="ref_02d5a128">[https://www.bitstamp.net/learn/blockchain/what-are-schnorr-signatures/ What are Schnorr Signatures?]</ref>
		+	# Another advantage of Schnorr signatures is increased privacy in terms of securing your bitcoins.<ref name="ref_02d5a128" />
		+	# By reducing the amount of signature data stored on the blockchain, Schnorr signatures free up block storage space.<ref name="ref_02d5a128" />
		+	# But scaling is not the only way Schnorr signatures can improve the Bitcoin protocol.<ref name="ref_02d5a128" />
		+	# The Schnorr signatures (Schnorr, n.d.) have been known before ECDSA signatures, yet they were not so widely used due to the patent which expired in the year 2008.<ref name="ref_a00e3450">[https://mareknarozniak.com/2021/05/25/schnorr-signature/ Schnorr Signature]</ref>
		+	# One of the advantages is the existence of proof that breaking the Schnorr signature is equivalent to breaking the discrete logarithm problem.<ref name="ref_a00e3450" />
		+	# If you like to know more, I based this tutorial on what the heck is Schnorr medium article and cryptography fandom Schnorr signature page.<ref name="ref_a00e3450" />
		+	# We have implemented Schnorr signatures on Bitcoin.<ref name="ref_2b5e61bd">[https://coingeek.com/schnorr-signatures-on-bitcoin/ Schnorr signatures on Bitcoin]</ref>
		+	# FROST is a threshold Schnorr signature protocol that contains two important components.<ref name="ref_adf8fce0">[https://blog.coinbase.com/frost-flexible-round-optimized-schnorr-threshold-signatures-b2e950164ee1 FROST: Flexible Round-Optimized Schnorr Threshold Signatures]</ref>
		+	# Afterwards, any t-out-of-n participants can run a threshold signing protocol to collaboratively generate a valid Schnorr signature.<ref name="ref_adf8fce0" />
		+	# In addition, FROST also requires each participant to demonstrate knowledge of their own secret by sending to other participants a zero-knowledge proof, which itself is a Schnorr signature.<ref name="ref_adf8fce0" />
		+	# To create a valid Schnorr signature, any t participants work together to execute this round.<ref name="ref_adf8fce0" />
		+	# In 2005, when elliptic curve cryptography was being standardized people built on top of DSA rather than Schnorr signatures that had advantages.<ref name="ref_3fd754e6">[https://diyhpl.us/wiki/transcripts/scalingbitcoin/milan/schnorr-signatures/ schnorr-signatures]</ref>
		+	# What I want you to take away from this is Schnorr signatures are not an established standard.<ref name="ref_3fd754e6" />
		+	# The security proof of Schnorr signatures says that they are existentially unforgeable under the assumptions I mentioned before.<ref name="ref_3fd754e6" />
		+	# It turns out if you take Schnorr signatures naively and apply it to an elliptic curve group it has a really annoying interaction with BIP 32 when used with public derivation.<ref name="ref_3fd754e6" />
		+	# But Schnorr signatures can add a new advantage to CoinJoin.<ref name="ref_626bfe1f">[https://bitcoinmagazine.com/culture/the-power-of-schnorr-the-signature-algorithm-to-increase-bitcoin-s-scale-and-privacy-1460642496 The Power of Schnorr: The Signature Algorithm to Increase Bitcoin's Scale and Privacy]</ref>
		+	# Note: The process of implementing Schnorr signatures in Bitcoin is still in the concept phase.<ref name="ref_626bfe1f" />
		+	# Schnorr signatures can be proved secure in the random oracle model (ROM) under the discrete logarithm assumption (DL) by rewinding the adversary; but this security proof is loose.<ref name="ref_d7c091b0">[https://www.semanticscholar.org/paper/Blind-Schnorr-Signatures-in-the-Algebraic-Group-Fuchsbauer-Plouviez/abfbac3d8b2de10803b9df6fe6625090feddb991 PDF Blind Schnorr Signatures in the Algebraic Group Model]</ref>
