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US 8,428,252 B1Granted
Using multiples above two with running totals in elliptic curve cryptography scalar multiplication acceleration tables
AssigneeEMC Corporation
InventorsDavid Paul Makepeace, Sean Parkinson, Mark Hibberd, Peter Alan Robinson
Life of this patent
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Abstract
A method, integrated circuit chip, and computer program product for cryptographically processing an input value with Elliptic Curve Cryptography (ECC) using ECC scalar multiplication are provided. The ECC scalar multiplication is performed with the use of an enhanced acceleration table (EAT). The EAT uses multiple running totals, at least one of which has a multiplier above 2.
Claims15
A method of providing security using elliptic curve cryptography (ECC), the method comprising:
- (A) receiving, from interface circuitry, an input signal which represents an input value;
- (B) performing, in a microprocessor coupled to the interface circuitry, a set of cryptographic operations to provide a cryptographically processed value (CPV) based on the input value, the set of cryptographic operations including:
- (i) calculating an intermediate ECC scalar multiplication result based on the input value using an enhanced acceleration table (EAT), the EAT including a plurality of sub-tables, the plurality of sub-tables being arranged in an order, each sub-table including a plurality of entries, wherein calculating the intermediate ECC scalar multiplication result includes:
- (a) generating a plurality of running totals including at least four running totals RT1, RT2, RT3, and RT4, each running total being associated with a respective positive integer multiplier, RT1 being associated with 1 as its associated positive integer multiplier, RT2 being associated with 2 as its associated positive integer multiplier, RT3 being associated with 3 as its associated positive integer multiplier, and RT4 being associated with 4 as its associated positive integer multiplier, wherein generating the plurality of running totals includes, for at least one sub-table of the plurality of sub-tables, (1) choosing an entry of the at least one sub-table based on the input value, and (2) adding a value associated with the chosen entry to one running total, the associated positive integer multiplier of that running total being greater than 2;
- and
- (b) calculating a sum of each running total multiplied by its respective associated positive integer multiplier, including:
- doubling RT4, thereby generating a first intermediate value;
- calculating a sum of RT2, RT3, and the first intermediate value, thereby generating a second intermediate value;
- doubling the second intermediate value, thereby generating a third intermediate value;
- and
- calculating a sum of RT1, RT3, and the third intermediate value, thereby generating the intermediate ECC scalar multiplication result;
- and
- (ii) applying an ECC based cryptographic processing algorithm to the input value to generate the CPV, the algorithm including a computation involving the intermediate ECC scalar multiplication result;
- and
- (C) outputting, from the interface circuitry, an output signal which represents the CPV, the input value and the CPV being related in a secure manner through use of the ECC based cryptographic processing algorithm.
12 more elements
An integrated circuit chip comprising:
- an interface portion for communicating with an external user interface;
- a high speed on-chip cache, the cache being constructed and arranged to store:
- the entire contents of an enhanced acceleration table (EAT), the EAT including a plurality of sub-tables, the plurality of sub-tables being arranged in an order, each sub-table including a plurality of entries, each entry including a pair of coordinate values representing a point along an elliptic curve;
- and
- instructions to be performed;
- and
- a controller, the controller being constructed and arranged to perform instructions stored in the cache, wherein performing instructions stored in the cache includes:
- (A) receiving, from the interface portion, an input value to be cryptographically processed;
- (B) performing a set of cryptographic operations to provide a cryptographically processed value (CPV) based on the input value, the set of cryptographic operations including:
- (i) calculating an intermediate ECC scalar multiplication result based on the input value using the EAT, wherein calculating the intermediate ECC scalar multiplication result includes:
- (a) generating a plurality of running totals including at least four running totals RT1, RT2, RT3, and RT4, each running total being associated with a respective positive integer multiplier, RT1 being associated with 1 as its associated positive integer multiplier, RT2 being associated with 2 as its associated positive integer multiplier, RT3 being associated with 3 as its associated positive integer multiplier, and RT4 being associated with 4 as its associated positive integer multiplier, wherein generating the plurality of running totals includes, for at least one sub-table of the plurality of sub-tables, (1) choosing an entry of that the at least one sub-table based on the input value, and (2) adding a value associated with the chosen entry to one running total, the associated positive integer multiplier of that running total being greater than 2;
- and
- (b) calculating a sum of each running total multiplied by its respective associated positive integer multiplier, including:
- doubling RT4, thereby generating a first intermediate value;
- calculating a sum of RT2, RT3, and the first intermediate value, thereby generating a second intermediate value;
- doubling the second intermediate value, thereby generating a third intermediate value;
- and
- calculating a sum of RT1, RT3, and the third intermediate value, thereby generating the intermediate ECC scalar multiplication result;
- and
- (ii) applying an ECC based cryptographic processing algorithm to the input value to generate the CPV, the algorithm including a computation involving the intermediate ECC scalar multiplication result;
- and
- (C) outputting, to the interface portion, an output signal which represents the CPV, the input value and the CPV being related in a secure manner through use of the ECC based cryptographic processing algorithm.
19 more elements
A computer program product comprising a non-transitory computer readable medium, the computer readable medium storing instructions thereon which, when performed by a computer, cause the computer to:
- (A) receive, from interface circuitry, an input signal which represents an input value;
- (B) perform, in a microprocessor coupled to the interface circuitry, a set of cryptographic operations to provide a cryptographically processed value (CPV) based on the input value, the set of cryptographic operations including:
- (i) calculating an intermediate ECC scalar multiplication result based on the input value using an enhanced acceleration table (EAT), the EAT including a plurality of sub-tables, the plurality of sub-tables being arranged in an order, each sub-table including a plurality of entries, wherein calculating the intermediate ECC scalar multiplication result includes:
- (a) generating a plurality of running totals including at least four running totals RT1, RT2, RT3, and RT4, each running total being associated with a respective positive integer multiplier, RT1 being associated with 1 as its associated positive integer multiplier, RT2 being associated with 2 as its associated positive integer multiplier, RT3 being associated with 3 as its associated positive integer multiplier, and RT4 being associated with 4 as its associated positive integer multiplier, wherein generating the plurality of running totals includes, for at least one sub-table of the plurality of sub-tables, (1) choosing an entry of the at least one sub-table based on the input value, and (2) adding a value associated with the chosen entry to one running total, the associated positive integer multiplier of that running total being greater than 2;
- and
- (b) calculating a sum of each running total multiplied by its respective associated positive integer multiplier, including:
- doubling RT4, thereby generating a first intermediate value;
- calculating a sum of RT2, RT3, and the first intermediate value, thereby generating a second intermediate value;
- doubling the second intermediate value, thereby generating a third intermediate value;
- and
- calculating a sum of RT1, RT3, and the third intermediate value, thereby generating the intermediate ECC scalar multiplication result;
- and
- (ii) applying an ECC based cryptographic processing algorithm to the input value to generate the CPV, the algorithm including a computation involving the intermediate ECC scalar multiplication result;
- and
- (C) output, from the interface circuitry, an output signal which represents the CPV, the input value and the CPV being related in a secure manner through use of the ECC based cryptographic processing algorithm.
12 more elements
Dependencies are inferred from the claim text.