module_14_digital_signatures.pptx

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The document discusses digital signatures and digital signature schemes (DSS). It defines a digital signature as allowing the holder of a secret key to sign a document such that anyone with the public verification key can verify the signature is valid from the signer. A DSS includes key generation, signing, and verification algorithms. It also discusses how DSS provides correctness by verifying valid signatures and unforgeability by making signature forgery difficult. The document contrasts DSS with message authentication codes (MACs) and provides examples of RSA and Schnorr signature schemes.

What is a digital signature
? A digital signature allows the holder of the secret key (the signing key)
to sign a document
? Everyone who knows the verification key can verify that the signature
is valid (correctness)
? No one can forge a signature even given the verification key even
though he is given a signature

Structure of digital signature
? ??? 1? → (??, ??)
? ?????? ? → ???
? ????? ?, ??? → {0,1}

Structure of digital signature scheme (DSS)
? ??? 1? → (??, ??)
? ?????? ? → ???
? ????? ?, ??? → {0,1}
? Correctness
? ????? ?, ??????(?) = 1
? Unforgeability
? To be continued

DSS VS MAC
? ??? 1? → (??, ??)
? ?????? ? → ???
? ????? ?, ??? → {0,1}
? ??? 1? → ?
? ???? ? → ?
? v??? ?, ? → {0,1}

Mac forgery game
M ← {}
?′
?′
k ∈? 0,1 ?
(?, ?)
Wins if
? ? ? ?
? ?????? ?, ? = 1
?′ ← ????(?′)
M ← ? ∪ {?′} Repeat as many times
as the adversary wants

Signature forgery game
M ← {}
?′
???′
??, ?? ← ???(1?
)
(?, ???)
Wins if
? ? ? ?
? ???????? ?, ??? = 1
???′ ← ??????(?′)
M ← ? ∪ {?′} Repeat as many times
as the adversary wants
??

Definition of signature scheme
? Correctness:
? Pr ????? ?, ?????? ? = 1 ??, ?? ← ??? 1? = 1
? Unforgeability
? For all PPT adversary ?, there exists negligible function ?,
? Pr ? ???? ??? ????????? ??????? ???? ≤ ?(?)

Relation between macs and signatures
? Every signature scheme is a message authentication code.
? A mac scheme is not necessarily a signature.
? Without the key, it may be impossible to verify a mac.

Signatures are expensive
? They require public-key operations for each signature you wish to do.
? Hash functions are relatively cheap

Hash and sign
? Let (???′, ????′, ??????′) be a signature scheme and let ? be a
collision resistant hash function, then the following
? ??? 1? ? ???′ 1?
? ?????? ? ? ??????
′
(? ? )
? ???????? ?, ??? ? ????????
′
? ? , ??? = 1

Security of hash and sign
? Let (???′, ????′, ??????′) be a signature scheme and let ? be a collision resistant hash function, then the
following
? ??? 1?
? ???′
1?
? ?????? ? ? ??????
′
(? ? )
? ???????? ?, ??? ? ??????′
? ? , ??? = 1
? Essentially the same proof as hash and mac
? Breaking security of this scheme means
? Finding a collision
? Finding a signature on an unsigned message

Interesting property of plaintext RSA
? ??, ?? ← ?????? 1? ? ????? ????? ? = ?
? Due to the fact that ?? ? = ?? ?
= ???

RSA signature scheme
? Let (??????, ???, ???) denote the RSA encryption scheme
? ??? 1? ? {?? ← ??′, ?? ← ?? ∣ ??′, ??′ ← ?????? 1? }
? ?????? ? ? ????? ?
? ???????? ?, ??? ? ????? ??? = ?

Insecure RSA signature scheme
? ??? 1? ? { ?? ← ??, ?? ← ??′ ∣ ??′, ??′ ← ?????? 1? }
? ?????? ? ? ????? ?
? ???????? ?, ?????? ? = ????? ????? ?
? ????? ????? ? = ?? ?
= ???? = ?

