Public Key Cryptography in Depth: Rivest Shamir Adleman (RSA), Elliptic Curves and Key Exchange

AdvancedFree5 modules · 15 lessons · ~2 min

About this course

A deep, practitioner-level course on how public key cryptography actually works: constructing and verifying a Rivest Shamir Adleman (RSA) key pair by hand, why padding schemes are mandatory rather than optional, how elliptic curve cryptography reaches equivalent security with far smaller keys, and how Diffie-Hellman key exchange delivers forward secrecy. You will finish able to evaluate a real public key deployment against the parameter, randomness and authentication failure modes that account for most real-world breaks.

What you'll learn

Key Pairs and Trust

The Key Distribution Problem and How Public Key Cryptography Solves It
Confidentiality Keys and Signing Keys: Why Real Systems Keep Them Separate
Establishing Trust in a Public Key: Why a Bare Key Is Not Enough

Rivest Shamir Adleman (RSA) Construction

Building an RSA Key Pair by Hand: A Worked Example
Why RSA Needs Padding: OAEP, PSS and the Trouble with Textbook RSA
RSA Failure Modes: Small Exponents, Shared Moduli and Reused Parameters

Elliptic Curve Cryptography

Elliptic Curves as Groups: The Structure Behind the Name
Why Smaller Keys Suffice: Strength Per Bit and Curve Choice in Practice
Elliptic Curve Diffie-Hellman: A Worked Key Exchange

01Key Pairs and Trust3 lessons

The Key Distribution Problem and How Public Key Cryptography Solves It
Confidentiality Keys and Signing Keys: Why Real Systems Keep Them Separate
Establishing Trust in a Public Key: Why a Bare Key Is Not Enough

02Rivest Shamir Adleman (RSA) Construction3 lessons

Common questions

How much does Safeguard Academy cost?

Nothing. Every course, exam, and certificate on the catalog is free — including retakes. All you need is a free Safeguard account.

What are the prerequisites?

None. The flagship course, Safeguard Certified Practitioner, is a beginner-level course — basic familiarity with how software is built helps, but every exam question is answerable from the lessons themselves.

Diffie-Hellman and Forward Secrecy

The Diffie-Hellman Key Exchange: A Worked Example Over Small Numbers
Forward Secrecy: Why Ephemeral Keys Change What a Later Compromise Costs
Unauthenticated Diffie-Hellman and the Machine-in-the-Middle Problem

Hybrid Encryption and Practical Failure Modes

Hybrid Encryption: Why Every Real System Combines Both Families
A Key Size Equivalence Table, and How to Read It Honestly
The Practical Failure Modes Checklist: Randomness, Parameters, Exponents and Authentication

Building an RSA Key Pair by Hand: A Worked Example

Why RSA Needs Padding: OAEP, PSS and the Trouble with Textbook RSA

RSA Failure Modes: Small Exponents, Shared Moduli and Reused Parameters

03Elliptic Curve Cryptography3 lessons

Elliptic Curves as Groups: The Structure Behind the Name
Why Smaller Keys Suffice: Strength Per Bit and Curve Choice in Practice
Elliptic Curve Diffie-Hellman: A Worked Key Exchange

04Diffie-Hellman and Forward Secrecy3 lessons

The Diffie-Hellman Key Exchange: A Worked Example Over Small Numbers
Forward Secrecy: Why Ephemeral Keys Change What a Later Compromise Costs
Unauthenticated Diffie-Hellman and the Machine-in-the-Middle Problem

05Hybrid Encryption and Practical Failure Modes3 lessons

Hybrid Encryption: Why Every Real System Combines Both Families
A Key Size Equivalence Table, and How to Read It Honestly
The Practical Failure Modes Checklist: Randomness, Parameters, Exponents and Authentication2 min

What happens if I fail the exam?

You can retake it after a 24-hour cooldown, as many times as you need. Retakes are free, and each attempt draws a fresh random set of questions.

How long is a certificate valid?

The Safeguard Certified Practitioner credential is valid for 24 months from issue. The expiry date is printed on the certificate and shown live on its public verification page. Renewing means passing the current exam again.