Public Key Cryptography and RSA algorithmIndra97065
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Public Key Cryptography and RSA algorithm.Explanation and proof of RSA algorithm in details.it also describer the mathematics behind the RSA. Few mathematics theorem are given which are use in the RSA algorithm.
Digital Signature Recognition using RSA AlgorithmVinayak Raja
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• OBJECTIVE: Basically, the idea behind digital signatures is the same as your handwritten signature. You use it to authenticate the fact that you promised something that you can't take back later. A digital signature doesn't involve signing something with a pen and paper then sending it over the Internet. But like a paper signature, it attaches the identity of the signer to a transaction.
• PROBLEM SOLVED: Signer authentication , Message authentication, Non-repudiation , Message integrity
Public Key Cryptography and RSA algorithmIndra97065
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Public Key Cryptography and RSA algorithm.Explanation and proof of RSA algorithm in details.it also describer the mathematics behind the RSA. Few mathematics theorem are given which are use in the RSA algorithm.
Digital Signature Recognition using RSA AlgorithmVinayak Raja
Â
• OBJECTIVE: Basically, the idea behind digital signatures is the same as your handwritten signature. You use it to authenticate the fact that you promised something that you can't take back later. A digital signature doesn't involve signing something with a pen and paper then sending it over the Internet. But like a paper signature, it attaches the identity of the signer to a transaction.
• PROBLEM SOLVED: Signer authentication , Message authentication, Non-repudiation , Message integrity
An introduction to asymmetric cryptography with an in-depth look at RSA, Diffie-Hellman, the FREAK and LOGJAM attacks on TLS/SSL, and the "Mining your P's and Q's attack".
traditional private/secret/single key cryptography uses one key
Key is shared by both sender and receiver
if the key is disclosed communications are compromised
also known as symmetric, both parties are equal
hence does not protect sender from receiver forging a message & claiming is sent by sender
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
RSA RivestShamirAdleman is an algorithm used by modern computers to encrypt and decrypt messages. The purpose of the paper is how to produce two different keys. This is also called public key cryptography, because one of the keys can be given to anyone. In this paper also represent how to separate unwanted character by using Linux command. Soe Moe Myint | Moe Moe Myint | Aye Aye Cho "A Study of RSA Algorithm in Cryptography" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26749.pdf Paper URL: https://www.ijtsrd.com/computer-science/database/26749/a-study-of-rsa-algorithm-in-cryptography/soe-moe-myint
An introduction to asymmetric cryptography with an in-depth look at RSA, Diffie-Hellman, the FREAK and LOGJAM attacks on TLS/SSL, and the "Mining your P's and Q's attack".
traditional private/secret/single key cryptography uses one key
Key is shared by both sender and receiver
if the key is disclosed communications are compromised
also known as symmetric, both parties are equal
hence does not protect sender from receiver forging a message & claiming is sent by sender
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
RSA RivestShamirAdleman is an algorithm used by modern computers to encrypt and decrypt messages. The purpose of the paper is how to produce two different keys. This is also called public key cryptography, because one of the keys can be given to anyone. In this paper also represent how to separate unwanted character by using Linux command. Soe Moe Myint | Moe Moe Myint | Aye Aye Cho "A Study of RSA Algorithm in Cryptography" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26749.pdf Paper URL: https://www.ijtsrd.com/computer-science/database/26749/a-study-of-rsa-algorithm-in-cryptography/soe-moe-myint
In cryptography, a block cipher is a deterministic algorithm operating on ... Systems as a means to effectively improve security by combining simple operations such as .... Finally, the cipher should be easily cryptanalyzable, such that it can be ...
Information and network security 33 rsa algorithmVaibhav Khanna
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RSA algorithm is asymmetric cryptography algorithm. Asymmetric actually means that it works on two different keys i.e. Public Key and Private Key. As the name describes that the Public Key is given to everyone and Private key is kept private
A brief introduction to Crytography,the various types of crytography and the advantages and disadvantages associated to using the following tyes with some part of the RSA algorithm
For a college course -- CNIT 140: "Cryptography for Computer Networks" at City College San Francisco
Instructor: Sam Bowne
More info: https://samsclass.info/141/141_S19.shtml
Based on "Serious Cryptography: A Practical Introduction to Modern Encryption", by Jean-Philippe Aumasson, No Starch Press (November 6, 2017), ISBN-10: 1593278268 ISBN-13: 978-1593278267
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
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In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Welcome to the first live UiPath Community Day Dubai! Join us for this unique occasion to meet our local and global UiPath Community and leaders. You will get a full view of the MEA region's automation landscape and the AI Powered automation technology capabilities of UiPath. Also, hosted by our local partners Marc Ellis, you will enjoy a half-day packed with industry insights and automation peers networking.