Secure RSA signature scheme
? Assumptions
? Random oracle ? (Hash function modeled as a random oracle
? ? = ?? where ?, ? are prime
? ??? 1?
? { ?? ← ??, ?? ← ??′ ∣ ??′
, ??′
← ?????? 1?
}
? ?????? ? ? ????? ?(?)
? ???????? ?, ?????? ? ? ? ? = ????? ????? ?(?)
? ????? ????? ?(?) = (?(?))? ?
??? ?
? (?(?))? ?
??? ? = ?(?)??? ??? ?(?)
(??? ?) = ?(?)

Schnorr signature scheme
? Based on
? Group G
? Generator ? for G
? Random oracle ?
? Discrete logarithm

Schnorr signature scheme
? Requirement: Group ?, ? = ?, generator ?, random oracle ?
? ??? 1?
? ?? ∈? ?
? ?? ← ???
? ????????(?, ???)
? ?, ? ← ???
? u ← ?? ? ????
? Output ? ?, ? = ?
? ?????? ?
? ? ∈? ?|?|
? ? ← ??
? ? ← ?(?, ?)
? ? ← ? ? ?? + ? (??? ?)
? Output (?, ?)

The document discusses digital signatures and signature schemes. It defines a digital signature as allowing the holder of a secret key to sign a document so that anyone with the public verification key can verify the signature is valid. It describes the basic structure of a digital signature scheme including key generation, signing, and verification. It compares digital signature schemes to message authentication codes and discusses how signatures provide non-repudiation while MACs do not. It also covers the security properties of correctness and unforgeability for digital signature schemes.

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Digital signatures allow a document to be signed by a secret key holder and verified by anyone with the public verification key. A digital signature scheme (DSS) consists of key generation, signing, and verification algorithms. DSS provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. Message authentication codes (MACs) are similar but do not provide non-repudiation like signatures since anyone can generate MACs given the secret key. The RSA and Schnorr signature schemes are examples of DSS that are based on computational hardness assumptions like factoring or discrete logarithms.

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A digital signature allows a document to be signed using a secret key, and verified using a public key. It provides correctness, meaning the verification will succeed for a valid signature, and unforgeability, meaning an adversary cannot generate a valid signature for a message they did not see signed. Digital signature schemes involve key generation, signing messages with the secret key, and verifying signatures with the public key. They differ from message authentication codes in that signatures can be verified by anyone with the public key, while MAC verification requires knowledge of the secret key. Popular digital signature schemes include RSA signatures and the Schnorr signature scheme.

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Digital signatures allow a document to be signed using a secret key so that the signature can be verified by anyone with the corresponding public key. A digital signature scheme (DSS) consists of key generation, signing, and verification algorithms. DSS provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. Message authentication codes (MACs) are similar but do not provide non-repudiation since anyone can generate valid MACs given the key. Common DSS include RSA signatures, which sign a hash of the message using the private key, and Schnorr signatures, which are based on discrete logarithm problems in groups.

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A digital signature allows the holder of a secret key to sign a document, and anyone with the verification key can verify the signature is valid and correct. A digital signature scheme (DSS) includes key generation, signing, and verification algorithms. DSS provides correctness, meaning verification will accept a valid signature, and unforgeability, meaning an adversary cannot generate a valid signature for a message they did not sign. While message authentication codes (MACs) are similar, they do not necessarily provide unforgeability without the key. Popular digital signature schemes include RSA signatures and the Schnorr signature scheme.

