Podcast
Questions and Answers
In asymmetric cryptography, what is the relationship between the public key and the private key?
In asymmetric cryptography, what is the relationship between the public key and the private key?
- The private key is derived from the public key through a simple mathematical function.
- Knowing the public key, it is computationally infeasible to determine the private key. (correct)
- Knowing the public key, it is computationally feasible to determine the private key.
- The public key and private key are identical and interchangeable.
In a scenario using asymmetric cryptography, Milhouse wants to send an encrypted message to Bart. How should Milhouse encrypt the message to ensure only Bart can read it?
In a scenario using asymmetric cryptography, Milhouse wants to send an encrypted message to Bart. How should Milhouse encrypt the message to ensure only Bart can read it?
- Milhouse encrypts the message using his own private key.
- Milhouse encrypts the message using Bart's private key.
- Milhouse encrypts the message using Bart's public key. (correct)
- Milhouse encrypts the message using his own public key.
Which of the following is a key advantage of asymmetric cryptography compared to symmetric cryptography?
Which of the following is a key advantage of asymmetric cryptography compared to symmetric cryptography?
- Asymmetric cryptography is significantly faster in encryption and decryption processes.
- Asymmetric cryptography requires both parties to securely exchange a secret key before communication.
- Asymmetric cryptography provides perfect forward secrecy, which symmetric cryptography cannot achieve.
- Asymmetric cryptography simplifies key distribution because only the private key needs to be kept secret. (correct)
Mr. Burns wants to ensure the integrity of the message he sends to Smithers, using asymmetric cryptography. How can he achieve this?
Mr. Burns wants to ensure the integrity of the message he sends to Smithers, using asymmetric cryptography. How can he achieve this?
In asymmetric cryptography, if a digital signature is created using a private key, what key should be used to verify the signature?
In asymmetric cryptography, if a digital signature is created using a private key, what key should be used to verify the signature?
Which of the following is a primary limitation of symmetric key cryptography that asymmetric cryptography aims to solve?
Which of the following is a primary limitation of symmetric key cryptography that asymmetric cryptography aims to solve?
In asymmetric cryptography, what is the purpose of the private key?
In asymmetric cryptography, what is the purpose of the private key?
If Bart wants to send a confidential message to Milhouse using asymmetric cryptography, which key should Bart use to encrypt the message?
If Bart wants to send a confidential message to Milhouse using asymmetric cryptography, which key should Bart use to encrypt the message?
In asymmetric cryptography, which key is used to verify the digital signature of a message?
In asymmetric cryptography, which key is used to verify the digital signature of a message?
What security goal does encrypting a message with the recipient’s public key achieve?
What security goal does encrypting a message with the recipient’s public key achieve?
Which of the following scenarios represents a disadvantage of asymmetric cryptography compared to symmetric cryptography?
Which of the following scenarios represents a disadvantage of asymmetric cryptography compared to symmetric cryptography?
What is the primary role of a Public Key Infrastructure (PKI) in the context of asymmetric cryptography?
What is the primary role of a Public Key Infrastructure (PKI) in the context of asymmetric cryptography?
Which of the following best describes the purpose of digital signatures in asymmetric cryptography?
Which of the following best describes the purpose of digital signatures in asymmetric cryptography?
In the context of digital signatures, what is the primary advantage of signing the hash of a message rather than the message itself?
In the context of digital signatures, what is the primary advantage of signing the hash of a message rather than the message itself?
Which of the following is NOT a service provided by digital signatures?
Which of the following is NOT a service provided by digital signatures?
What role does a Certificate Authority (CA) play in asymmetric key systems?
What role does a Certificate Authority (CA) play in asymmetric key systems?
What is the purpose of a Certificate Revocation List (CRL) issued by a Certificate Authority (CA)?
What is the purpose of a Certificate Revocation List (CRL) issued by a Certificate Authority (CA)?
In a Public Key Infrastructure (PKI), what is the role of the Registration Authority (RA)?
In a Public Key Infrastructure (PKI), what is the role of the Registration Authority (RA)?
What security issue does the Public Key Infrastructure (PKI) aim to solve?
What security issue does the Public Key Infrastructure (PKI) aim to solve?
Which attack is PKI designed to primarily prevent?
Which attack is PKI designed to primarily prevent?
A contract is digitally signed by a person. What does this ensure?
A contract is digitally signed by a person. What does this ensure?
Which of the following is a fundamental disadvantage of asymmetric cryptography?
Which of the following is a fundamental disadvantage of asymmetric cryptography?