đź“• Curious on our agenda? Wait no more!
10:00 Welcome note - UiPath Community in Dubai
Lovely Sinha, UiPath Community Chapter Leader, UiPath MVPx3, Hyper-automation Consultant, First Abu Dhabi Bank
10:20 A UiPath cross-region MEA overview
Ashraf El Zarka, VP and Managing Director MEA, UiPath
10:35: Customer Success Journey
Deepthi Deepak, Head of Intelligent Automation CoE, First Abu Dhabi Bank
11:15 The UiPath approach to GenAI with our three principles: improve accuracy, supercharge productivity, and automate more
Boris Krumrey, Global VP, Automation Innovation, UiPath
12:15 To discover how Marc Ellis leverages tech-driven solutions in recruitment and managed services.
Brendan Lingam, Director of Sales and Business Development, Marc Ellis
Le nuove frontiere dell'AI nell'RPA con UiPath Autopilot™UiPathCommunity
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In questo evento online gratuito, organizzato dalla Community Italiana di UiPath, potrai esplorare le nuove funzionalitĂ di Autopilot, il tool che integra l'Intelligenza Artificiale nei processi di sviluppo e utilizzo delle Automazioni.
đź“• Vedremo insieme alcuni esempi dell'utilizzo di Autopilot in diversi tool della Suite UiPath:
Autopilot per Studio Web
Autopilot per Studio
Autopilot per Apps
Clipboard AI
GenAI applicata alla Document Understanding
👨‍🏫👨‍💻 Speakers:
Stefano Negro, UiPath MVPx3, RPA Tech Lead @ BSP Consultant
Flavio Martinelli, UiPath MVP 2023, Technical Account Manager @UiPath
Andrei Tasca, RPA Solutions Team Lead @NTT Data
Enhancing Performance with Globus and the Science DMZGlobus
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ESnet has led the way in helping national facilities—and many other institutions in the research community—configure Science DMZs and troubleshoot network issues to maximize data transfer performance. In this talk we will present a summary of approaches and tips for getting the most out of your network infrastructure using Globus Connect Server.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
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In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
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Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
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Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
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Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
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Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
A tale of scale & speed: How the US Navy is enabling software delivery from l...
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RSA
1. Public Key Cryptography
and the
RSA Algorithm
Cryptography and Network Security
by William Stallings
Lecture slides by Lawrie Brown
Edited by Dick Steflik
2. Private-Key Cryptography
• traditional private/secret/single key cryptography
uses one key
• Key is shared by both sender and receiver
• if the key is disclosed communications are
compromised
• also known as symmetric, both parties are equal
• hence does not protect sender from receiver forging a
message & claiming is sent by sender
3. Public-Key Cryptography
• probably most significant advance in the 3000
•
•
•
•
year history of cryptography
uses two keys – a public key and a private key
asymmetric since parties are not equal
uses clever application of number theory concepts
to function
complements rather than replaces private key
cryptography
4. Public-Key Cryptography
• public-key/two-key/asymmetric cryptography
involves the use of two keys:
