The Foundation: Two Different Approaches to Public Key Cryptography
RSA and ECDSA are two different algorithms for creating public key cryptography systems. Both are widely used in SSL/TLS certificates, but they work differently, have different performance characteristics, and different levels of security. Understanding the differences helps you choose the right algorithm for your use case and understand the implications of different certificate types.
RSA (Rivest-Shamir-Adleman) is older, more widely supported, and based on the difficulty of factoring large numbers. ECDSA (Elliptic Curve Digital Signature Algorithm) is newer, more efficient, and based on the properties of elliptic curves. Neither is fundamentally "better"—they represent different trade-offs.
RSA: The Traditional Approach
How RSA Works: RSA security depends on the difficulty of factoring the product of two large prime numbers. To create an RSA key pair:
- Choose two large prime numbers (p and q), each hundreds of digits long
- Multiply them together (N = p × q)
- Create a public key and private key from N and other values
- Keep the private key secret; share the public key
Factoring large numbers is computationally difficult. While the public key (N) is known, figuring out the original primes (p and q) is nearly impossible without the private key.
Key Sizes: RSA security depends on key size:
- 1024-bit: Deprecated, no longer considered secure
- 2048-bit: Currently acceptable, widely used
- 3072-bit: Very secure, rarely used
- 4096-bit: Extremely secure, rarely needed
- 8192-bit: Impractical for most uses
A 2048-bit RSA key provides approximately 112 bits of security strength.
Advantages:
- Widely supported (every browser, server, and system supports RSA)
- Standardized since the 1990s
- Well-understood, extensively studied
- Can be used for both encryption and signing
- Large ecosystem of tools
Disadvantages:
- Larger key sizes required for equivalent security
- Slower operations (key generation, signing, verification)
- Larger certificates and signatures
- More power consumption
- Larger network overhead
ECDSA: The Modern Approach
How ECDSA Works: ECDSA (Elliptic Curve Digital Signature Algorithm) is based on the properties of elliptic curves. Instead of factoring numbers, it exploits the difficulty of solving the discrete logarithm problem on elliptic curves.
Elliptic curves are equations of the form: y² = x³ + ax + b
Points on the curve can be added together following special mathematical rules. The security comes from the difficulty of finding, given a point P and a multiple of P (say, Q = kP), what the multiplier k is.
Key Sizes and Security: ECDSA provides equivalent security with much smaller key sizes:
- P-256 (256-bit): Equivalent to ~3072-bit RSA (128-bit security)
- P-384 (384-bit): Equivalent to ~7680-bit RSA (192-bit security)
- P-521 (521-bit): Equivalent to ~15,360-bit RSA (256-bit security)
A 256-bit ECDSA key provides equivalent security to a 3072-bit RSA key.
Advantages:
- Smaller key sizes for equivalent security
- Faster signing and verification
- Smaller certificates and signatures
- Lower power consumption
- Better for constrained devices
- Smaller network overhead
Disadvantages:
- Less widely supported than RSA (though support is growing rapidly)
- More complex mathematics (harder to implement correctly)
- Shorter history (harder to audit completely)
- Patent concerns in some jurisdictions (though most essential patents have expired)
- Limited to digital signatures (not encryption)
Comparing Key Strengths
| RSA Key Size | Equivalent ECDSA Curve | Security Strength |
|---|---|---|
| 2048-bit | P-224 (not recommended) | 112 bits |
| 3072-bit | P-256 | 128 bits |
| 7680-bit | P-384 | 192 bits |
| 15,360-bit | P-521 | 256 bits |
Notice the dramatic difference: 256-bit ECDSA provides the same security as 3072-bit RSA.
Performance Comparison
Key Generation:
- RSA 2048-bit: ~5-10 seconds (moderate)
- ECDSA P-256: ~100 milliseconds (extremely fast)
Signing:
- RSA 2048-bit: ~5 milliseconds
- ECDSA P-256: ~1-2 milliseconds (2-5x faster)
Verification:
- RSA 2048-bit: ~1 millisecond
- ECDSA P-256: ~1-2 milliseconds (similar)
File Size:
- RSA 2048-bit certificate: ~1200 bytes
- ECDSA P-256 certificate: ~700 bytes
ECDSA wins decisively on performance and size, particularly for key generation.
Real-World Usage
HTTPS/TLS Certificates: Modern web servers use ECDSA certificates. Let's Encrypt defaults to ECDSA P-256 for new certificates. However, many production servers still use RSA 2048-bit due to legacy support requirements.
Certificate Compatibility:
- RSA: Supported by all browsers, all servers, all clients
- ECDSA: Supported by all modern browsers and servers (iOS 4+, Chrome 1+, Firefox 12+, Edge 12+, etc.)