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iam free indeed.pptxiam free indeed.pptxmuhweziart

april 2024 paper 2 ms. english non fictionomokoredeolasunbomi

Data-Models-in-DBMS-An-Overview.pptx.pptxhfebxtveyjxavhx

stages-of-moral-development-lawrence-kohlberg-pdf-free.pdfesguerramark1991

Introduction to database and analysis software’s suitable for.pptxnabinparajuli9

Stasiun kernel pengolahan kelapa sawit indonesiafikrimanurung1

加拿大成绩单购买原版(鲍颁毕业证书)卡尔加里大学毕业证文凭taqyed

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2025-03-03-Philly-AAAI-GoodData-Build Secure RAG Apps With Open LLMTimothy Spann

Analyzing Consumer Spending Trends and Purchasing Behavioromololaokeowo1

This project explores consumer spending patterns using Kaggle-sourced data to uncover key trends in purchasing behavior. The analysis involved cleaning and preparing the data, performing exploratory data analysis (EDA), and visualizing insights using ExcelI. Key focus areas included customer demographics, product performance, seasonal trends, and pricing strategies. The project provided actionable insights into consumer preferences, helping businesses optimize sales strategies and improve decision-making.

A Relative Information Gain-based Query Performance Prediction Framework with...suchanadatta3

To improve the QPP estimate for neural models, we propose to use additional information from a set of queries that express a similar information need to the current one (these queries are called variants). The key idea of our proposed method, named Weighted Relative Information Gain (WRIG), is to estimate the performance of these variants, and then to improve the QPP estimate of the original query based on the relative differences with the variants. The hypothesis is that if a query’s estimate is significantly higher than the average QPP score of its variants, then the original query itself is assumed (with a higher confidence) to be one for which a retrieval model works well.

The Marketability of Rice Straw Yarn Among Selected Customers of Gantsilyo Gurukenyoncenteno12

CH. 4.pptxt and I will be there in aboutmiesoabdela57

vnptloveeeeeeeeeeeeeeeeeeeeeeeeeeee.pptxdeomom129

Boosting MySQL with Vector Search Scale22X 2025.pdfAlkin Tezuysal

MTC Supply Chain Management Strategy.pptxRakshit Porwal

Presentation.2 .reversal. reversal. pptxsiliaselim87

Stasiun kernel pabrik kelapa sawit indonesiafikrimanurung1

Cost sheet. with basics and formats of sheetsupreetk82004

Class 3-Workforce profile updated P.pptxangelananalucky

原版复刻加拿大多伦多大学成绩单(UTSG毕业证书) 文凭taqyed

iam free indeed.pptxiam free indeed.pptxmuhweziart

april 2024 paper 2 ms. english non fictionomokoredeolasunbomi

Data-Models-in-DBMS-An-Overview.pptx.pptxhfebxtveyjxavhx

stages-of-moral-development-lawrence-kohlberg-pdf-free.pdfesguerramark1991

Introduction to database and analysis software’s suitable for.pptxnabinparajuli9

Stasiun kernel pengolahan kelapa sawit indonesiafikrimanurung1

加拿大成绩单购买原版(鲍颁毕业证书)卡尔加里大学毕业证文凭taqyed

2025-03-03-Philly-AAAI-GoodData-Build Secure RAG Apps With Open LLMTimothy Spann

Analyzing Consumer Spending Trends and Purchasing Behavioromololaokeowo1

A Relative Information Gain-based Query Performance Prediction Framework with...suchanadatta3

module_14_digital_signatures.pptx

1. Digital signatures

2. What is a digital signature ? A digital signature allows the holder of the secret key (the signing key) to sign a document ? Everyone who knows the verification key can verify that the signature is valid (correctness) ? No one can forge a signature even given the verification key even though he is given a signature

3. Structure of digital signature ? ??? 1? → (??, ??) ? ?????? ? → ??? ? ????? ?, ??? → {0,1}

4. Structure of digital signature scheme (DSS) ? ??? 1? → (??, ??) ? ?????? ? → ??? ? ????? ?, ??? → {0,1} ? Correctness ? ????? ?, ??????(?) = 1 ? Unforgeability ? To be continued

5. DSS VS MAC ? ??? 1? → (??, ??) ? ?????? ? → ??? ? ????? ?, ??? → {0,1} ? ??? 1? → ? ? ???? ? → ? ? v??? ?, ? → {0,1}

6. Mac forgery game M ← {} ?′ ?′ k ∈? 0,1 ? (?, ?) Wins if ? ? ? ? ? ?????? ?, ? = 1 ?′ ← ????(?′) M ← ? ∪ {?′} Repeat as many times as the adversary wants

7. Signature forgery game M ← {} ?′ ???′ ??, ?? ← ???(1? ) (?, ???) Wins if ? ? ? ? ? ???????? ?, ??? = 1 ???′ ← ??????(?′) M ← ? ∪ {?′} Repeat as many times as the adversary wants ??