		+	# The written specication for Schnorr signatures should fully describe the algorithm.<ref name="ref_b8368f56">[https://courses.csail.mit.edu/6.857/2020/projects/4-Elbahrawy-Lovejoy-Ouyang-Perez.pdf Analysis of bitcoin improvement proposal 340]</ref>
		+	# In the Bitcoin specication of Schnorr signatures, the public key Q is 32 bytes, and it can be converted from existing generated public keys by dropping the rst byte (the prex).<ref name="ref_b8368f56" />
		+	# The Schnorr signature scheme is constructed by applying the Fiat-Shamir heuristic to Schnorrs identication protocol.<ref name="ref_b8368f56" />
		+	# Schnorr signature is an alternative algorithm to Bitcoin’s original ECDSA.<ref name="ref_ee937991">[https://www.telemediaonline.co.uk/schnorr-signatures-role-in-bitcoin-transactions/ Schnorr Signatures Role in Bitcoin Transactions]</ref>
		+	# Schnorr signatures are the second type of signatures scheme introduced with the Taproot upgrade to address some of the flaws of the ECDSA protocol.<ref name="ref_ee937991" />
		+	# Schnorr signatures offer that advantage, allowing the Bitcoin network to optimize payment processing and data storage.<ref name="ref_ee937991" />
		+	# That makes it impossible for chain analysis to distinguish between multi-sig and single-sign Bitcoin transactions with Schnorr signatures, ensuring enhanced privacy.<ref name="ref_ee937991" />
		+	# In this blog post we will explain one of the main advantages of Schnorr signatures’: its native support for Multi-Signatures (MultiSig).<ref name="ref_d65743ce">[https://hackernoon.com/a-brief-intro-to-bitcoin-schnorr-multi-signatures-b9ef052374c5 A brief intro to Bitcoin Schnorr Multi-signatures]</ref>
		+	# Package schnorr implements the vanilla Schnorr signature scheme.<ref name="ref_a63ab04b">[https://pkg.go.dev/go.dedis.ch/kyber/sign/schnorr go.dedis.ch/kyber/sign/schnorr]</ref>
		+	# We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group rep- resentations such as those which occur in elliptic curve groups.<ref name="ref_6d25ea82">[http://www.neven.org/papers/schnorr.pdf Hash function requirements]</ref>
		+	# First, since security does not rely on the hash function being collision resistant, Schnorr signatures can still be securely instantiated with SHA-1/SHA- 256, unlike DSA signatures.<ref name="ref_6d25ea82" />
		+	# Apart from instantiation candidates for the hash function, our results have a number of other important implications for the eciency and security of Schnorr signatures.<ref name="ref_6d25ea82" />
		+	# Our work uses Schnorr signatures and leverages Bitcoin recent Taproot upgrade, allowing us to create a checkpointing transaction of constant size.<ref name="ref_0d6bbf83">[https://arxiv.org/pdf/2208.05408 Pikachu: securing pos blockchains from long-range attacks by]</ref>
		+	# To overcome these weaknesses in the Ma-Chen scheme, we propose a new scheme based on the Schnorr signature.<ref name="ref_cf714458">[https://arxiv.org/pdf/cs/0504019 5]</ref>
		+	# == r = (H(m) + r.x) (H(m) + r.x)1 (cid:0)k1(cid:1)1 G = k G = R 2.1.2 Schnorr The Schnorr signature variant over ECC has multiple standards.<ref name="ref_398d6469">[https://arxiv.org/pdf/2110.00274 1]</ref>
		+	# This property allows Schnorr signatures to be aggregated easily to construct a multi-party signature.<ref name="ref_398d6469" />
		+	===소스===
		+	<references />

← 이전 판		2022년 9월 16일 (금) 02:27 판
77번째 줄:		77번째 줄:
	* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]		* [{'LOWER': 'schnorr'}, {'LOWER': 'signature'}, {'LEMMA': 'algorithm'}]
	* [{'LOWER': 'sdsa'}]		* [{'LOWER': 'sdsa'}]
		+
		+	== 노트 ==
		+
		+	===말뭉치===
		+	# In the near future, Bitcoin will enable Schnorr signatures in addition to ECDSA signatures.<ref name="ref_db591c4c">[https://river.com/learn/what-are-schnorr-signatures/ What Do Schnorr Signatures Do for Bitcoin?]</ref>
		+	# Schnorr signatures will be introduced to Bitcoin through Taproot upgrade, which will hopefully be activated around 2022.<ref name="ref_db591c4c" />
