The Cryptography Chronicles

The Cryptography Chronicles
4/24/2017 5:55 AM SIA400 The Cryptography Chronicles Explaining the Unexplained: Part One Andy Malone CEO & Founder The Cybercrime Security Forum © 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

Note: Although this is a level 400 session. It is designed to be a training session providing history, development and practical uses of Cryptography and as such if you already consider yourself an expert in cryptography then this session will be 300 Level.

Part One: The Geeky Stuff!
The Purpose & History of Cryptography Types of Cryptographic Algorithms Classical Cryptography Secret Key Cryptography Public-Key Cryptography The Uses of Cryptography Modern Cryptographic Standards A Closer Look at Symmetric Vs Asymmetric Cryptography Inside The Advanced Encryption Standard (Rijndael) Inside The Diffie-Hellman Key Exchange Session Review

In Part 2: Putting Cryptography to Work!
The Controversies With Cryptography Data in Transit Solutions at Work Remote Networking Cryptography – IPSec - SSL Trust Models Public Key Certificates and Certification Authorities PGP Web of Trust Data at Rest Protection Solutions Strengths & Weaknesses Emerging Cryptographic Technologies Theft Resistant Cryptography Bimolecular Cryptography Quantum Cryptography Conclusions!

Let’s Start at the Beginning!
Cryptography Let’s Start at the Beginning!

First: What is Cryptography?
Cryptography is the Means of Transforming Data into a Way that Renders it Unreadable by Anyone Except the Intended Recipient. Secret Writing Steganography Cryptography Substitution Transposition Code Cipher

Why use Cryptography! Authentication: Authorization / Access Control
The process of proving one's identity. (The primary forms of host-to-host authentication on the Internet today are name-based or address-based, both of which are notoriously weak.) Authorization / Access Control Access to an object requires access to the associated crypto keys in many systems (e.g. login) Privacy/confidentiality: Ensuring that no one can read the message except the intended receiver. Integrity: Assuring the receiver that the received message has not been altered in any way from the original. Non-repudiation: A mechanism to prove that the sender really sent this message.

Where to Use Cryptography?
Military Use Defence Against External/Internal Hackers Defence against Industrial Espionage Securing E-commerce Securing Bank Accounts/Electronic Payment Technologies Securing Intellectual Property Avoiding Liability

Next! Learn to Speak like a Crypto Geek!
Plaintext – Message in its Natural Format Readable by an Anyone Ciphertext – Message altered to be Unreadable by Anyone Except the Intended Recipients Key – Sequence that Controls the Operation and Behavior of the Cryptographic Algorithm Keyspace – Total Number of Possible Values of Yeys in a Crypto Algorithm Initialization Vector – Random Values used with Ciphers to Ensure no Patterns are Created during the Encryption Process Cryptosystem – The Combination of Algorithm, Key, and Key Management Functions used to Perform Cryptographic Operations

Cryptography How it all Began…

How it all Began! Ancient Egyptian Atbash
Giovanni Battista Della Porta 1535

Classical Cryptography!
Dates Back to at Least 2000 B.C. Scytale – Spartan method involved wrapping a belt around a rod of a given diameter and length Atbash – Hebrew cipher which mirrored the normal alphabet. As seen in The DaVinci Code Caesar – moves all letters by a given number of letters in the alphabet Vignère – Use of a key and multiple alphabets to hide repeated characters in an encrypted message

Atbash (Substitution Cipher)
An Early Substitution Cipher Designed for the Hebrew Alphabet. Enciphers Plaintext by Inverting the Alphabet. Thus 'A' Becomes 'Z', 'B' Becomes 'Y', and so on Options Include Choosing Fold Points so That the Alphabet Key can be Decided Prior to Inversion. ת ש ר ק צ פ ע ס נ מ ל כ י ט ח ז ו ה ד ג ב א Hebrew Version A B C D E F G H I J K L M N O P Q R S T U V W X Y Z English Version

Julius Caesar’s Cipher
B C D E F G H I J K L M N O P Q R S T U V W X Y Z Early Example of a Substitution Cipher Invented by Julius Caesar Each Letter is Replaced by the Letter Three Positions Further Down the Alphabet Thus: MICROSOFT TECHED Becomes: PLFURVRIW WHFKHG

Julius Caesar Cipher Mathematical version!
Mathematically, map letters to numbers: Then the general Caesar cipher is: c = EK(p) = (p + k) mod 26 p = DK(c) = (c – k) mod 26 Can be generalized to any alphabet. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 P = Plain text C= Cipher Text K= Key Space EK = Encryption Key DK= Decryption Key

Problems of Caesar Cipher
Uses a Simple Key space: {0, 1, ..., 25} Vulnerable to Brute-Force Attacks Pattern Matching Attack E.g., Break Ciphertext "ZH DUI DOO JHHNV” Easy to Recognize When have the Plaintext or Key What if the Plaintext is in Arabic or Mandarin?