A company wants to ensure both confidentiality and authentication for their emails. Which cryptographic tool should they use?
A company wants to ensure both confidentiality and authentication for their emails. Which cryptographic tool should they use?
In the context of RSA, what is the significance of selecting two large prime numbers, $p$ and $q$, during key generation?
In the context of RSA, what is the significance of selecting two large prime numbers, $p$ and $q$, during key generation?
What is the role of $\phi(n)$ in the RSA key generation process?
What is the role of $\phi(n)$ in the RSA key generation process?
Given $C = M^e \mod n$ in RSA, what operation is performed to recover the original message, $M$?
Given $C = M^e \mod n$ in RSA, what operation is performed to recover the original message, $M$?
Which security property of RSA is most directly compromised if an attacker can efficiently factor the modulus $n$?
Which security property of RSA is most directly compromised if an attacker can efficiently factor the modulus $n$?
What distinguishes the Diffie-Hellman key exchange protocol from RSA?
What distinguishes the Diffie-Hellman key exchange protocol from RSA?
Why is a mathematical breakthrough that provides a feasible way to factor large numbers a significant threat to RSA?
Why is a mathematical breakthrough that provides a feasible way to factor large numbers a significant threat to RSA?
In RSA, given $p = 13$ and $q = 11$, what is the value of $n$?
In RSA, given $p = 13$ and $q = 11$, what is the value of $n$?
Using RSA, if $p = 17$ and $q = 13$, what is the value of $\varphi(n)$?
Using RSA, if $p = 17$ and $q = 13$, what is the value of $\varphi(n)$?
In RSA, if $\varphi(n) = 120$, which of the following values of 'e' is a valid choice?
In RSA, if $\varphi(n) = 120$, which of the following values of 'e' is a valid choice?
Given $e = 7$ and $\varphi(n) = 20$, what value of 'd' satisfies the condition for RSA key generation (i.e., $e*d mod \space \varphi(n) = 1$)?
Given $e = 7$ and $\varphi(n) = 20$, what value of 'd' satisfies the condition for RSA key generation (i.e., $e*d mod \space \varphi(n) = 1$)?
In RSA encryption, if $M = 5$, $e = 3$ and $n = 21$, what is the ciphertext $C$?
In RSA encryption, if $M = 5$, $e = 3$ and $n = 21$, what is the ciphertext $C$?
In RSA decryption, given a ciphertext $C = 8$, $d = 7$, and $n = 33$, what is the original message $M$?
In RSA decryption, given a ciphertext $C = 8$, $d = 7$, and $n = 33$, what is the original message $M$?
Why is asymmetric cryptography, like RSA, typically used to exchange symmetric keys rather than for bulk encryption?
Why is asymmetric cryptography, like RSA, typically used to exchange symmetric keys rather than for bulk encryption?
What is the primary factor determining the security strength of the RSA algorithm?
What is the primary factor determining the security strength of the RSA algorithm?
Flashcards
Private Key
Private Key
Key used to decrypt messages
Public Key
Public Key
Key used by others to encrypt messages for you
Asymmetric Cryptography
Asymmetric Cryptography
Cryptography using a separate key pair (public and private) for encryption and decryption.