		+	# Although developers have added all necessary code to Bitcoin Core, Bitcoin nodes must accept the upgrade in order to consider Schnorr signatures valid.<ref name="ref_db591c4c" />
		+	# In this post I will explain what Schnorr signatures are and how they intuitively work.<ref name="ref_3440f6d6">[https://suredbits.com/introduction-to-schnorr-signatures/ Introduction to Schnorr Signatures]</ref>
		+	# And that is all there is to the actual computation surrounding “vanilla” Schnorr signatures!<ref name="ref_3440f6d6" />
		+	# But Schnorr signatures are much more elegant and simple, and it has one more magical property; linearity.<ref name="ref_27782bb7">[https://medium.com/bitbees/what-the-heck-is-schnorr-52ef5dba289f What The Heck Is Schnorr]</ref>
		+	# Schnorr signature was invented by Claus-Peter Schnorr back in the 1980s.<ref name="ref_27782bb7" />
		+	# Because of his patent, the Schnorr signature algorithm did not see any widespread use for decades.<ref name="ref_27782bb7" />
		+	# Six more years later, in 2014 the first talk of implementing Schnorr signature on Bitcoin protocol came up in the bitcoin-talk forum.<ref name="ref_27782bb7" />
		+	# In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr.<ref name="ref_492c923b">[https://www.geeksforgeeks.org/schnorr-digital-signature/ Schnorr Digital Signature]</ref>
		+	# Note: When you construct the signature like this, it’s known as a Schnorr signature, which is discussed in a following section.<ref name="ref_440c07d2">[https://tlu.tarilabs.com/cryptography/introduction-schnorr-signatures Introduction to Schnorr Signatures]</ref>
		+	# The Schnorr signature is considered the simplest digital signature scheme to be provably secure in a random oracle model.<ref name="ref_440c07d2" />
		+	# We have implemented Schnorr signatures on Bitcoin.<ref name="ref_2b5e61bd">[https://coingeek.com/schnorr-signatures-on-bitcoin/ Schnorr signatures on Bitcoin]</ref>
		+	# Historically, EdDSA is known as a variant of Schnorr signatures, which are well-studied and suitable for efficient thresholdization,...<ref name="ref_6a94b9af">[https://csrc.nist.gov/publications/detail/nistir/8214b/draft NISTIR 8214B (Draft), Notes on Threshold EdDSA/Schnorr Signatures]</ref>
		+	# Schnorr signatures are quite simple compared to other schemes.<ref name="ref_dd62bb89">[https://academy.binance.com/en/articles/what-do-schnorr-signatures-mean-for-bitcoin What do Schnorr Signatures Mean for Bitcoin?]</ref>
		+	# Schnorr signatures have been touted as a solution to these privacy and scalability issues.<ref name="ref_dd62bb89" />
		+	# As with most upgrades to the Bitcoin protocol, it could take time for the broader community of Bitcoin users to agree on the Schnorr signature inclusion.<ref name="ref_dd62bb89" />
		+	# Schnorr signatures could be merged into the code as a soft fork , meaning that a change would not split the network.<ref name="ref_dd62bb89" />
		+	# We aim at designing a leakage-resilient variant of the Schnorr signature scheme whose secret key’s storage space is constant, independently of the amount of leakage that it can tolerate.<ref name="ref_4e437487">[https://link.springer.com/chapter/10.1007/978-3-642-45239-0_11 A Leakage-Resilient Pairing-Based Variant of the Schnorr Signature Scheme]</ref>
		+	# We proceed by first proposing a pairing analogue of the Schnorr signature scheme, that we next transform to include split signing key updates.<ref name="ref_4e437487" />
		+	# As the increased uptake in connected devices revives the interest in resource-constrained signature algorithms, we introduce a variant of Schnorr signatures that mutualises exponentiation eorts.<ref name="ref_d70872a7">[https://eprint.iacr.org/2018/069.pdf Reusing nonces in schnorr signatures]</ref>
		+	# Sharing a nonce is a deadly blow to Schnorr signatures, but is not a security concern for our variant.<ref name="ref_d70872a7" />