A Monoalphabetic Substitution Cipher
Ah but what Happens when you Shuffle the Letters and Map each Plaintext Letter to a Random Ciphertext Letter? A B C D E F G H I J K L M N O P Q R S T U V W X Y Z I H O P E Y U N J T C D W Z F X V Q

Monoalphabetic Substitution Cipher
With this Method we have a Total of 26! = 4 x 1026 keys With so Many keys, it’s Possible to Secure Against Brute-Force Attack, But Not Against some Cryptanalytic Attacks Problem with Substitution crypto is that they are all based on Language Characteristics.

Monoalphabetic Brute force Attack
Ciphertext = IGKYGXOYOTYKIAXK Decrypt(IGKYGXOYOTYKIAXK, 1) = HFJXFWNXNSXJHZWJ Decrypt(IGKYGXOYOTYKIAXK, 2) = GEIWEVMWMRWIGYVI Decrypt(IGKYGXOYOTYKIAXK, 3) = FDHVDULVLQVHFXUH Decrypt(IGKYGXOYOTYKIAXK, 4) = ECGUCTKUKPUGEWTG Decrypt(IGKYGXOYOTYKIAXK, 5) = DBFTBSJTJOTFDVSF Decrypt(IGKYGXOYOTYKIAXK, 6) = CAESARISINSECURE

Take a Look at this Example!
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

Look a Little Closer! UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

And Again… UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

And So On… UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

English Language / Frequency Analysis
Human Languages are Not Random Letters are Not Equally or Frequently Used. In English, the Most Common Letters are E,T, R, N, I, O, A, S Other Letters like Z, J, K, Q, X are Rarely Used. Tables Exist of Single, Double & Triple Letter Frequencies which are Available for Various Languages

Thus the Cryptanalysis of Our Problem Reveals…
First Count Relative Letter Frequencies We then Guess that {P, Z} = {E,T} Of double letters, ZW has highest frequency, so guess ZW = Th and thus ZWP = “The” Then a Little Trial & Error Reveals: P H 5.83 F B C Z D 5.00 W 3.33 G K S E 5.00 Q Y L U V 4.17 T I N O X 4.17 A J R M

Now We Know The Key! UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ Z=T W=H U=I S=A O=S P=E

Cracking the Code Now Reveals!
Decrypted Text Circa 1971 “It was disclosed yesterday that several informal but direct contacts have been made with political representatives of the Viet Cong in Moscow”

Vigenere Cipher Designed by Bellaso in 1553
Uses a Series of Different Caesar Ciphers based on the Letters of a Keyword. As Seen in The Da Vinci Code Uses a Simple Form of Polyalphabetic Substitution, E.g. Use a different Caesar Cipher per Letter = MORESECURETHANCAESAR (Ciphertext) + SECRETSECRETSECRETSE (Key) = FTUWXYVZUWYBTSFSJMTW M (13) + A (19) = F (6) mod 26 O (15) + E (5) = T (20) mod 26 Giovanni Battista Bellaso 1535

Cryptography The Modern Age Begins…

Shhh Someone Might Hear You…
1871 1837 1903 1942 1975 – Present Day 1946 – Present Day

The Next Step: Mechanical Era!
In The Industrial Age, Cryptography Moved from Manual to one Performed by Machines. The Invention of Cipher Disks and Rotors Allowed for the Creation of Much More Complex Algorithms. Enigma used a Series of Rotating Cylinders.

The German “Enigma” Machine
Widely Used in World War II. Implemented a Polyalphabetic Substitution Cipher of period K. With 3 cylinders, K = 263 =17,576. With 5 cylinders, K = 265 =12 x 106. What Would be the Key? If the Adversary has a Machine If the Adversary Doesn’t have a Machine Try The Enigma Simulator For Yourself:

German Secret Setting Sheets
Stolen Code Books Retrieved by the Allies Provided Details of Todays Date Which Rotors to Use (There Were Ten Rotors) Ring Setting For that Day Plug Board Setting for that Day

The Enigma Rotor Settings

Using Strong Encryption
Confusion Changes Key Values each Time Around Performed through Substitution Complicates Plaintext/key Relationship Diffusion Change location of Plaintext in Ciphertext Done through a Transposition Process Strong Encryption Uses a Combination of Both These Attributes to Attain a Sufficiently Complex Algorithm.