Asymmetric Encryption
Asymmetric Encryption
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Asymmetric Decryption
Asymmetric Decryption
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Asymmetric Encryption for Confidentiality
Asymmetric Encryption for Confidentiality
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Asymmetric Encryption for Integrity
Asymmetric Encryption for Integrity
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Key Exchange
Key Exchange
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Symmetric Key Distribution Limitation
Symmetric Key Distribution Limitation
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Digital Signature
Digital Signature
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Key Pair
Key Pair
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Integrity (in Crypto)
Integrity (in Crypto)
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Authentication (in Crypto)
Authentication (in Crypto)
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Non-Repudiation
Non-Repudiation
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Diffie-Hellman
Diffie-Hellman
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RSA
RSA
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El Gamal
El Gamal
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n (RSA)
n (RSA)
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φ(n) in RSA
φ(n) in RSA
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e (RSA)
e (RSA)
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d (RSA)
d (RSA)
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M (RSA)
M (RSA)
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C (RSA)
C (RSA)
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RSA Security
RSA Security
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Asymmetric Encryption Usage
Asymmetric Encryption Usage
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Integrity in Asymmetric Encryption
Integrity in Asymmetric Encryption
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Digital Signature Scheme
Digital Signature Scheme
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Digital Signatures - Provides
Digital Signatures - Provides
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Signing Message Hashes
Signing Message Hashes
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Man-in-the-Middle (MitM) Attack
Man-in-the-Middle (MitM) Attack
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Public Key Infrastructure (PKI)
Public Key Infrastructure (PKI)
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Study Notes
Asymmetric Encryption Overview
- It is important to understand the introduction, advantages, and disadvantages of asymmetric cryptography
Review of Symmetric Cryptography
- Confidentiality involves Stream and Block ciphers
- Integrity is achieved using cryptographic hash functions
- A limitation is that the sender and receiver must share the same key
- A secure channel for key distribution is necessary
- Establishing communication is impossible for two parties without a prior relationship
- Many keys are required for n parties to communicate
Key Exchange
- Traditionally, secure encrypted communication between two parties requires the exchange of keys through a secure physical channel, such as paper key lists transported by a trusted courier
Asymmetric Cryptography Basics
- In asymmetric cryptography, both the sender and receiver possess both a public and a private key
- Public keys are publicly available
- Private keys must be kept secret
Key Usage in Asymmetric Cryptography
- Milhouse's public key can reveal messages encrypted with Milhouse's private key
- Milhouse's private key can reveal messages encrypted with Milhouse's public key
- Bart's public key can reveal messages encrypted with Bart's private key
- Bart's private key can reveal messages encrypted with Bart's public key
Asymmetric Cryptography - Confidentiality
- To ensure confidentiality, Milhouse hides a message using Bart's public key
- Only Bart can reveal the message using his private key
- Only Bart can read the message
Asymmetric Cryptography - Integrity
- To ensure integrity, Milhouse hides a message using his private key, then Mr Burns modifies the content and hides the message using his private key
- Anyone with Milhouse's public key can reveal the message, but the modified message will cause the receiver to distrust it
Asymmetric Cryptography – Integrity and Confidentiality
- Combined integrity and confidentiality begins with Milhouse hiding a message using his private key
- Milhouse then hides the message again using Bart's public key
- Bart reveals the message using his private key
- Then he reveals the message using Milhouse's public key
Asymmetric Cryptography - Recap
- Each party has a pair of keys: a public key (PubK) used for encryption and a private key (PrivK) used for decryption
- Knowing the public-key PubK, it is computationally infeasible to compute the private-key PrivK
- The public-key PubK can be made publicly available
- Many can encrypt using the public key, but only one can decrypt using the private key
Asymmetric Cryptography - Advantages
- Only the private key must be kept secret, the public key can be shared freely
- A key pair is generated once and used forever, unless the private key is compromised
- Offers confidentiality, integrity, authentication, and non-repudiation through digital signatures
Asymmetric Cryptography - Disadvantages
- Strength depends on the infeasibility of solving difficult problems, such as discrete logarithm and factoring large numbers
- Calculating 19*31=589 is easy, but determining the two prime factors of a large number is computationally difficult
- In real systems, the product term is very large
- A mathematical breakthrough could provide a feasible way to solve the problem and break the encryption
- Faster computers and quantum computers could facilitate breaking encryption
Public Key Cryptography - Early History
- Public-key encryption was proposed in 1970 by James Ellis James Ellis
- The paper was made public in 1997 by the British Governmental Communications Headquarters
- Diffie and Hellman proposed the concept in 1976 "New Directions in Cryptography"
