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Implementation of ECC in Combo6X Card

Implementation of ECC in Combo6X Card. Tomáš Davidovič, Martin Havlan , Martin Novotný, Pavel Bezpalec CTU FEE in Prague. Outline. Introduction Cryptographic Processor Arithmetic units Controller and I/O Conclusions. Elliptic Curve Cryptography (ECC).

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Implementation of ECC in Combo6X Card

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  1. Implementation of ECC in Combo6X Card Tomáš Davidovič, Martin Havlan, Martin Novotný, Pavel Bezpalec CTU FEE in Prague

  2. Outline • Introduction • Cryptographic Processor • Arithmetic units • Controller and I/O • Conclusions

  3. Elliptic Curve Cryptography (ECC) • ECC – belongs to class of asymmetric ciphers (public key cryptography) • ECC gradually replaces RSA algorithm (smart cards, ID systems, …) • ECC needs simpler hardware for the same strength • e.g.: ECC: 160 bit keys  RSA:1024 bit keys

  4. Cryptographic Processor • Should evaluate the scalar point multiple Q = kP = P + P + … + P (k-times) where: Q, P – points on elliptic curve k – integer • Point coordinates are elements of binary finite field GF(2m) • Point coordinates can be represented in both polynomial and normal basis • Interchangeable arithmetic units (polynomial basis AU  normal basis AU)

  5. Cryptographic Processor • Polynomial Basis AU • Normal Basis AU Or • Both AU switched on-the-fly Interchangeable Arithmetic Unit

  6. Polynomial AU – Inverter • Both multiplication and inversion • One set of registers for both • Multiplication – digits of arbitrary length • Inversion – speed up still researched • Several versions are tested • Two sets of registers • cost more in the means of DFF, but require less logic. • Worse for ASIC, but possibly better for FPGA

  7. AU – Squarer • Purely combination circuit • Logic depth max 3 XOR gates for 162 bits • Structure dependant on • Key length • Reducing polynomial for the length • Previously: Netlist generated by C program

  8. AU – current Squarer • State-of-the-art synthesis tools allow more • Behavioral description synthesized correctly • Only need: • List of polynomials • Required length • Transparent code • No need of external tools • Possibly better synthesis options

  9. I/O unit • Arbitrary width of input • Arbitrary frequency of input • Full bound handshake • Two types of access possible • Serial • Always assumes read/write of adequate length • Shift registers • Addressed • Requires more complicated control from sender • Allows random access to the polynomials

  10. Controller • Programmable: • Program in ROM for more effective synthesis • Reprogrammable for further firmware modifications • Custom designed micro-ASM • Java compiler • Generates both ROM and RAM versions of program

  11. Future work • Perform evaluation in hardware • Combo6X FPGA • ASIC • Incorporate into Combo6X framework • Devise protocol using ECC authentication

  12. Conclusions • Bugs fixed – polynomial unit redesigned • Design passes all simulations • Both Polynomial and Normal basis AU are scalable • Design highly modular and programmable

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