Modern Cryptographic Algorithms
Symmetric / Secret Key Cryptography Use a Single Key for Both Encryption and Decryption Asymmetric / Public Key Cryptography Uses One Key for Encryption and Another for Decryption Hash Functions Uses a Mathematical Transformation to Irreversibly “Encrypt" Information

Current Cryptographic Standards
Encryption (Privacy & Confidentiality) Symmetric Key Algorithm Key Management ISA/KMP IKE SKIP Photuris Diffe-Helman ElGamal Discrete Log DSA ECC Public Key Infrastructure (PKI) PXIX SPKI SDS PGP DNSEC Stream Cipher RC4 SEAL WAKE A5 PKZIP Digital Signatures Authentication / Non Repudiation Message Integrity Public Key Asymmetric Algorithm Message Digest Hash Algorithm MD2 MD5 SHA SHA-1 SHA-2 SHA-3 (Pending) Ripe-MD160 Block Cipher AES, DES, 3DES RC2,RC5,RC6 Blowfish, Twofish, Serpent Mars, Cast, Idea Factoring RSA LUC

Symmetric Key Cryptography
Fast Solution to Encrypt and Decrypt, Suitable for Large Volumes of Data Uses a Single Key Solution A well Designed Cipher is only Subject to Brute Force Attack; Thus Key Strength is Directly Related to the Key Length Great for: Data at Rest DAR Solutions (EFS, TrueCrypt, Bitlocker, Databases, Credit Cards etc. Both Sender & Receiver Must Know Key! Problem - How & Where Do you Distribute the Keys? (See Part 2)

Symmetric key Cipher Types
Categorized as being either Stream Ciphers or Block Ciphers. Stream Ciphers Operate on a Single bit Byte at a Time and Implement some form of Feedback Mechanism so that the Key Constantly Changes. Block Ciphers are so-called Because the scheme encrypts one Block of Data at a Time using the same Key on Each Block.

Symmetric Cryptography - Examples
DES - 56 bit key length, designed by IBM 1975 > Adopted by National Security Agency (NSA) 3DES - Effective key length 112 bits Rijndael - AES (Advanced Encryption Standard) – 128, 192, 256 bit key length Blowfish bits, optimized for fast operation on 32-bit microprocessors IDEA bits, patented (requires a license for commercial use)

A Closer Look at AES (Rijndael):
Winners of the NIST 2001 AES Design Competition Joan Daemen and Vincent Rijmen

A Closer Look at AES (Rijndael):
Rijndael was the 2001 NIST Winner in a competition to Replace Triple (3)DES Rijndael is a Block Cipher Designed by Joan Daemen and Vincent Rijmen, Based in Belgium AES Uses a Variable Block Length and Key Length; Including 128, 192, or 256 bits and Blocks of Length 128, 192, or 256 bits. FIPS 197 describes a 128-bit block cipher employing a 128-, 192-, or 256-bit key and became the formal Adoption as the AES Standard in December 2001. Free for Public Use!

To Understand AES You Have to Think BIG!
Firstly With AES You’ve got to Think BIG! In Terms of Numbers 1 in 261 Odds of Winning the Lottery and Being Hit by Lightning on the Same Day 292 Atoms in the Average Human Body 2128 Possible keys in a 128-bit Key 2170 Atoms in the Planet 2190 Atoms in the Sun 2233 Atoms in the Galaxy 2256 Possible Keys in a 256-Bit Key = × 1077 (Whoa That’s BIG!