• a public-key, which may be known by anybody, and
can be used to encrypt messages, and verify
signatures
• a private-key, known only to the recipient, used to
decrypt messages, and sign (create) signatures
• is asymmetric because
• those who encrypt messages or verify signatures
cannot decrypt messages or create signatures
6. Why Public-Key Cryptography?
• developed to address two key issues:
• key distribution – how to have secure
communications in general without having to
trust a KDC with your key
• digital signatures – how to verify a message
comes intact from the claimed sender
• public invention due to Whitfield Diffie &
Martin Hellman at Stanford U. in 1976
• known earlier in classified community
7. Public-Key Characteristics
• Public-Key algorithms rely on two keys
with the characteristics that it is:
• computationally infeasible to find decryption
key knowing only algorithm & encryption key
• computationally easy to en/decrypt messages
when the relevant (en/decrypt) key is known
• either of the two related keys can be used for
encryption, with the other used for decryption
(in some schemes)
9. Public-Key Applications
• can classify uses into 3 categories:
• encryption/decryption (provide secrecy)
• digital signatures (provide authentication)
• key exchange (of session keys)
• some algorithms are suitable for all uses,
others are specific to one
10. Security of Public Key Schemes
• like private key schemes brute force exhaustive
•
•
•
•
•
search attack is always theoretically possible
but keys used are too large (>512bits)
security relies on a large enough difference in
difficulty between easy (en/decrypt) and hard
(cryptanalyse) problems
more generally the hard problem is known, its just
made too hard to do in practise
requires the use of very large numbers
hence is slow compared to private key schemes
11. RSA
• by Rivest, Shamir & Adleman of MIT in 1977
• best known & widely used public-key scheme
• based on exponentiation in a finite (Galois) field
over integers modulo a prime
• nb. exponentiation takes O((log n)3) operations (easy)
• uses large integers (eg. 1024 bits)
• security due to cost of factoring large numbers
• nb. factorization takes O(e log n log log n) operations (hard)
12. RSA Key Setup
• each user generates a public/private key pair by:
• selecting two large primes at random - p, q
• computing their system modulus N=p.q
• note ø(N)=(p-1)(q-1)
• selecting at random the encryption key e
• where 1<e<ø(N), gcd(e,ø(N))=1
• solve following equation to find decryption key d
• e.d=1 mod ø(N) and 0≤d≤N
• publish their public encryption key: KU={e,N}
• keep secret private decryption key: KR={d,p,q}
13. RSA Use
• to encrypt a message M the sender:
• obtains public key of recipient KU={e,N}
• computes: C=Me mod N, where 0≤M<N
• to decrypt the ciphertext C the owner:
• uses their private key KR={d,p,q}
• computes: M=Cd mod N
• note that the message M must be smaller
than the modulus N (block if needed)
14. Why RSA Works
• because of Euler's Theorem:
• aø(n)mod N = 1
• where gcd(a,N)=1
• in RSA have:
•
•
•
•
N=p.q
ø(N)=(p-1)(q-1)
carefully chosen e & d to be inverses mod ø(N)
hence e.d=1+k.ø(N) for some k
• hence :
Cd = (Me)d = M1+k.ø(N) = M1.(Mø(N))q = M1.(1)q = M1 =
M mod N
15. RSA Example
1.
2.
3.
4.
5.
Select primes: p=17 & q=11
Compute n = pq =17Ă—11=187
Compute ø(n)=(p–1)(q-1)=16×10=160
Select e : gcd(e,160)=1; choose e=7
Determine d: de=1 mod 160 and d < 160
Value is d=23 since 23Ă—7=161= 10Ă—160+1
6. Publish public key KU={7,187}
7. Keep secret private key KR={23,17,11}
16. RSA Example cont
• sample RSA encryption/decryption is:
• given message M = 88 (nb. 88<187)
• encryption:
C = 887 mod 187 = 11
• decryption:
M = 1123 mod 187 = 88
17. Exponentiation
•
•
•
•
can use the Square and Multiply Algorithm
a fast, efficient algorithm for exponentiation
concept is based on repeatedly squaring base
and multiplying in the ones that are needed to
compute the result
• look at binary representation of exponent
• only takes O(log2 n) multiples for number n
• eg. 75 = 74.71 = 3.7 = 10 mod 11
• eg. 3129 = 3128.31 = 5.3 = 4 mod 11
19. RSA Key Generation
• users of RSA must:
• determine two primes at random - p, q
• select either e or d and compute the other
• primes p,q must not be easily derived from
modulus N=p.q
• means must be sufficiently large
• typically guess and use probabilistic test
• exponents e, d are inverses, so use Inverse
algorithm to compute the other
20. RSA Security
• three approaches to attacking RSA:
• brute force key search (infeasible given size of
numbers)
• mathematical attacks (based on difficulty of
computing ø(N), by factoring modulus N)
• timing attacks (on running of decryption)
21. Factoring Problem
• mathematical approach takes 3 forms:
• factor N=p.q, hence find ø(N) and then d
• determine ø(N) directly and find d
• find d directly
• currently believe all equivalent to factoring
• have seen slow improvements over the years
• as of Aug-99 best is 130 decimal digits (512) bit with GNFS
• biggest improvement comes from improved algorithm
• cf “Quadratic Sieve” to “Generalized Number Field Sieve”
• barring dramatic breakthrough 1024+ bit RSA secure
• ensure p, q of similar size and matching other constraints
22. Timing Attacks
• developed in mid-1990’s
• exploit timing variations in operations
• eg. multiplying by small vs large number
• or IF's varying which instructions executed
• infer operand size based on time taken
• RSA exploits time taken in exponentiation
• countermeasures
• use constant exponentiation time
• add random delays
• blind values used in calculations
So far all the cryptosystems discussed have been private/secret/single key (symmetric) systems. All classical, and modern block and stream ciphers are of this form.