		+	# We start by reminding how the original Schnorr signature scheme works and explain how we extend it assuming that k is randomly drawn from Zp1.<ref name="ref_d70872a7" />
		+	# 3.1 Our Signature Scheme Similar to the Schnorr signature scheme, our scheme is a tuple of algorithms (Setup, KeyGen, Sign, and Verify), which we dene as follows: Setup(1): Generate primes q1, . .<ref name="ref_d70872a7" />
		+	# This has lead to a long line of research investigating the existence of tighter security proofs for Schnorr signatures.<ref name="ref_1b944f9d">[https://eprint.iacr.org/2013/418.pdf On tight security proofs for schnorr signatures]</ref>
		+	# We begin with the hypothesis that there exists a tight generic re- duction R from some hard non-interactive problem to the UUF-NMA-security of Schnorr signatures.<ref name="ref_1b944f9d" />
		+	# I'm trying to understand the security of the short schnorr signature a little bit better.<ref name="ref_d5ffc39f">[https://crypto.stackexchange.com/questions/95345/security-proof-of-short-schnorr-signature Security Proof of Short Schnorr Signature]</ref>
		+	# So Schnorr signature solves these 2 problems, it is non-malleable, which means #Bitcoin network becomes more secure.<ref name="ref_3c9b8920">[https://www.linkedin.com/pulse/cryptography-digital-signatures-schnorr-taproot-upgrade-nitesh-balusu Cryptography: Digital Signatures and Schnorr Signatures Explained-#Bitcoin Taproot Upgrade]</ref>
		+	# A Schnorr signature is a digital signature produced by the Schnorr signature algorithm.<ref name="ref_02d5a128">[https://www.bitstamp.net/learn/blockchain/what-are-schnorr-signatures/ What are Schnorr Signatures?]</ref>
		+	# Another advantage of Schnorr signatures is increased privacy in terms of securing your bitcoins.<ref name="ref_02d5a128" />
		+	# By reducing the amount of signature data stored on the blockchain, Schnorr signatures free up block storage space.<ref name="ref_02d5a128" />
		+	# But scaling is not the only way Schnorr signatures can improve the Bitcoin protocol.<ref name="ref_02d5a128" />
		+	# The Schnorr signatures (Schnorr, n.d.) have been known before ECDSA signatures, yet they were not so widely used due to the patent which expired in the year 2008.<ref name="ref_a00e3450">[https://mareknarozniak.com/2021/05/25/schnorr-signature/ Schnorr Signature]</ref>
		+	# One of the advantages is the existence of proof that breaking the Schnorr signature is equivalent to breaking the discrete logarithm problem.<ref name="ref_a00e3450" />
		+	# If you like to know more, I based this tutorial on what the heck is Schnorr medium article and cryptography fandom Schnorr signature page.<ref name="ref_a00e3450" />
		+	# FROST is a threshold Schnorr signature protocol that contains two important components.<ref name="ref_adf8fce0">[https://blog.coinbase.com/frost-flexible-round-optimized-schnorr-threshold-signatures-b2e950164ee1 FROST: Flexible Round-Optimized Schnorr Threshold Signatures]</ref>
		+	# Afterwards, any t-out-of-n participants can run a threshold signing protocol to collaboratively generate a valid Schnorr signature.<ref name="ref_adf8fce0" />
		+	# In addition, FROST also requires each participant to demonstrate knowledge of their own secret by sending to other participants a zero-knowledge proof, which itself is a Schnorr signature.<ref name="ref_adf8fce0" />
		+	# To create a valid Schnorr signature, any t participants work together to execute this round.<ref name="ref_adf8fce0" />
		+	# In 2005, when elliptic curve cryptography was being standardized people built on top of DSA rather than Schnorr signatures that had advantages.<ref name="ref_3fd754e6">[https://diyhpl.us/wiki/transcripts/scalingbitcoin/milan/schnorr-signatures/ schnorr-signatures]</ref>