Then Start to Think in Hex !
Decimal Hex 1 11 B 21 15 2 12 C 22 16 3 13 D 23 17 4 14 E 24 18 5 F 25 19 6 10 26 1A 7 27 1B 8 28 1C 9 29 1D A 20 30 1E 31 or = 1F 32 or = 20 And so on…

Understanding AES: Starting with a Random Number which is Converted into a State Array The AES Process then Uses a Complex System of 4 Functions over 10 Rounds Transformations (and then Inverses) SubBytes ShiftRows MixColumns AddRoundKey Final Stage: Key Expansion

Symmetric Encryption: AES
Animation Symmetric Encryption: AES The AES Inspector Click Me

Symmetric Encryption: AES
Animation Symmetric Encryption: AES With Special Thanks to Enrique Zabala Click Me

Asymmetric (Public Key) Cryptography
Encryption/Decryption Digital Signatures Key Exchange Secure Communications

Normally Classified into 3 Categories: Encryption/Decryption: Provide Secrecy Digital Signatures: Provide Authentication Key Exchange: Of Session Keys Normally Uses 2 Keys: Public & Private Most Commonly Used to Secure Separate Endpoints Not Ideal for Use in One Location Examples to Follow in Part 2…

Many Mathematicians argue that Large Mathematical Operations Make it 1000x Less Efficient than Symmetric Cryptography Public Keys are Freely Available!) Scales Better since only a Single Key Pair needed Per Individual Provides Both Authentication and Nonrepudiation Examples Include: Diffie-Hellman, RSA, El Gamal, ECC Etc.

Some Common Uses: Web Browsers (SSL) IPSec Remote Networking Solutions (RAS) Virtual Private Networks (VPN) Digital Signatures Securing Wireless Communications Secure Shell (SSH) Multi Factor Authentication Secure FTP Secure

A Closer Look at: Diffie Hellman
Considered to be The Fathers of Public Key Cryptography Whitfield Diffie and Martin Hellman

Alice’s Secret Integer
Diffie Hellman (1976) Bob’s Network Alice’s Network Formulae 3 Formulae 1 Prime Number Alice’s Secret Integer Base Number A Prime Number Bob’s Secret Integer Base Number B Bob’s Public Value Y Alice's Public Value X Formulae 4 Formulae 2 Shared Secret Z Alice’s Value X Alice's Secret Integer Prime Number Bob’s Value Y Alice's Secret Integer Prime Number Same Value Secret Key Secret Key

Diffie Hellman: Simple but Brilliant!
+ F(x) Y X One Way Function Given X, It’s easy to Compute f(x) But Given f(x) It’s Hard to Compute X X

Diffie-Hellman Key Exchange (1)
First Understand the basics of Modular Arithmetic (Clock or Mod P) Brilliantly Simple: Assumes Same Mathematical result can be computed from different sets of inputs E.g. 2 x 3 x 5 = 30 or 2 x 15 = 30 or 3 x 5 = 15 x 2 = 30 Alice & Bob are Two Strangers use Two Separate Numbers which when Calculated form the same result (Shared Secret) Modular Arithmetic: All Integers, Natural Numbers Map to a small set of Numbers which range Between 0 to N-1, where N is a number that you choose (Small or Large)

Alice & Bob select Value of N They also select a Route or R which is added to the Number N+R = (Shared Secret) Alice Now Picks a Very Large Number, Difficult to Remember. This is Alice's Secret Key or A Once selected Alice Raises RA No Matter how large the number is A Will Eventually Map into a Range Between 0 & N -1 = X Tools Exist to Calculate X From A to Raise RA(A) and find X is easy. This is called a One way function. Thus A to X is easy but X to A is Very difficult.

If Alice sends Bob X (Public Key). Bob would find it very difficult to find A from X (Alice’s Secret Key) and so would an Evil hacker (Marcus ) Thus Giving Bob X preserves A as a secret. Bob does the Same on his part (B=Secret Number) Raises RB (Y) and Computes a Number called Y and then Communicate it to Alice. Thus Alice cannot reverse engineer or Change B Bob’s private Number) from Y ?

To Review: Alice has a private Key: A Bob has a private Key: B + X (Alice’s Public Key) Bobs Public Key Y Raise RAxB = Z (same as 2x3x5 etc) There are Multiple ways RA(X) A = X Now Raise XB Can Bob Do the Same “Yes” because he has X Bob Raises XB = Z) Alice Takes RB (Y) Results then do the Reverse YA (Z) Alice Raises Y (Bob’s public Key) to YA (her secret ) Finally Bob Calculates to the result Z (Shared Secret) Now Only A or B (Both) can calculate Z (Shared Secret) Even if a Third Party (Marcus) Discovers A or B He will be Unable to Calculate Z

One-Way Hashing Functions
Fast Mathematical Function that Generates a fixed Length result Regardless of the Amount of Data you Pass Through it Easy to compute the hash value for any given message Infeasible to generate a message that has a given hash or Modify a Message without Changing the Hash In Theory you Cannot find Two Sets of Data that Produce the Same Fixed-length Result. If you do this is called a collision.

