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K-MOSAIC Size Quick Reference

Quick lookup table for kMOSAIC cryptographic component sizes.

At a Glance

MOS-128:  823 KB key  |  5.7 KB ciphertext  |  140 B signature
MOS-256:  3.3 MB key  | 10.5 KB ciphertext  |  140 B signature

Complete Size Table

MOS-128 (128-bit Security)

Component Size Range Typical Use
Public Key 823.6 KB 820-830 KB Public key exchange, certificate storage
Secret Key ~100 KB - Local storage only
Ciphertext 5.7 KB 5.6-6.0 KB Encrypted messages, key encapsulation
Signature 140 B Always 140 B Digital signatures, authentication
Binding Hash 32 B Always 32 B Internal (part of public key)

MOS-256 (256-bit Security)

Component Size Range Typical Use
Public Key 3.33 MB 3.3-3.4 MB Public key exchange, certificate storage
Secret Key ~400 KB - Local storage only
Ciphertext 10.5 KB 10.0-11.0 KB Encrypted messages, key encapsulation
Signature 140 B Always 140 B Digital signatures, authentication
Binding Hash 32 B Always 32 B Internal (part of public key)

Classical Cryptography (Reference)

Algorithm Public Key Ciphertext Signature Notes
X25519 32 B 32 B - ECDH key exchange
Ed25519 32 B - 64 B Digital signatures
kMOSAIC (MOS-128) 25,738x 178x 2.2x Larger due to post-quantum security

Size Formula

MOS-128

Public Key ≈ (384 × 512 × 4) + 55,000 ≈ 823 KB
           = SLSS(786 KB) + TDD(55 KB) + overhead(~10 KB)

Ciphertext ≈ 1,500 + 1,500 + 2,300 ≈ 5.7 KB
           = SLSS(c1) + TDD(c2) + EGRW(c3) + NIZK proof

Signature = 32 + 32 + 64 + 12 = 140 B
          = commitment + challenge + response + headers

MOS-256

Public Key ≈ (768 × 1024 × 4) + 186,000 ≈ 3.33 MB
           = SLSS(3.1 MB) + TDD(186 KB) + overhead(~20 KB)

Ciphertext ≈ 2,500 + 3,500 + 4,500 ≈ 10.5 KB
           = SLSS(c1) + TDD(c2) + EGRW(c3) + NIZK proof

Signature = 32 + 32 + 64 + 12 = 140 B
          = commitment + challenge + response + headers (same as MOS-128)

Storage Requirements

Per User

Security Level Public Key Secret Key Total
MOS-128 824 KB 100 KB ~1 MB
MOS-256 3.3 MB 400 KB ~3.7 MB
Classical 32 B 32 B ~64 B

For 1 Million Users

Security Level Public Keys Total
MOS-128 824 GB ~825 GB
MOS-256 3.3 TB ~3.3 TB
Classical 32 GB ~32 GB

Network Transmission

Typical packet sizes for different operations:

Key Exchange

Operation Size Notes
Send public key (MOS-128) 824 KB One-time per peer
Send public key (MOS-256) 3.3 MB One-time per peer
TLS certificate chain 2-10 KB Typical modern certificate

Message Authentication

Operation Size Notes
Sign + Signature Original + 140 B Attached to messages
Verify operation 140 B input Constant time

Encryption

Operation Size Notes
Encapsulate (MOS-128) 5.7 KB Ephemeral ciphertext
Encapsulate (MOS-256) 10.5 KB Ephemeral ciphertext
Typical AES message 1-100 KB Application dependent

Bandwidth Impact

For Public Key Infrastructure

Scenario MOS-128 MOS-256 Classical Impact
Upload new public key 824 KB 3.3 MB 32 B +25,000x
Download peer's key 824 KB 3.3 MB 32 B +25,000x
Sync key directory (1M keys) 825 GB 3.3 TB 32 GB +25,000x

For Message Signing

Scenario MOS-128 MOS-256 Classical Impact
Sign message Negligible Negligible Negligible 1x
Send signed message Msg + 140 B Msg + 140 B Msg + 64 B +2.2x
Verify signature Negligible Negligible Negligible 1x

Performance Characteristics

Generation Speed

Operation Time Security Level
Generate public key 1-10 ms MOS-128
Generate public key 10-50 ms MOS-256
Generate signature 1-5 ms Both

Validation Speed

Operation Time Security Level
Verify signature 0.5-2 ms Both
Verify ciphertext 5-20 ms Both

Practical Implications

When Size Matters

✓ Use Cases Favoring Classical:

  • IoT devices with limited storage
  • Resource-constrained embedded systems
  • High-frequency transaction systems
  • Bandwidth-limited networks

✓ Use Cases Favoring kMOSAIC:

  • Long-term data protection (harvest-now-decrypt-later attacks)
  • Government/military communications
  • Financial systems with long-term security requirements
  • Systems expecting quantum computing threats

Optimization Strategies

  1. Compress public keys in transit (gzip: ~30% reduction)
  2. Store secret keys encrypted on disk
  3. Use key derivation to avoid storing multiple keys
  4. Batch signatures for multiple messages
  5. Pair with classical cryptography for hybrid security

Implementation Notes

Serialization Overhead

  • Length prefixes: 4 bytes per component
  • Domain separators: Included in hash values
  • Alignment padding: None (efficient variable-length encoding)

Determinism

✓ All size values are deterministic for a given security level ✓ Same key material always serializes to same size ✓ No random padding or variable-length components

Validation

Run bun test test/validate-sizes.test.ts to verify actual sizes match expectations.

Last Updated: December 31, 2025 Test Coverage: All components validated Status: All tests passing ✓