Will now discuss the radically different public key systems, in which two keys are used. Anyone knowing the public key can encrypt messages or verify signatures, but cannot decrypt messages or create signatures, counter-intuitive though this may seem. It works by the clever use of number theory problems that are easy one way but hard the other. Note that public key schemes are neither more secure than private key (security depends on the key size for both), nor do they replace private key schemes (they are too slow to do so), rather they complement them.
Stallings Fig 9-1.
The idea of public key schemes, and the first practical scheme, which was for key distribution only, was published in 1977 by Diffie & Hellman. The concept had been previously described in a classified report in 1970 by James Ellis (UK CESG) - and subsequently declassified in 1987. See History of Non-secret Encryption (at CESG). Its interesting to note that they discovered RSA first, then Diffie-Hellman, opposite to the order of public discovery!
Public key schemes utilise problems that are easy (P type) one way but hard (NP type) the other way, eg exponentiation vs logs, multiplication vs factoring. Consider the following analogy using padlocked boxes: traditional schemes involve the sender putting a message in a box and locking it, sending that to the receiver, and somehow securely also sending them the key to unlock the box. The radical advance in public key schemes was to turn this around, the receiver sends an unlocked box to the sender, who puts the message in the box and locks it (easy - and having locked it cannot get at the message), and sends the locked box to the receiver who can unlock it (also easy), having the key. An attacker would have to pick the lock on the box (hard).
Stallings Fig 9-4.
Here see various components of public-key schemes used for both secrecy and authentication. Note that separate key pairs are used for each of these – receiver owns and creates secrecy keys, sender owns and creates authentication keys.
Public key schemes are no more or less secure than private key schemes - in both cases the size of the key determines the security. Note also that you can't compare key sizes - a 64-bit private key scheme has very roughly similar security to a 512-bit RSA - both could be broken given sufficient resources. But with public key schemes at least there's usually a firmer theoretical basis for determining the security since its based on well-known and well studied number theory problems.
RSA is the best known, and by far the most widely used general public key encryption algorithm.
This key setup is done once (rarely) when a user establishes (or replaces) their public key. The exponent e is usually fairly small, just must be relatively prime to ø(N). Need to compute its inverse to find d. It is critically important that the private key KR={d,p,q} is kept secret, since if any part becomes known, the system can be broken. Note that different users will have different moduli N.
Can show that RSA works as a direct consequence of Euler’s Theorem.
Here walk through example using “trivial” sized numbers.
Selecting primes requires the use of primality tests.
Finding d as inverse of e mod ø(n) requires use of Inverse algorithm (see Ch4)
Rather than having to laborious repeatedly multiply, can use the "square and multiply" algorithm with modulo reductions to implement all exponentiations quickly and efficiently (see next).
Both the prime generation and the derivation of a suitable pair of inverse exponents may involve trying a number of alternatives, but theory shows the number is not large.
See Stallings Table 9-3 for progress in factoring.
Best current algorithm is the “Generalized Number Field Sieve” (GNFS), which replaced the earlier “Quadratic Sieve” in mid-1990’s. Do have an even more powerful and faster algorithm - the “Special Number Field Sieve” (SNFS) which currently only works with numbers of a particular form (not RSA like). However expect it may in future be used with all forms. Numbers of size 1024+ bits look reasonable at present, and the factors should be of similar size