Hashing: One Way Encryption
Fox Hash Function DFCD35454 BBEA788A 751A696C 24D97009 CA992D17 The Red Fox runs Across the ice. Hash Function 52ED879E 70F71D92 6EB E03CE4 CA6945D3 The Red Fox walks Across the ice. Hash Function C7FB0 A B94AE214 26EB3CEA Note the significant change in the hash sum for minor changes in the input. Note that the hash sum is the same length for varying input sizes. This is extremely useful.

Hashing Function Examples
Unix crypt() function, based on DES, 56 bits (not secure) MD5 (Message Digest 5) bit hash (deprecated) Still No Feasible Method to Create a Document which has a Given MD5 Digest SHA1 (Secure Hash Algorithm) bits No collisions have yet been found in SHA-1, but in 2005 It Was Compromised and will be phased out in the next few years. See for details. No Successful Attacks have yet been Reported on SHA-2 SHA-3, is Currently under Development NIST Hash Function Competition is Scheduled to End This Year!!

Animation Useful Crypto Tools Free & Available

OWASP: Some Cryptographic Storage Top Tips!
Only store sensitive data that you need E.g. eCommerce businesses utilize third party payment providers to store credit card information for recurring billing. Only use strong cryptographic algorithms Only use Approved public algorithms such as AES, RSA public key cryptography, and SHA-256 or better for hashing. Do not use Weak Algorithms such as MD5 or SHA1 Ensure that Random Numbers are Cryptographically Strong Ensure that all random numbers, file names, GUIDs,& strings are generated in a cryptographically strong fashion. Also ensure that random algorithms are seeded with sufficient entropy Only use Widely Accepted Implementations of Cryptographic Algorithms Do not implement an existing cryptographic algorithm on your own, no matter how easy it appears. Instead. If possible, use an implementation that is FIPS certified Prefer Authenticated Encryption Modes Use cryptographic cipher modes that offer both confidentiality and authenticity. Recommended modes include counter with CBC-MAC (CCM) mode and Galois/counter mode (GCM

OWASP: Cryptographic Storage Top Tips!
Ensure that the cryptographic protection remains secure even if access controls fail Access controls (usernames, passwords, privileges, etc.) are one layer of protection. Storage encryption should add an additional layer of protection Ensure that any secret key is protected from unauthorized access Define a key lifecycle Normally Key’s Should change every Three years Store unencrypted keys away from the encrypted data Use independent keys when multiple keys are required Protect keys in a key vault Document concrete procedures to handle a key compromise Open Web Application Security Project

Finally…Now You Are a True Geek!
The Purpose & History of Cryptography Types of Cryptographic Algorithms Classical Cryptography Secret Key Cryptography Public-Key Cryptography The Uses of Cryptography Modern Cryptographic Standards A Closer Look at Symmetric Vs Asymmetric Cryptography Inside The Advanced Encryption Standard (Rijndael) Inside The Diffie-Hellman Key Exchange Session Review

In Part 2: Putting Cryptography to Work!
The Controversies With Cryptography Data in Transit Solutions at Work Remote Networking Cryptography – IPSec - SSL Trust Models Public Key Certificates and Certification Authorities PGP Web of Trust Data at Rest Protection Solutions Strengths & Weaknesses Emerging Cryptographic Technologies Theft Resistant Cryptography Bimolecular Cryptography Quantum Cryptography Conclusions!

Related Content SIA400:The Cryptography Chronicles: Explaining the Unexplained Part 1 SIA401:The Cryptography Chronicles: Explaining the Unexplained Part 2 SIA301 Lock, Stock & Two Smoking Smart Devices! SIA203 Cyber Threats Security Panel Find Me Later At…Ask The Experts

Track Resources www.microsoft.com/twc www.microsoft.com/security

Complete an evaluation on CommNet and enter to win!
Required Slide Complete an evaluation on CommNet and enter to win!

MS Tag Scan the Tag to evaluate this session now on myTechEd Mobile

Thanks For Attending :-)
4/24/2017 5:55 AM Thanks For Attending :-) Andy Malone CEO & Founder The Cybercrime Security Forum Follow © 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

4/24/2017 5:55 AM © 2012 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION. © 2009 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

The Cryptography Chronicles

Similar presentations

Presentation on theme: "The Cryptography Chronicles"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

The Cryptography Chronicles

Similar presentations

Presentation on theme: "The Cryptography Chronicles"— Presentation transcript:

Similar presentations

About project

Feedback