Public key cryptography uses two keys - a public key that can encrypt messages but not decrypt them, and a private key that can decrypt messages but not encrypt them. The RSA algorithm is a commonly used public key cryptosystem. It works by having users generate a public/private key pair using large prime numbers, then messages can be encrypted with the public key and decrypted with the private key. The security of RSA relies on the difficulty of factoring large numbers.
Today in modern era of internet we share some sensitive data to information transmission. but need to ensure security. So we focus on Cryptography modern technique for secure transmission of information over network.
What is Steganography and its types, steps of steganography, methods of steganography, text steganography, image steganography, audio steganography, video steganography, steganography software, applications of steganography
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
Today in modern era of internet we share some sensitive data to information transmission. but need to ensure security. So we focus on Cryptography modern technique for secure transmission of information over network.
What is Steganography and its types, steps of steganography, methods of steganography, text steganography, image steganography, audio steganography, video steganography, steganography software, applications of steganography
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
In cryptography, a one-time pad (OTP) is an encryption technique that cannot be cracked if used correctly. In this technique, a plaintext is paired with a random ...
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".
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
For a college course -- CNIT 141: Cryptography for Computer Networks, at City College San Francisco
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
Instructor: Sam Bowne
More info: https://samsclass.info/141/141_S19.shtml
This presentation contains the contents pertaining to the undergraduate course on Cryptography and Network Security (UITC203) at Sri Ramakrishna Institute of Technology. This covers the Elliptic Curve Cryptography and the basis of elliptic curve arithmetics.
In cryptography, a one-time pad (OTP) is an encryption technique that cannot be cracked if used correctly. In this technique, a plaintext is paired with a random ...
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".
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
For a college course -- CNIT 141: Cryptography for Computer Networks, at City College San Francisco
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
Instructor: Sam Bowne
More info: https://samsclass.info/141/141_S19.shtml
This presentation contains the contents pertaining to the undergraduate course on Cryptography and Network Security (UITC203) at Sri Ramakrishna Institute of Technology. This covers the Elliptic Curve Cryptography and the basis of elliptic curve arithmetics.
Public Key Cryptography and RSA algorithmIndra97065
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.
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
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
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A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
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UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
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
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
UiPath Test Automation using UiPath Test Suite series, part 3
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. Select primes: p=17 & q=11
2. Compute n = pq =17×11=187
3. Compute ø(n)=(p–1)(q-1)=16×10=160
4. Select e : gcd(e,160)=1; choose e=7
5. Determine d: de=1 mod 160 and d < 160
Value is d=23 since 23×7=161= 10×160+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
23. Summary
• have considered:
• principles of public-key cryptography
• RSA algorithm, implementation, security
Editor's Notes
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 &quot;square and multiply&quot; 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