- Includes public-key encryption schemes, public key distribution systems, Diffie-Hellman key agreement protocol, and digital signature digital signature
- The concept of digital signature is originally due to Diffie & Hellman
Public Key Encryption Algorithms
- Most public-key encryption algorithms use number theory, modular arithmetic, or elliptic curves
RSA and El Gamal
- Security relies on the hardness of factoring large numbers
- El Gamal Security relies on the hardness of solving discrete logarithm
RSA Algorithm - History
- Invented in 1978 by Ron Rivest, Adi Shamir, and Leonard Adleman
- Security relies on the difficulty of factoring large composite numbers
- Discovered the same algorithm in 1973 by Clifford Cocks
RSA Public Key Crypto System - Key Generation
- Select 2 large prime numbers of about the same size, p and q
- Compute n = pq, and $(n) = (q-1)(p-1)
- Select e: 1<e<$(n) s.t. gcd(e, $(n))= 1
- Compute d: 1 < d < $(n) s.t. ed mod $(n) = 1
- Public key: (e, n)
- Private key: d
RSA Public Key Crypto System - Encryption
- Given a message M, 0 < M<n
- the public key (e, n) is used to compute C = Me mod n
RSA Public Key Crypto System - Decryption
- Given a ciphertext C
- the private key (d) is used to compute Cd mod n -> (Me mod n) mod n -> Med mod n = M
RSA Properties
- Plaintext is M
- Ciphertext is C
- C = Me mod n (Encryption)
- Cd mod n (Decryption)
- It is difficult to compute p and q from n
- It is difficult to compute d from (n, e)
- It is difficult to compute M from (n, e) and C
RSA Security
- Security depends on the difficulty of factoring n
- Factoring n allows the computation of d from (e, φ(n))
- The length of n=pq determines the strength of the encryption
- 700-bit n was factored in 2007 and 768-bit n in 2009
- 1024 bits provides minimal security today but may be breakable in the near future
- A minimum of 2048 bits is recommended for current usage
- NIST suggests using 15360-bit RSA keys
Real World Usage of Public Key Encryption - Efficiency
- Asymmetric Cryptography encryption often implies heavy performance issues
- It is far less efficient than symmetric cryptography, making it unsuitable for real-time or bulk encryption
- RSA speed is quadratic in key length
- Asymmetric Cryptography encryption can exchange the symmetric key over an unsecure channel
- Then, use the shared key for real communication using symmetric cryptography
Real World Usage of Asymmetric Encryption - Integrity
- Consider real-life examples where a signature on a credit card payment is verified against the signature on the card
- Contracts are valid if they are signed
- Signatures provide non-repudiation, ensuring that a party cannot dispute the validity of a statement or contract
Digital Signatures
- A data string that associates a message with some originating entity
- Usually one party generates the signature and many parties can verify it
- A digital signature scheme includes signing and verification algorithms
- Signing takes a message and a private signing key and outputs a signature
- Verification takes a public verification key, a message, and a signature
- Provides authentication, data integrity, and non-repudiation
Digital Signatures and Hash Functions
- Digital signatures are often used with hash functions where the hash of a message is signed instead of the message itself
MitM Attack Against Asymmetric Key Systems
- How do we know we are really talking to the right party, since anyone can send you a public key to use?
- A digital signature ties a message to a private key, not to a person
- We need a way to bind a public/private key pair to a specific individual
Asymmetric Key Systems - Solution
- Public Key Infrastructure (PKI) is a solution to asymmetric key system problems
- A trusted third party, called certificate authority (CA), vouches for the individuals and their keys
- A registration authority (RA) issues digital certificates that bind key pairs to identities
- Certificates can be created for people, organizations, or specific computers
- PKI includes mechanisms to issue, revoke, and verify certificates
Public Key Infrastructure (PKI) Explained
- The issuer digitally signs the certificates, allowing verification of authenticity and integrity
- There may be multiple layers of certificates verifying others in a 'tree of trust' or 'web of trust'
- A CA has one or more root certificates that must be trusted implicitly
- Certificates have an expiration date
- The CA may issue a certificate revocation list (CRL) of certificates that have not expired but should not be trusted
Public Key Certificates
- Certificate Authority verifies the identity of Mario Rossi and encrypts with his Private Key
- Identity information and Public Key of Mario Rossi:
- Name: Mario Rossi
- Organization: Wikimedia
- Address: via .......
- Country: United States
- Certificate of Mario Rossi:
- Name: Mario Rossi
- Organization: Wikimedia
- Address: via .......
- Country: United States
- Validity: 1997/07/01-2047/06/30
- Public Key of Mario Rossi and Digital Signature of the Certificate Authority
- Digitally Signed by Certificate Authority
X.509 Certificates
- Defines a framework for authentication services
- The most widely accepted certificate format is defined by the ITU-T X.509 version 3 international standards
- Certificates are encoded using OSI ASN.1 DER
- Used by numerous applications, including SSL, IPSec, and SET
How to Obtain a Certificate
- Define your own CA (using openssl or Java Keytool), but these certificates are unlikely to be accepted by others
- Obtain certificates from vendors like VeriSign and Thawte
- The CA verifies the CSR and at some point returns a signed digital certificate Signed Certificate Path and/or its URL are stored locally
CAs and Trust
- Certificates are trusted if the CA's signature verifies
- A chain of CAs can be formed, with the head CA called the root CA
- The public key of the root CA is needed to verify the signature
- Trust is centralized (to root CAs) and hierarchical
- Disasters can occur if the root CA system is compromised
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Description
Explore the core principles of asymmetric cryptography. Understand the roles of public and private keys in secure communication, encryption, and digital signatures. Learn how this method overcomes limitations of symmetric cryptography.