8. Definition of signature scheme ? Correctness: ? Pr ????? ?, ?????? ? = 1 ??, ?? ← ??? 1? = 1 ? Unforgeability ? For all PPT adversary ?, there exists negligible function ?, ? Pr ? ???? ??? ????????? ??????? ???? ≤ ?(?)

9. Relation between macs and signatures ? Every signature scheme is a message authentication code. ? A mac scheme is not necessarily a signature. ? Without the key, it may be impossible to verify a mac.

10. Signatures are expensive ? They require public-key operations for each signature you wish to do. ? Hash functions are relatively cheap

11. Hash and sign ? Let (???′, ????′, ??????′) be a signature scheme and let ? be a collision resistant hash function, then the following ? ??? 1? ? ???′ 1? ? ?????? ? ? ?????? ′ (? ? ) ? ???????? ?, ??? ? ???????? ′ ? ? , ??? = 1

12. Security of hash and sign ? Let (???′, ????′, ??????′) be a signature scheme and let ? be a collision resistant hash function, then the following ? ??? 1? ? ???′ 1? ? ?????? ? ? ?????? ′ (? ? ) ? ???????? ?, ??? ? ??????′ ? ? , ??? = 1 ? Essentially the same proof as hash and mac ? Breaking security of this scheme means ? Finding a collision ? Finding a signature on an unsigned message

13. Interesting property of plaintext RSA ? ??, ?? ← ?????? 1? ? ????? ????? ? = ? ? Due to the fact that ?? ? = ?? ? = ???

14. RSA signature scheme ? Let (??????, ???, ???) denote the RSA encryption scheme ? ??? 1? ? {?? ← ??′, ?? ← ?? ∣ ??′, ??′ ← ?????? 1? } ? ?????? ? ? ????? ? ? ???????? ?, ??? ? ????? ??? = ?

15. Insecure RSA signature scheme ? ??? 1? ? { ?? ← ??, ?? ← ??′ ∣ ??′, ??′ ← ?????? 1? } ? ?????? ? ? ????? ? ? ???????? ?, ?????? ? = ????? ????? ? ? ????? ????? ? = ?? ? = ???? = ?

16. Secure RSA signature scheme ? Assumptions ? Random oracle ? (Hash function modeled as a random oracle ? ? = ?? where ?, ? are prime ? ??? 1? ? { ?? ← ??, ?? ← ??′ ∣ ??′ , ??′ ← ?????? 1? } ? ?????? ? ? ????? ?(?) ? ???????? ?, ?????? ? ? ? ? = ????? ????? ?(?) ? ????? ????? ?(?) = (?(?))? ? ??? ? ? (?(?))? ? ??? ? = ?(?)??? ??? ?(?) (??? ?) = ?(?)

17. Schnorr signature scheme ? Based on ? Group G ? Generator ? for G ? Random oracle ? ? Discrete logarithm

18. Schnorr signature scheme ? Requirement: Group ?, ? = ?, generator ?, random oracle ? ? ??? 1? ? ?? ∈? ? ? ?? ← ??? ? ????????(?, ???) ? ?, ? ← ??? ? u ← ?? ? ???? ? Output ? ?, ? = ? ? ?????? ? ? ? ∈? ?|?| ? ? ← ?? ? ? ← ?(?, ?) ? ? ← ? ? ?? + ? (??? ?) ? Output (?, ?)

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module_14_digital_signatures.pptx

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