For most modern web use, ECDSA is sufficiently supported. However, if you need to support very old clients (IE 8, Android 2, etc.), RSA is necessary.
Hybrid Approach: Dual Certificates
Many production systems use both RSA and ECDSA certificates simultaneously:
# Server configuration (nginx example)
server {
ssl_certificate /path/to/ecdsa_cert.crt;
ssl_certificate_key /path/to/ecdsa_key.key;
ssl_certificate /path/to/rsa_cert.crt backup;
ssl_certificate_key /path/to/rsa_key.key backup;
}
Clients use ECDSA if they support it (faster, smaller), and fall back to RSA if needed. This provides both performance benefits and maximum compatibility.
Creating ECDSA and RSA Certificates
Generating ECDSA Keys:
# Generate ECDSA private key
openssl ecparam -genkey -name prime256v1 -out private.key
# Generate CSR (Certificate Signing Request)
openssl req -new -key private.key -out request.csr
# View the private key type
openssl ec -in private.key -text -noout
Generating RSA Keys:
# Generate RSA private key (2048-bit)
openssl genrsa -out private.key 2048
# Generate CSR
openssl req -new -key private.key -out request.csr
# For 4096-bit (more secure but slower)
openssl genrsa -out private.key 4096
# View the private key type
openssl rsa -in private.key -text -noout
Checking a Certificate's Algorithm:
# View certificate details
openssl x509 -in certificate.crt -text -noout
# Look for "Public Key Algorithm" in output:
# "Public Key Algorithm: rsaEncryption" (RSA)
# "Public Key Algorithm: id-ecPublicKey" (ECDSA)
Security Considerations
RSA Vulnerabilities: No known practical breaks in RSA's core mathematics, but:
- 1024-bit RSA was broken (don't use)
- Performance impacts from large key sizes
- Side-channel attacks possible with poor implementation
ECDSA Vulnerabilities:
- Requires high-quality random number generation for key generation
- Some elliptic curves have been questioned (P-1305 concerns about NSA involvement)
- Safer curves: P-256, P-384, P-521 are considered secure
- Controversial curve: P-1305 (suspected NSA influence)
Future-Proofing: For long-term security:
- Use 4096-bit RSA, or
- Use ECDSA P-384 or P-521
RSA 2048-bit and ECDSA P-256 are currently acceptable but might be considered weak in 15-20 years.
Government and Industry Standards
NIST Recommendations:
- Recommends transitioning from RSA to ECDSA
- RSA 2048 acceptable until 2030
- ECDSA P-256 recommended for new applications
Federal Standard: The NSA's Commercial National Security Algorithm Suite recommends ECDSA (specifically, P-384).
PCI DSS: Payment card security standard requires RSA 2048 or better, or ECDSA P-256 or better.
Which Should You Use?
Choose RSA if:
- You need maximum compatibility with very old systems
- You need non-signing cryptographic operations
- Your infrastructure is already RSA-heavy
Choose ECDSA if:
- You're building new infrastructure
- Performance and efficiency matter
- You can verify ECDSA support in your client base
- You want smaller certificates and faster operations
Best Practice: For new deployments, use ECDSA P-256 or P-384. If you need to support older clients, use dual certificates (both ECDSA and RSA). Avoid RSA 1024-bit entirely. RSA 2048-bit is still acceptable but increasingly considered legacy.
Transitioning from RSA to ECDSA
Step 1: Verify Client Support: Check your analytics to see if your users support ECDSA. If 99%+ use modern browsers, ECDSA-only is feasible.
Step 2: Deploy ECDSA Certificate: Obtain ECDSA certificate from your CA (Let's Encrypt supports ECDSA).
Step 3: Monitor for Issues: Deploy ECDSA and monitor error rates. If no increase in connection failures, you're good.
Step 4: Optional - Use Dual Certificates: For maximum compatibility, use both ECDSA (preferred) and RSA (fallback).
Step 5: Deprecate RSA: Once confident in ECDSA support, optionally remove RSA certificates.
Conclusion
ECDSA and RSA are fundamentally different approaches to public key cryptography, each with different strengths and weaknesses. RSA is more widely supported and has a longer history, but ECDSA offers superior performance, smaller key sizes, and equivalent or better security. For new deployments, ECDSA P-256 or P-384 should be the default choice. For systems requiring maximum compatibility, dual certificates using both ECDSA and RSA provide the best of both worlds. Understanding these differences enables you to make informed decisions about certificate algorithms that balance security, performance, and compatibility for your specific needs.