		+	# What I want you to take away from this is Schnorr signatures are not an established standard.<ref name="ref_3fd754e6" />
		+	# The security proof of Schnorr signatures says that they are existentially unforgeable under the assumptions I mentioned before.<ref name="ref_3fd754e6" />
		+	# It turns out if you take Schnorr signatures naively and apply it to an elliptic curve group it has a really annoying interaction with BIP 32 when used with public derivation.<ref name="ref_3fd754e6" />
		+	# But Schnorr signatures can add a new advantage to CoinJoin.<ref name="ref_626bfe1f">[https://bitcoinmagazine.com/culture/the-power-of-schnorr-the-signature-algorithm-to-increase-bitcoin-s-scale-and-privacy-1460642496 The Power of Schnorr: The Signature Algorithm to Increase Bitcoin's Scale and Privacy]</ref>
		+	# Note: The process of implementing Schnorr signatures in Bitcoin is still in the concept phase.<ref name="ref_626bfe1f" />
		+	# Schnorr signatures can be proved secure in the random oracle model (ROM) under the discrete logarithm assumption (DL) by rewinding the adversary; but this security proof is loose.<ref name="ref_d7c091b0">[https://www.semanticscholar.org/paper/Blind-Schnorr-Signatures-in-the-Algebraic-Group-Fuchsbauer-Plouviez/abfbac3d8b2de10803b9df6fe6625090feddb991 PDF Blind Schnorr Signatures in the Algebraic Group Model]</ref>
		+	# Schnorr signature is an alternative algorithm to Bitcoin’s original ECDSA.<ref name="ref_ee937991">[https://www.telemediaonline.co.uk/schnorr-signatures-role-in-bitcoin-transactions/ Schnorr Signatures Role in Bitcoin Transactions]</ref>
		+	# Schnorr signatures are the second type of signatures scheme introduced with the Taproot upgrade to address some of the flaws of the ECDSA protocol.<ref name="ref_ee937991" />
		+	# Schnorr signatures offer that advantage, allowing the Bitcoin network to optimize payment processing and data storage.<ref name="ref_ee937991" />
		+	# That makes it impossible for chain analysis to distinguish between multi-sig and single-sign Bitcoin transactions with Schnorr signatures, ensuring enhanced privacy.<ref name="ref_ee937991" />
		+	# The written specication for Schnorr signatures should fully describe the algorithm.<ref name="ref_b8368f56">[https://courses.csail.mit.edu/6.857/2020/projects/4-Elbahrawy-Lovejoy-Ouyang-Perez.pdf Analysis of bitcoin improvement proposal 340]</ref>
		+	# In the Bitcoin specication of Schnorr signatures, the public key Q is 32 bytes, and it can be converted from existing generated public keys by dropping the rst byte (the prex).<ref name="ref_b8368f56" />
		+	# The Schnorr signature scheme is constructed by applying the Fiat-Shamir heuristic to Schnorrs identication protocol.<ref name="ref_b8368f56" />
		+	# Package schnorr implements the vanilla Schnorr signature scheme.<ref name="ref_a63ab04b">[https://pkg.go.dev/go.dedis.ch/kyber/sign/schnorr go.dedis.ch/kyber/sign/schnorr]</ref>
		+	# In this blog post we will explain one of the main advantages of Schnorr signatures’: its native support for Multi-Signatures (MultiSig).<ref name="ref_d65743ce">[https://hackernoon.com/a-brief-intro-to-bitcoin-schnorr-multi-signatures-b9ef052374c5 A brief intro to Bitcoin Schnorr Multi-signatures]</ref>
		+	# We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group rep- resentations such as those which occur in elliptic curve groups.<ref name="ref_6d25ea82">[http://www.neven.org/papers/schnorr.pdf Hash function requirements]</ref>
		+	# First, since security does not rely on the hash function being collision resistant, Schnorr signatures can still be securely instantiated with SHA-1/SHA- 256, unlike DSA signatures.<ref name="ref_6d25ea82" />
		+	# Apart from instantiation candidates for the hash function, our results have a number of other important implications for the eciency and security of Schnorr signatures.<ref name="ref_6d25ea82" />
		+	===소스===
		+	<references />